Aphid

Aphids are parthenogenic which means that the mothers do not require fathers to reproduce. As a result, many aphids have only one parent, a mother. Each daughter is identical to every one of their siblings and also to their mother except for size. In effect they are clones, and they are their own mother’s identical twin. In the summer, aphids give birth to potentially billions of clone daughters. But in the spring, they give birth to both sons and daughters. The sons are genetically identical to the mother as well, except for the lack of an X chromosome. Even more interesting is that an aphid often gives birth to its own granddaughter which may already be developing in her daughter who is already pregnant when born!

- – - – -

Sheepshead

California sheepsheads are fish that are all born female. Later in life they all turn into males. The timing of the transition depends on the environmental conditions. There are no old ladies or young boys! And all romances are of the May-December variety.

- – - – -

New Mexico Whiptail

New Mexico Whiptail Lizards are exclusively female. They give birth to their own genetically identical daughters without the participation of males or male genetic material. They have no fathers. However, they still require a mating ritual in which another female plays the role of a male, mounting her to stimulate reproduction. They no longer need the males, but clearly they miss them!

- – - – -

Blacktip Shark

It was recently discovered that certain species of sharks such as the Blacktips and Bonnetheads can reproduce asexually (females giving birth without the need of a father) under certain conditions in which a father is not available. Asexually reproducing female sharks, unlike reptiles like the whiptail lizard (above), can only produce female offspring. Therefore, a single such shark cannot spawn a new generation on her own.

- – - – -

Komodo Dragon

Komodo Dragons normally reproduce sexually, but in times when there are no males present, females can reproduce asexually. This ability is thought to be useful when one female drifts to an island and populates the species there entirely on her own! This is possible because asexual reproduction in reptiles, unlike in fish and most insects, produces all males rather than all females. The male offspring can then sexually reproduce with the mother to form new generations.

- – - – -

Gecko

Though most geckos are ‘normal’ with both males and females who reproduce sexually, some populations are entirely female and reproduce asexually. But even in sexually reproducing populations, individuals can switch sex if needed. Geckos lay eggs which are normally fertilized by a male. But in asexual populations, the eggs do not require fertilization. The Geico gecko from the commercials, the one who appears to be a bit effeminate, perhaps he’s a she!

- – - – -

And by the way, about the parthenogenic mammals. Well actually, there are none in nature. All mammals reproduce sexually and require both a mother and father. While scientists have successfully created fatherless rabbits, mice, and even monkeys by using an electrical or chemical stimulus, such mammals are deformed and are not viable. Unlike fish and reptiles, mammalian reproduction involves a process known as genomic imprinting which necessitates genetic material from both mother and father. Therefore people will always require both a mother and father to produce offspring. While we hear of cases of virgin birth among sharks, lizards, fish, plants and insects, in humans it’s simply precluded by the reproduction mechanism.

- – - – -

Marmorkreb

Marmorkrebs are parthenogenic crayfish that were discovered in the pet trade in the 1990s. Offspring are genetically identical to the parent (mother).

- – - – -

Little Fire Ant

Little fire ants are very special because both the males and females reproduce asexually. In this sense, some of the males and females don’t even belong to the same species! Queens produce more queens asexually, giving birth to their clonal daughters. Sterile workers are usually produced from eggs fertilized by males. But in some of the eggs fertilized by males, the fertilization can cause the female genetic material to be discarded (a process called ameiotic parthenogenesis). This is the first recognized example of an animal species where both females and males can reproduce clonally resulting in a complete separation of male and female gene pools.

- – - – -

Seahorse

Seahorses are the only animals in which the males become pregnant and give birth. Following an elaborate courting ritual, the male receives eggs from the female, fertilizes them, and incubates them in a special pouch on his chest. In about six weeks, he gives birth to as many as 200 babies. Then a month later he does it again! Seahorses are monogamous. The male doesn’t roam around very much. He stays in the same area and eats nearby food while the female travels far off each day in search of food. But the female returns every day to repeat a mating dance with the pregnant father in which they entwine their tails and spiral to the surface.

- – - – -

Update: In April 2009  University of Arizona researchers announced the discovery of the first ant species that consists of only females and reproduces only when the queen clones herself. Read story.

Splenda (sucralose) has overtaken Equal (aspartame) in the artificial sweetener market thanks to a marketing campaign that claims Splenda is closely related to sugar and is by implication safer and less artificial. Splenda’s slogan “Made from Sugar. So it tastes like sugar.” can be found on every packet and appears in every ad. But that claim is misleading and was even the subject of a highly publicized lawsuit. Should advertisers be permitted to take advantage of gullible consumers by making misleading claims, even if those claims are based on truth?

Those who express a preference for Splenda over other artificial sweeteners believe that Splenda is derived from real sugar and is therefore likely to be more natural, safer, or better tasting. Not surprisingly those ideas stem mostly from the company’s marketing campaign. Some quick fact-checking reveals that those claims are both based on true facts and are intentionally misleading. The success of this product is an example of savvy marketers taking advantage of gullible consumers. And by gullible, I don’t mean stupid. I’m including most people, those like myself and my friends who shouldn’t be expected to research every detail of every claim made by every product. We prefer to trust that advertisers will only go so far in stretching the truth, and that the checks and balances of the legal system and the government are enough to keep marketers on their toes. What makes this case so interesting is that those checks were not enough, and an unscrupulous marketing campaign succeeded in bamboozling the public.

McNeil Nutritionals and the chemists who designed Splenda (originally intended as an insecticide) knew very well that the link to sugar was both valuable and misleading. In fact, the original slogan included a few more words “But it’s not sugar.” However, with that simple added dose of truth on every packet, the product did not sell well. It only took off after they removed those words. Clearly the company had a tough decision, perhaps too tough, fail with too much truth, or succeed wildly with just a bit less. It might be a good example of why we need strong oversight by impartial well-informed regulators. Others might believe in a literal version of caveat emptor (let the buyer beware). I’m not on that side in this case, but I understand it, and I accept that many free-market proponents feel strongly that only the market should decide what’s right or wrong, particularly in cases where no direct fraud or lies are involved. You can decide for yourself, but here are some things to consider.

Made from sugar? So it tastes like sugar?

Technically, the manufacturing of Splenda does begin with pure cane sugar (sucrose). But the sugar that is used in the process is entirely destroyed during manufacturing, chemically destroyed so that it is no longer sugar. Sugar is not an ingredient in the product at all, and by law they cannot claim that it is. The company has patented several alternate ways to manufacture Splenda that do not even involve sugar, but still result in the identical product. One might then ask why sugar is still used to make Splenda. I don’t know the answer. It may simply be the cheapest way. But if it was not, we could certainly imagine that it would continue to be used, if only to protect the marketing claims.

In terms of chemical structure, Splenda (sucralose) is similar to sugar. As you can see in the diagram, you can convert sugar into Splenda simply by replacing three hydroxide ions (HO) with Chlorine ions (Cl). To us non-chemists, this makes Splenda and sugar appear almost the same. But it’s misleading because we’re dealing with basic chemistry where the smallest change can make a world of difference. Remember from high school that the difference between water and flammable hydrogen gas is just one Oxygen atom. Or consider that you can create deadly Chlorine gas (Cl2) from Splenda simply by replacing the Oxygen and Hydroxide ions with Chlorine ions! Would it be ethical to market “Deadly poison made from Splenda. So it tastes like sugar.”?

Chemists cringe

A senior editor of the journal Nature summarizes the reaction by chemists:

This is the kind of advertising campaign that makes most chemists cringe, and – though this may sound like a petty dispute between two rival companies – I think we need to hold companies accountable for exploiting the general public’s lack of scientific knowledge. Unfortunately many people will think: Splenda is not sugar, but it is made from sugar – so it must be safe, right? (Wasn’t palytoxin made from sugar?) Though this sort of ad campaign wouldn’t work on many scientists, it certainly worked on the general public: “sales of Splenda were weak in 2001, when McNeil launched an ad campaign saying the sweetener is made from sugar and including the phrase ‘but it’s not sugar.’” Since then, “Splenda has eclipsed Equal in the lucrative artificial sweeteners market” – and it’s not like Merisant can counter with an ad campaign, saying that Aspartame’s “made from phenylalanine, so it tastes like phenylalanine”…

One example of a chemist’s reaction can be found here.

And as often happens, it’s not just the ignorance of those who buy into the advertising claims that worries scientists. The ultra-cynical, alarmists, and conspiratorial-minded also feed on ignorance. This process of replacing OH’s with Cl’s creates what are called Chlorocarbons which is what Splenda is. And one of the reasons that some people consider Splenda a potential danger is that many other Chlorocarbons are poisonous and sometimes disastrous to humans. Those include Chloriform, DDT (the banned pesticide), and the poisonous Trichloroethane. So far, after much testing, safety concerns of Splenda remain unfounded.

But the important point is that it’s not much more valid to assume based only on chemical structure that Splenda is safe or tastes like sugar, than it is to believe it’s toxic and doesn’t taste like sugar. Both lines of reasoning are questionable without evidence to back them up. But there’s one that we want to believe, and clever marketers have used it to their advantage. The other scares us and gives ammunition to alarmists. From the experts’ viewpoint, consumers need reliable information to make informed decisions, and that information should be based on evidence rather than what sells. Advertisers whose products stand to affect the diets and health of millions of consumers should be held to the highest standards of integrity. Naturally, conscientious scientists are always concerned when scientific information resulting from their efforts are undermined on such a large scale in the name of greed.

Controversy and lawsuit

The Food and Drug Administration regulates nutritional advertising to a certain extent. But there are always loopholes and uncharted territory. In those cases, whether we like it or not, our system tends to rely on the courts, and lawyers, and lawsuits to expose the truth and punish wrongdoers. In this case, Merisant, the makers of rival Nutrasweet (aspartame) sued McNeil Nutritionals, the makers of Splenda, for damages contending deceptive advertising. The suit was settled in June 2007 without a trial for an undisclosed amount rumored to be about $30 million dollars. No further action seems to have been taken by the FDA or congress. So it appears that this type of deception worked, was well worth the cost, and will continue to be a standard part of doing business in this country.

There have been very few ambidexterous pitchers in baseball. Wikipedia lists only a few, and most played in the 1800s. The only modern era switch pitcher was natural righty Greg Harris, who in 1995 with the Montreal Expos faced just two batters left-handed in the next-to-last game of his career. But now there is a switch pitcher in the Yankees minor league organization named Pat Venditte who regularly pitches with both arms. His father trained him to throw with both hands since the age of three.

Pat Venditte – Switch Pitcher

Pat Venditte – YouTube

YouTube: Switch-pitcher Venditte encounters switch hitter; chaos ensues

When the Yankees signed Venditte, the rulebook had to be changed to allow for switch pitching. The Venditte rule was added. It states that the pitcher must clearly indicate which arm he’ll throw with as he approaches the mound (generally based on which hand he wears his glove). The batter then chooses which side he will bat from. Each may change once during an at-bat and must clearly declare the change to the umpire. No additional warm-up pitches are afforded.

Fielding is another issue because baseball gloves are designed to be either left-handed or right-handed. Switch pitchers like Pat Venditte cannot bring multiple gloves onto the field and switch when changing throwing hands. Nor can they run to the dugout between batters to switch gloves. Fortunately, Louisville Slugger manufactures a custom glove (shown) with two symmetric thumbs that can be used on either hand. There’s some question about whether this glove conforms to the MLB equipment regulations, but it’s been accepted in the NCAA and would be expected to be legal in the majors as well.

First, they are different animals, though both names are shared by the opossum which is the animal found in the Southeastern United States, most common is the Virginia Opossum (shown). It’s the only marsupial of any kind, that is found naturally outside of the Australian continent. Marsupials are of course mammals that bear live young and nurse them for a time in the mother’s pouch (like kangaroos and koalas).

As if that were not enough, here are some fascinating facts about opossums:

• Opossums play dead when distressed. It’s not quite the pretense that people tend to imagine. It’s an involuntary reaction to a threatening situation in which the opossum falls prone, experiences decreased respiration and heartbeat, and secretes a musky decaying odor from its rectum. One can imagine the stepwise evolutionary development of this behavior in which successively more convincing death acts enabled ever increasing chances of survival. For example, did the odor come before or after the decreased metabolism???
• Opossums cannot hibernate. In cold climates, they are often found with frostbite as a result.
• The opossum is the only mammal that has an odd number of nipples. The Virginia Opossum has 13. Though an odd number, they remain symmetrical with one in the center and the other twelve in a surrounding circle.
• The opossum frequently has litters larger than the number of available nipples. As a marsupial, a newborn requires a nipple to latch onto or they die immediately. Therefore a great many babies die at birth. Let the Intelligent Design proponents explain that one.
• The opossum has the shortest gestation period of any mammal, 12 days.

Types of Twins

Most people are familiar with fraternal twins, identical twins, triplets, quadruplets, and conjoined twins. But there are many other types of twins and many variations on the former.

Fraternal twins are simply two normal siblings who happen to be born at the same time. They share few additional similarities compared to ordinary siblings (other than the same birthday, and some marginal added commonality due to coincidental development). Fraternal twins can be same sex or different and can be as similar or different as any brothers and sisters. On average they share exactly half of the DNA similarities of each other and all other siblings, though like other siblings, in extraordinarily rare cases they can still actually be identical (more about that later). Fraternal twins are actually properly called dizygotic (two eggs) or DZ because they occur when the mother releases two separate eggs and both are fertilized by different sperm from the father.

Identical twins occur when the egg splits after fertilization. The proper term is monozygotic or MZ. Both twins develop from the same egg and sperm and therefore are identical. It’s important to realize that identical twins are not actually 100% identical but we use that term because they usually look very similar and have almost identical DNA and genes.

Higher order multiples such as triplets and quadruplets are more rare forms of twins. They are most commonly fraternal due to the fertilization of multiple eggs. However, higher order multiples can be any combination of dizygotic (DZ) and monozygotic (MZ) twins.

Conjoined twins occur when the egg splits after development is further along and the (usually) two twins do not fully separate. Conjoined or colloquially siamese twins can be joined just about anywhere and their survival prospects and outlook depends heavily on how much they share. Conjoined twins are thus alway MZ and same sex,

Mirror Image twins are identical twins where the egg splits after seven days but before the point that conjoining would result. About 25% of identical twins are mirror image. Mirror image typically means that one twin is superficially mirrored in the other. One may be right-handed while the other left-handed, their hair whorls may be opposite, and they may have markings or moles on opposite sides. In very rare cases, mirror image twins can be entirely reflections of each other right down to the arrangement of organs. For example, it’s possible for a mirror image twin to have their heart on the right side, their liver on the left side, and their appendix on the left side. (imagine the difficulty in doing a heart transplant!)

Polar body twins or half-identical twins occur when the egg splits before fertilization and each half (the egg itself and it’s polar body) is fertilized by a different sperm and develops separately. In such cases, the twins are halfway between fraternal and identical and share on average 75% of their DNA in common. There is considerable controversy over polar body twinning and its frequency. No easy tests are yet available to determine it. Kate and Ashley Olsen are thought by some to be polar body twins.

Twins of two is a term that means half-fraternal twins. This occurs when the mother releases two eggs and each is fertilized by a different partner’s sperm. The twins happen to both be viable and are born at the same time. Such twins have 25% identical DNA just like half-siblings.

Vanishing twin. Some conjoined twins, and most identical twins for that matter never reach birth to develop as separate individuals. The second twin is more often not viable on its own due to some defect or disadvantage in development. Often this second twin is never known to have existed. Only one twin is born normally and the other vanishes (doesn’t mature).

Parasitic twin. Rather than vanishing completely an underdeveloped conjoined twin can occasionally even develop within the other twin and survive parasitically for years.

Identical or not?

Parents of twins usually want to know whether they are identical or not. Currently there’s not a foolproof way to tell, but the only highly reliable way is a DNA test (99.9% conclusive). One of the best ways to tell is by taking a simple questionaire about visible similarities. Twins that look remarkably alike are usually MZ twins, and obviously those that do not are DZ. Many new mothers are told whether their twins are DZ or MZ based on whether they share a chorionic sac or placenta. However, that method is wrong at least 25% of the time because MZ twins can sometimes have separate sacs or placentas. The opposite is much rarer but can also occur. Half-identical twins are even harder to determine. It’s largely still a question of speculation because reliable DNA test haven’t been established to determine this type of twin. Since identical twins are never actually entirely identical, sometimes the mother will assume they are DZ when they are not. And conversely, because DZ twins can look remarkably alike, they will often be mistaken for MZ twins.

Genetic Similarity

Perhaps the most interesting thing about twins is that they can have a wider variety of genetic similarity than most siblings. For comparison, each person gets exactly half their genes from their mother and half from their father. This means that you are exactly half identical genetically to both your parents. It also means that you are very close to half-identical to your non-twin siblings – it’s very likely that this is very very close to half identical, but it’s a random process so it’s possible (perhaps so rare that it has not even happened) that you could be anywhere from 0% to 100% identical to a sibling! If you have half brothers and sisters, you are 25% identical to those (like your cousins on average), but it can range from 0% to 50%. Interestingly, when identical twins have babies, those children are genetically siblings (50% identical) rather than being genetically cousins (25% identical).

Fraternal twins are exactly the same case as ordinary non-twin sibblings (50%). Identical MZ twins are 100% similar genetically. Whereas half-identical twins are 75% genetically identical. And twins of two are 25% genetically identical. Of these, the really interesting cases are MZ and polar body (half identical) twins because they exhibit genetic similarities that do not occur in other ways in the general population (disregarding the random possibility that it will occur between ordinary siblings on astronomically rare occasions). Scientists use MZ twins to test theories about what is determined genetically, so called nature vs nurture. The idea is that if two people with the exact same genes react or develop differently, the thing being study much have a nuture or environmental component. It’s not that simple as we’ll see below, but it’s still fascinating to see what differences MZ twins develop and what similarities they maintain.

What’s identical in MZ twins?

People often ask whether identical twins have the same fingerprints, eye color, sex, hair color, or personalities. The answer varies. For traits that are determined genetically, the answer is usually yes (sex, eye color, hair color, etc.) For traits that are phenotypic (determined by development) such as fingerprints and personality, the answer is no. Even with genetic traits such as handedness (most often), there is the case of mirror image effects that can cause a difference.

Are identical twins actually 100% DNA identical?

In general the answer is yes. At least their DNA is as similar as any two people’s can be (other than clones which have not yet been raised). MZ twins were conceived from a single zygote (fertilized egg) of which half of its DNA came from the father and half from the mother. When the eg split, both halves of the division had identical DNA and so the twins develop with this identically matching DNA. One clear exception is the mitochondrial DNA which is always different in MZ twins and can also cause some biological differences.

For many years MZ twins have been used to determine whether certain conditions, diseases, and traits were genetic (nature) or environmental (nurture). The assumption being obvious that if both twins had the condition, it was most likely due to their common genes. If only one had the condition it was due to their environment or upbringing, or phenotypic differences (those caused by different embryology and development such as fingerprints and many other traits). But once certain conditions and traits were proven to be genetic, scientists found that not all identical twins had similar conditions. Recent research has shown that there are a variety of reasons why MZ twins’ DNA may not match exactly. The different processes and reasons are too complicated for me to fully understand much less summarize here, but it’s been shown conclusively that MZ twins’ DNA does not always match exactly, and may never match exactly. Current DNA tests compare key samples of DNA rather than testing the whole DNA strand which is much to long and difficult, so the direct evidence is still sketchy about just how much DNA MZ twins share.

Twin trivia

• Twins do sometimes develop secret languages between one another.
• Twins cannot read each other’s minds, but they often have amazing abilities to understand the other or know how they are feeling.
• Female identical twins are more common than male identical twins.
• Twins have about twice the likelihood of being left-handed than non-twins.
• Twins are almost always born prematurely, moreso the higher the number of multiples.
• Twins can be born minutes, days, or even months apart. Typically true twins are born minutes apart and its not significant which is born first.
• The idea of an evil twin and a good twin is a myth. Though often one identical twin can be larger, stronger, or more dominant than the other based on how they developed.
• Identical twins make excellent organ donors for one another.
• It’s exceedingly rare but still possible (3 known cases) for identical twins to be different sexes.
• Cats, sheep, and ferret have very high incidences of twins
• Eating Yams can increase your chances of having twins
• Older mothers, african mothers, and mothers that have had twins are more likely to have twins
• A predisposition to have fraternal twins may be mildly hereditary, but identical twins are simply luck. It’s a myth that twins skip a generation.
• Recent usage of fertility drugs has increased the occurence of twins, especially higher order multiples.
• Half of all MZ twins sharing the same chorionic sac die due to umbilical chord entanglement.
• Identical twins occur in 1 out of 150 births worldwide.
• There’s a town in Brazil that has a 10% twinning rate.
• Identical twins have different fingerprints but similar fingerprint patterns.
• Identical twins have identical gender, eye color, hair color, and blood types.
• Identical twins live longer than fraternal twins

Interesting facts about the Platypus:

• The plural of platypus is platypuses, platypus, or platypoda. Platypi is actually wrong but is used so often colloquially that it’s now acceptable.
• The duck-billed platypus is obviously named after its unusual snout. Interestingly, there are no other varieties of platypi.
• Platypi are often incorrectly identified as the only mammals that lay eggs. Actually all monotremes lay eggs. However, the only other extant monotremes are the echidnas (including the spiny anteater).
• Platypi have a single orifice that combines reproductive functions, and solid and liquid waste disposal. (This is the definition of a monotreme.)
• The platypus has mammary glands but NO nipples! The mother’s pink milk oozes out of pores and collects on a fold of skin where the babies lap it up. It’s the only mammal without teats.
• Platypi have TEN sex chromosomes. We, like most mammals, have only two (XY).
• The platypus is one of only five venomous mammals. The male has a poisonous claw on its hind legs that administers a toxin that is not lethal to grown humans, but is extremely painful. The pain can last weeks or months.
• The platypus is carnivorous, primarily feeding on insects and worms it catches in the water. However, it does not open its eyes under water. Instead, it is the only mammal that uses electrolocation.
• It’s ears are located at the ends of its snout.
• It’s the only mammal that swims with an alternate rowing motion of its front feet. The back feet are webbed, but for unknown reason are not used for swimming.
• Females have two ovaries, but only the left one is functional – another conundrum for the Intelligent Design guys.

Update May, 2008 – Platypus Genome Mapped!

On May 8, 2008 Nature published the research of a group of international scientists that sequenced the DNA of the platypus for the first time, funded in part by the U.S. National Human Genome Research Institute (NHGRI). Its genome contained roughly 18,500 genes. The scientists compared the platypus genome with human, mouse, dog, chicken, and opossum genomes and found that the platypus shares 82 percent of its genes with these animals. A central goal was to determine which platypus features were inherited from reptilian ancestors and which evolved independently. Platypus DNA was found to include a number of genes not found in other mammals, such as genes for egg yolk proteins shared only with reptiles and fish.

The new information confirms that platypus egg-laying is truly a holdover from its primitive reptile ancestors as commonly assumed. On the other hand, mammal genes for lactation (milk production) were also found in the platypus genome. While milk production and giving birth to live young would seem to go hand in hand, the platypus genome shows that the two common mammalian traits evolved at very different times. “The presence of the full repertoire of milk genes confirms that lactation evolved at least 166 million years ago, way before live-bearing,” said project co-leader Jennifer Graves, of the Australian National University in Canberra.

It’s a fool’s errand to try to support an answer as the one and only correct solution, but it’s interesting to probe into the oddities of the game for possible answers. It’s also more than enough of a challenge. A good list of candidate answers accompanied by references to the official rules of baseball, done properly, appears to be sorely needed. I’ll assume that we’re interested only in legal ways that are allowed in the official rules of baseball as published on MLB.COM, and that can occur during a regulation major league baseball game.

Answers

1. Walk
   A walk is normally construed as a base on balls, four pitches outside of the strike zone. However, there are a number of interesting ways to get awarded ball four and advance to first base. Some people consider these different ways of getting to first base. Others argue (as would I) that they are simply other ways of getting a walk.
   (a) Base on balls – the batter takes a pitch outside the strike zone for ball four
   (b) Intentional walk
   Some people consider an intentional walk different from an unintentional walk for intuitive reasons, and because it is scored differently.
   (c) Umpire calls ball four due to a balk caused by an illegal pitch (quick pitch) with no runners on base (see rule 8.05(e))
   This one is a bit obscure and confusing because it is listed in the rules under balk, can occur with no runners on base flying in the face of many people’s idea of a balk, and can result in ball four called to the batter. It is scored as a base on balls. Note that other forms of balks affect only the base runners, not the batter.
   (d) Umpire calls ball four when the pitcher illegally brings his pitching hand in contact with his mouth or lips while on the mound (see rule 8.02(a)(1)). The rule states explicitly that a ball should be called as the penalty in this case. But for other, more blatant violations such as spitting on the ball, the only penalty is ejection and suspension (not calling a ball).
   (e) Umpire calls ball four when the pitcher takes more than 12 seconds to make the pitch when the bases are unoccupied (see rule 8.04).
   (f) Ball four gets lodged in the catcher’s mask or the umpire’s equipment (see rule 5.09(g))
2. Hit by pitch
3. Batter reaches first base on 3rd Strike
   There are several varieties of this case that most people would count as a single way to reach first base.
   (a) Catcher drops 3rd strike with two out or first base unoccupied (and batter beats the play)
   (b) Passed ball on 3rd strike (and batter beats the play, or ball goes out of bounds)
   Usually occurs when the batter swings and misses an errant pitch.
   (c) Wild pitch on 3rd strike (and batter beats the play, or ball goes out of bounds)
   Usually occurs when the batter swings and misses an errant pitch.
   (d) The 3rd strike gets lodged in the catcher’s mask or the umpire’s equipment (see rule 5.09(g))
4. Interference
   There are several type of intereference that can result in a batter being awarded first base. These are usually counted as a single way that the batter reaches first, although (e) is often considered another way by itself.
   (a) Fielder interference
   This occurs when the catcher or another fielder interferes with the batter’s attempt to reach first base while the fielder is in possession of the ball or actively involved in the play. It is scored as an error charged to the offending fielder.
   (b) Obstruction
   Obstruction occurs when a fielder who does not have possession of the ball and is not actively involved in the play illegally interferes with the batter reaching first base. It is also scored as an error charged to the fielder who committed the obstruction. This would be a very rare way to reach first base because it would require interference by a fielder not involved in the play that would otherwise be an out. For example, I suppose it could be called if the pitcher blocked the base path while a routine ground out was played from third base.
   (c) Spectator interference
   If a batter is interfered with by a spectator on the way to first base, the umpire can award first to the batter, although I believe this is scored as a hit.
   (d) Umpire interference
   If a batted ball hits an umpire before passing a fielder other than the pitcher, the batter is awarded fist base. This is scored as a hit.
   (e) Runner interference
   If a batted ball hits a runner other than the batter, the runner is out and the batter is awarded first base. This is scored as a hit.
5. Fielder’s choice
   A fielder’s choice is defined a little differently in the rules and in the scorekeeping rules. The best definition is when the batter reaches base when the fielder could get him out but chooses instead not to make the putout. This choice is made in order to put out a different base runner (or runners) instead, or to attempt to do so. It’s also a fielder’s choice if the fielder simply allows the batter to reach base without attempting the out. For example, with a man on second base and no outs, the batter grounds to the pitcher, he could conceivably intentionall allow the batter to reach first. It can also occur when a fielder intentionally drops a fly ball in order to attempt a double play (when not covered by the infield fly rule).
6. Error
   A batter can reach first on a fielder error, typically when the fielder misplays a routine ball. Some other cases (such as interference and obstruction) are ruled errors for the purpose of scorekeeping but are usually still counted a distinct ways to reach first without getting a hit.
7. Pinch runner
   Technically a player can reach first base without getting a hit by being designated a substitute runner for a player who already reached first base. Some people count this as a way to reach first without getting a hit, and others consider it beyond the spirit of the question because it does not apply to the batter. When the question does not mention a batter, I prefer to reward the creativity of this answer. There’s an even more creative and questionable case in which a batter reaches first, the game is suspended (many variations), then the batter is traded (many variations), and another player takes his place. All of these seems clearly to be simply runner substitutions and should probably not be counted separately.
8. NOT Sacrifice
   A batter can reach first on a sacrifice without getting a hit. This case is highly questionable as a distinct way to reach first because it always involves either an error or a fielder’s choice. Some people will count it anyway. Some will even count a sacrifice bunt and a sacrifice fly differently.
9. NOT Blown call by umpire
   When the umpire calls a batter safe at first when he should have been called out, you could argue that he did not get a hit, even though it will be scored as such. This is a judgement call. I prefer not to count it because it opens a can of worms of other bad calls.
10. NOT Catcher balk
    When the pitcher pitches and the catcher is not in the catcher’s box, it is ruled a balk. But in this case, even if no runners are on base, the rules do not state that the batter is awarded a ball nor could he reach first base (see rule 8.05(l))

I count at least 8 (1 through 7 plus 4e), and as many as 19.

Make a Fortune

Suppose you could walk up to a craps table and place a bet of any size on a Don’t Come point number, just as if you’d already played a Don’t Come bet and a point was rolled. The greater part of the house advantage of the Don’t Come bet arises from the risk to your bet on the first roll. If a 7 or 11 is rolled as the first roll you lose your wager. If a 2 or 3 is rolled you win. And if a 12 is rolled you push. The chances of rolling a 7 or 11 is 8/36 (0.2222) much more likely than the chances of rolling a 2 or 3 which is only 3/36 (0.0833). If you escape the high risk of the opening roll and establish your wager on a Don’t Come point, you are a heavy favorite to win the bet. From then on (until the bet is resolved as a winner or loser), a 7 that wins the bet is more likely to be rolled than the point number that loses the bet.

If you could establish your bet on a Don’t Come point without risking the initial roll, you would always have an advantage over the house. This system proposes a simple process to accomplish this, placing you firmly in control with no chance to lose over an extended length of play. It’s a compelling claim if true. In fact, we can calculate the odds as 18.79% in our favor (that calculation is shown later in this article for those interested), actually returning $0.0314 per roll of the dice on average per dollar bet. If you played $100 at a time eight hours a day, assuming 150 rolls per hour, you would earn (100 * 0.0314 * 150 * 8 * 365) or about $1.4 million a year! And because the odds are always in your favor, there’s no reason not to play even higher stakes. Play $1000 per bet and make $14 million dollars per year. Does it sound too good to be true? From the casino’s point of view, imagine that a casino has six craps tables, with an average limit of $2000 per table, each with room for 12 players. The casino could potentially lose (6 * 12 * 24 * 150 * 365 * 2000 * 0.0314) or a staggering $6 billion dollars per year. The minute they hear of this system, every casino in the world will close down their craps tables! So why do they have craps tables at all? Let’s see. But first I’ll describe how to play the system.

How to Play the System

1. Start by making BOTH a Pass and Don’t Pass bet on the Come Out roll. $10 each for example. Every casino will allow this. It’s not particularly uncommon. But it’s also not going to mark you as the most savvy gambler.

Some people think this alone is a system that lets them play indefinitely without losing, like putting equal amounts on red and black in roulette. The flaw to that idea is that roulette has a green “0″ and most likely an even worse “00″ which lose both bets once in a while, and with NO chance at all of winning! Craps has something similar. If a 12 comes up, the Pass bet loses, but the Don’t Pass bet pushes (it doesn’t win or lose). On it’s own, the only plausible reason I can think of for playing this way is to have the privilege of rolling the dice for the least cost possible – a Pass and/or Don’t Pass bet is required of the shooter. In this system there’s a justification for this questionable opening move. So we’ve already identified one red flag, but it’s only part of the problem and it will be explained away later.

1. When you get a ‘point’ (by rolling a 4,5,6,8,9, or 10 on the Come Out) you lay odds on your Don’t Pass bet such that if it wins, you’ll win $10. This means that you add “odds” to the Don’t Pass bet based on the payout of the point. For a 6 or 8, you add $12 because it pays $5 for every $6 you bet. For 5 or 9, you add $15. And for 4 or 10 you add $20.

This is a standard way to play, though most players prefer to play Odds on the Pass bets so they don’t need to lay higher bets than they’ll win. But the Odds bets in craps are actually FAIR and add nothing to the house advantage when played. That is to say the payout exactly matches the odds of winning. Thus if you could play only Odds bets forever, you’d end up even. That’s why Odds bets are only allowed to be added onto existing bets for which the house has a built-in advantage. Because of this basic true and well-known fact about Odds bets, this step of the system does not appear to involve any risk to the player. Taken on it’s own, that is absolutely correct.

1. After adding your Odds bet, place an equal Don’t Come bet ($10). On the next roll, you seem to have no risk. If craps comes up, you win the Don’t Come, pocket $10 and start over. Your Pass and Don’t Pass bets can be ignored because they will always cancel each other out when they are eventually resolved. If instead a 7 comes up, you will LOSE the Don’t Come bet, but you will WIN the Odds bet on the Don’t Pass, breaking even. So there’s still apparently no risk of losing. (you might notice one possibility that’s ignored here)
2. When the second roll establishes a new point, remove the Odds on your Don’t Pass bet – eliminating that money from any risk.

Many players don’t realize that you can remove Odds bets at any time. But every casino will in fact allow this because Odds bets are never to the house’s advantage. In variations of this system the Odds bet becomes a new Come bet, but we’ll ignore that complication as it complicates the analysis but does not improve the system.

Now you have a bet ($10 in this example) on a Don’t Come point and $10 each on the Pass and Don’t Pass lines, which you are guaranteed to get back. And if a seven comes up before the point, which is always the most likely outcome, you win $10. Without taking any risk, you have a bet that is in your favor! Do this enough times and you’re rich!

What’s the Catch?

There are three catches with this system. The first two are minor and relatively simple. They reduce the potential advantage that the player can supposedly achieve over the house. The third is the true flaw of the system. It eliminates the perceived player advantage and restores the house advantage. This third flaw is also more subtle and difficult to explain. Proponents of the system will dismiss the flaws with distracting rationalizations which I’ll prepare you for.

A Minor Flaw: 12 on the Come-out

If a 12 is rolled on the Come-Out roll, the bet is lost before you have successfully established a so-called ‘free’ Don’t Come bet. The reason is that the 12 loses the Pass bet, but results in a Push of the Don’t Pass bet. A Push means simply that the bet neither wins nor loses, the dealer just slides “pushes” your money back to you. Therefore, if you bet $10 on Pass and $10 on Don’t Pass as in our example, a 12 will result in a $10 loss. Proponents of the system correctly point out that this will only happen in one Come Out roll out of 36, and this relatively rare risk is a small price to pay for the other 35 plays that are all very much in your favor.

If you don’t like that risk, proponents suggest you play $1 on the “12” proposition bet on each Come Out roll. The 12 bet pays 30-1 in the event of a 12, but it costs $1 for every Come Out. Savvy players understand that the 12 is one of the worst bets on the table (house advantage of 13.89%). Adding a bad bet to hedge another bet never works (discussed later). It simply increases the odds in favor of the house. So this solution to the problem is at best a comfort measure.

But the low frequency of a twelve, rolled only once in 36 plays, does seems like a compelling defense (against it being a major flaw in this system) and seems to be worth examining further. When we do the math, we find that when 12s are accounted for on the Come Out roll, our anticipated advantage over the house is reduced from 18.79% down to 13.5%. Our per-roll profits assuming $1000 bets is decreased from $31.40 to $22.80. As long as we maintain the edge, we’re happy. Our hopes of having a system that can win us $14 million per year has simply been reduced to about $10 million. Perhaps more significant is the realization that we’ve uncovered a cost in establishing a Don’t Come number where many proponents of the system claim there is none. That might tip us off that more disappointments are to come.

Another  Minor Flaw: 11 on the Come-out

If an 11 is rolled on the Come-Out roll, the Don’t Come bet is lost but the original bet and odds bets are not affected. This amounts to another small ‘leak’ in the system which we glossed over in the strategy. It’s small, happens only once in 18 sequences and only loses the Don’t Come portion. Whether or not this case is covered in descriptions of the strategy varies. (I left it out of my original description by accident.) Like the previous flaw, it doesn’t break the system, but it does reduce the expected outcome, which remains positive until the next flaw is accounted for.

Major Flaw: Repeating Point

When the Come Out roll is a point (4, 5, 6, 8, 9, or 10) and the very next roll is a repeat of the same number, we lose the Odds wager that we laid on our Don’t Pass bet. The repeated number becomes the point for the Don’t Come bet. But in this case, we can’t take back the odds bet because it’s lost. This is another case where it wasn’t free to establish the Don’t Come number.

Overloading

But what happened to the idea that Odds bets are always fair and never cause us to win or lose over the long run? Now we seem to be saying that there’s a case where losing the Odds bet causes an overall loss in our system. The reason this represents a flaw is due to something called overloading and it’s as subtle as it is critical, well worth taking the time to understand if you’re playing any craps system.

Recall that we assume the Odds bets are always fair and represent no risk. This is in fact true as long as we don’t use the wins to cancel out other losses in the same play. But also recall that the reason the seven can’t hurt us on the second roll is that the winnings from the Odds bet covers the loss of the Don’t Come bet. So in effect we’re counting on the winnings from the Odds bets both to cover losses due to sevens, and to cover losses from the point being made. If we’re to presume that the Odds bet has no house advantage, we cannot think of any of its winnings as compensating for any losses other than losses from the same Odds bet. This subtle point remains true when we don’t collect the winnings but instead use them to cover the losing Don’t Come bet. One way to look at this is that the Odds bet win does not cover the Don’t Come loss. Another way to look at it is that the repeating point represents another risk in arriving at a “free” Don’t Come number, thus it is not free at all!

Proponents of the system simply dismiss the combined effect of overloading. It’s a subtle effect so this is a fairly easy way to undermine its importance. They simply state two truths that are obviously true when taken seperately: (1) The Odds bet is a fair bet so it does not give the house any advantage, and (2) if a seven is rolled on the second roll, the winnings from the Odds bet cancel out the loss from the Don’t Come bet. In reality, what you actually lose in case (2) is not your bet, but the income needed to compensate for eventual loses of the Odds bets and hence to make (1) true.

If you manage to convince proponents of the system that the overloading represents a risk and therefore is a flaw in the system, they will likely suggest that the chances of the same number being rolled twice in a row are low. For example, a five comes up once in 9 rolls, therefore it repeats only once is 81 sequences of two rolls. Didn’t we just show that a 12 which occurs just once in 36 rolls did not break the system? So maybe we’d be lured into thinking that an even more rare outcome wouldn’t break the system either. If indeed the point never repeats itself, the overloading is irrelevant and our advantage over the house is secure.

This is a bit of a red herring because the real problem is that the Don’t Come bet is lost, not that the Odds bet has any disadvantage (in fact increasing the Odds bet always decreases the total house advantage). But we can easily show that the chances of a point repeating are higher than you might think, and furthermore the amount you lose is more than your initial bet because you’ve laid the odds.

First, we need to acknowledge that many gamblers believe in a concept called the gambler’s fallacy or equivalently the law of averages. This is the belief that following a sequence of ten heads occurring in a row from the flip of a coin, the next flip is more likely to be a tail than a head because heads and tails have to even out to 50/50 over time. This is false reasoning. The chances of heads being flipped is 50/50 regardless of history. But some gamblers incorrectly assume that a number is less likely to be rolled if it was just rolled. Some people will never accept this (even some very bright people), but it’s a fact nonetheless. For more on this see The Gambler’s Fallacy. Those who believe in the Gambler’s Fallacy, tend to dismiss the chances of the same number being rolled twice in a row as being significant.

Another reason players underestimate the frequency of points repeating is they don’t account for all the points and all the ways the outcome of the dice can result in the point. While the five will repeat only once in 81 plays, so will the 9. The 4 will repeat once in 144 plays, as will the 10. And the 6 will repeat once in about 52 plays as will the 8. So actually some point will repeat itself once in about 13 plays (1/144 + 1/144 + 1/81 + 1/81 + 1/51.84 + 1/51.84 = 1/12.96)! Another way to think of this is from the time that a point is established and we have an Odds bet at risk, the chances that the point will repeat is more often than one in 9!

Accounting for this major flaw, our remaining 13.5% advantage dissolves into a disappointing 6.29% disadvantage. Now that we’re firmly based in reality, I’ll switch to a more traditional method of measuring house advantage, so the real vigorish is 1.01% which I’ll explain later. In firm monetary terms, we can now expect to lose $0.01134 per roll for every dollar level we bet. So rather than winning $10 million per year, our strategy will actually cost us (1000 * 0.01134 * 150 * 8 * 365) about $4 million per year! The hypothetical casino mentioned earlier, rather than losing $6 billion per year, can now safely pocket (6 * 12 * 24 * 150 * 365 * 2000 * 0.01134) over $2 billion per year if everyone plays this system. We’ve discredited our system, but saved the casinos from bankruptcy! Oh well. It’s still a fun way to play and lets us root for those sevens.

Further Analysis

I stated the house advantages and returns on amounts bet without yet justifying them. For those who are curious, and those who might want to review my findings, I’ll go into more detail on how the probabilities were calculated. If you’d like to verify my methods or conclusions, or refer to a more authoritative source, please visit Professor Micheal Shackleford’s excellent web site http://wizardofodds.com/craps.

About Vigorishes and Systems

A vigorish or house advantage is a semi-standard way to measure how fair a bet is to the player. In the simplest of terms, if a certain bet has a house advantage of 5.26% (like Vegas roulette tables with zero and double-zero), it means that for every $100 you bet, you’ll lose on average $5.26.

In very simple games like American Roulette, the vigorish is straight-forward. However, in craps, where certain bets can be ties, there are multiple ways to determine house advantage. And when examining a craps system where multiple bets are played simultaneously, it can get even more arbitrary and confusing.

The most standard way to calculate a house advantage is to sum the average return of all possible outcomes, (weighted by the probability of each individual outcome) and divide by the average bet. In the case where the bet varies, this is a weighted average of the total bet en-route to each possible outcome. This method yields the house advantage including ties as money wagered and is especially nice for a casino to predict its expected income over time from a certain wager.

Some people prefer to not count ties as money wagered. This is a matter of preference, even among experts. It’s simply a different approach that results in a higher house advantage, but it is not as useful for measuring money made or lost over a period of time or a fixed number of plays.

Here’s the event table for a simple Don’t Come bet showing the different ways to compute house advantage. Note that the results correspond precisely with accepted published values and therefore help verify our methods.

Systems, especially craps systems, can be measured in terms of house advantage either including or excluding ties, yielding a number that we can use to compare to other forms of betting. However, because systems tend to use hedging extensively, the house advantage can appear relatively good due to the more money wagered, but still be worse in terms of your ability to win. There’s yet another method of calculating house advantage that works better in this case. In this method, we look at only the payouts to and from the player without regard for how much was wagered, and calculate a house advantage based on the ratio of wins and loses. Take for example the simple system of betting on Pass and Don’t Pass simultaneously, a classic and extreme hedge bet. In terms of simple house advantage, it’s 1.59% or about halfway between that of a Pass bet and that of a Don’t Pass bet. That looks like a good vig, and indeed it is in terms of how slowly you will lose money as a percentage of what you bet. But note half the money you bet is hedged against the other half! So with this system you will NEVER WIN A SINGLE BET, EVER. If the casino wins every bet, I prefer to call this 100% house advantage. In this case we can simply use the method of not counting ties. However when the system is more complex like the one we examine in this post, not counting ties isn’t enough because there are a variety of hedgings included.

For examining a system such as the No Risk Don’t Come, and it’s advantages under different assumptions, it’s best and clearest to use a simpler method of expressing advantage. We’ll simply determine the average amount won or lost per roll of the dice based on the method of play, our betting level, and the favorability of the system. When we say “betting level” it’s not the same as “amount wagered”. For example, the betting level we use for this system is $10, but at that betting level we actually wager about $36 per bet because we put 10 on Pass, 10 on Don’t Pass, odds, and come bets. But because we’re doing so much hedging, the bet level is clearer. By tallying our expected wins or losses per roll we can predict exactly what the value of the system is to us (or the house) without too much emphasis placed on the definition of house advantage.

Expected House Advantage (If the system Worked)

In showing how advantageous this system would be if it really was equivalent to putting a free bet on the Don’t Come Point I arrived at a player advantage of 18.79%.

Here’s how that figure is calculated:

Above is the event table representing the ideal conditions suggested by proponents of this system. It starts at the point where you establish a Don’t Come number (remember that establishing the Don’t Come point is considered free and without risk), and ends when the bet is either won or lost. Each row represents a possible combination of events and the combined probability of the event. It calculates the probability of winning under each circumstance. If we could actually pick the point, we’d always choose the four or ten, but since we have to rely on chance, we weight each point by its probability of coming up (second column). The sum of the probabilities of winning in each of the six ways is 0.5940. We can tell it’s in our favor because it exceeds 0.5. The amount won or lost is always even money and the same regardless of the point, so no further weighting of the result is necessary. The probability of winning is converted to a vigorish by multiplying by two and subtracting from 1.0, then expressing that as a percentage. A negative vigorish reflects a game that’s in the player’s advantage, also known as a Positive Expectation Game.

The Probability Event Table for the No Risk Don’t Come System

This is the actual probability table for the No Risk Don’t Come System that we’re looking at (click to enlarge) including all the real possible dice rolls and the probabilities of each, weighted by the return on your wagers. The result is the true house advantage which unfortunately is a disadvantage to the player.

In explanation of the table, note that a play consists of one roll if the bet is resolved on the come-out, a second roll that establishes a point, and then as many rolls as needed to resolve the final bet in the event that the play is not resolved on the second roll. Each line in the table represents a possible outcome of the play and the probability of that outcome. The raw probability of each line as an outcome is given in the column labels (p1*p2*p3) which by definition must all add up to 1.0.
One column that requires some explanation is the column labeled P3. This is the probability that determines the result of the final come bet if it is not eliminated in roll two. It is either the chance of the repeat point being made again vs. a seven being rolled first, or (this is the tricky part) the chance of a non-repeating point (any point other than that which repeated) being made vs. a seven being rolled first.

The total return in column “Total$” is the sum of the returns (net gains) of all four possible bets that were involved in this line of play. The column labeled p(W$) is the weighted probability (raw probability times total return) or average return for each winning row. The column labeled p(L$) is the weighted probability (raw probability times total return) or average return for each losing row. The sum of these two columns are the total average winning return (2.7441) and the total average losing return (3.1128). And the final weighted winning probability is 0.4685 which is w/(w+l) where w is the total average winning return (2.7441) and l is the total average losing return (3.1128). And then the final weighted winning probability is converted to a payout vigorish by the formula (v = 1.0 – 2*0.4685 = 6.29%).

This table yields a standard vigorish of 1.01% in the house’s advantage (including ties as wagered money).

Further Comments

First of all, the result of this analysis should not surprise us because betting systems simply do not work, at least not in the sense of changing the house advantage into a player advantage. Using the definition of house advantage which includes ties as money wagered, we can even say that no betting system can alter the house advantages in any way, in your favor or against you. They can merely manipulate volatility. For more on this click here. Yet there are some interesting subtleties when it comes to craps.

One thing that is special about the game of craps is that a number of very different wagers are placed simultaneously whose outcomes are dictated by the same rolls of dice. In other words, not all wagers are independent. This gives rise to the lure that a combination of bets placed in a certain way at the same time, could in concept improve your odds by decreasing the house advantage. While the rules of craps are carefully designed such that no combination of bets can ever give the player an advantage, there are combinations of bets (which could be called betting systems) which improve your odds above those of the individual bets (again based on certain interpretations and terminologies only). In other words, there are ways to play normal wagers, that gives the house more or less of an advantage. We’ll examine three to illustrate this point, one that makes your odds much worse than the individual bets, and two that seem to improve your odds.

1. 

   Betting equal on Pass and Don't Pass

   It’s well known that the house advantage of a Pass bet alone (no odds) is 1.414%. It’s also well known that the house advantage of a Don’t Pass Bet (again no odds) is 1.364% (including ties). However, some people play both of these bets simultaneously thinking that it reduces the house advantage to zero because every play will be a tie. Actually, the opposite is true, because a 12 loses the Pass bet and pushes the Don’t Pass bet, the house advantage (NOT including ties) is 100%. In other words, when you play the system of always placing these two bets (two of the best odds bets in all of organized gambling when played separately), you turn it into the worst bet in all of gambling! This will be discussed below under hedging. A purist might point out that the house advantage including ties is actually a respectable 1.39% using this system. That figure simply shows that your bankroll will last a long time, but you will never win a single bet, so you can’t even dream of winning. So I think it’s fair to evaluate it in terms of the more pessimistic figure. I submit that this is a betting system that is much worse than most based on the presumed goal of winning as much as possible (as opposed to losing slowly).

2. 

   Place equal bets, multiples of $6 each, on both the six and eight.

   More interesting is a case (which can also be called a system) in which playing two bets simultaneously in a certain manner results in a lower house advantage. A place bet on the six or on the eight is well known for having a vig of 1.52% (calculated as ((5/11)*7+(6/11)*(-6))/6). However, when you play a place bet on the eight simultaneously and meticulously put both bets up at the same time and remove them both when either wins, the house advantage is only 1.04% (calculated as ((10/16)*7+(6/16)*(-12))/12)!

3. 

   Anything but Seven

   Another similar case occurs with the so-called Mensa Anything But Seven system. You place a one-roll bet for $22 ($6 each on the place 6 and 8, $5 on the field, and $5 on the place 5). The house advantage on this bet (verified here) is only 1.136%, less than any of the individual bets placed separately.

The last two cases are fascinating, but to be perfectly candid, the effect on house advantage is somewhat of an illusion. In both cases, a combination of bets allows us to win on average in fewer rolls of the dice, and then take down other bet(s) that will no longer be in jeopardy. In effect, we’re getting the decrease in house advantage by decreasing the time that the bets are at risk. If you examine the returns of the individual bets over time, they still exactly correspond to the known house advantages. It’s a matter of interpretation, but you can at least make a case that these betting systems alter the house advantage in a way that could be favorable to the player. At the very least, complexities like these help make investigating craps betting systems interesting. But in the end, you are ALWAYS left with the same conclusion, that the house advantage of every bet is firm and unbeatable, and no system can ever change that. In fact, all you can do by combining bets (hedging) is make things worse.

Hedging

One fundamental truth about craps is that combining any bet with a hedge bet decreases your chances of winning in favor (hopefully) of increasing the average amount of time until you exhaust your bankroll. Example (1) above shows this dramatically, as does the debunking of the No Risk Don’t Come system itself. If for example you have a lot of money on points that will all lose if a seven is rolled, it’s not to your advantage to put a small bet on the seven just in case. In fact, doing so will cost you more money in the end, unless of course you do it only when a seven will be rolled next – but if you have that kind of foresight you can simply win the lottery each week and save the trouble of playing dice at all.

Is there ever a plausible reason to hedge a bet? There are only two I can think of. One is to increase your “action” by having a lot of things going on at once, knowing that you’re paying a price for the added action. The second is a cowardly retreat – this is the real legitimate use of a “hedge”. Suppose you all of a sudden realize that you have so much money bet that you cannot afford to lose. Say you put $1000 on a Pass bet, rolled a point, bet the Odds, added several Come bets with Odds and you now have more money at risk than you can afford to lose. So to avoid financial ruin you put some more money on the seven for every roll. That’s a plausible thing to do but in no way is it smart. [If you ever screw up that bad, you're better off taking down your odds bets. If there's still too much at risk, consider swallowing your pride, calling over the floor manager and asking if they will allow you to take down a portion of your bet in exchange for surrendering a portion to the house - I've never heard of doing that, but it's a reasonable request, especially if you're the only one at the table. Don't expect to be welcome back, and consider giving up gambling.]

It’s good policy to never hedge bets. In the game of craps that means only playing multiple bets if none are hedged against the others. That means never make a bet that can win on the same roll of the dice that another bet can lose.

There’s a convention you’ll often see on the craps table that helps drive home the importance of avoiding hedging. Many savvy players like to add Place bets when they’re betting “right” (making Pass bets and Come bets as opposed to Don’t Come and Don’t Pass). Place bets, particularly the 6 and 8 are among the better bets you can make provided you place them rather than using the Big 6 and Big 8. But Place bets can carry over to the next Come Out roll because they may not be resolved if the shooter makes the point. Therefore, on the Come Out they could become hedge bets (a seven wins the Come Out but loses the Place bets). You have the choice of declaring that your Place bets are on hold (“not working”) or in effect (“working”) on the Come Out roll. By default the casino will treat your place bets as “not working”, that is if a seven is rolled, on the Come Out, you’ll not lose your Place bets (nor win if the Place number is rolled). If instead you prefer your Place bets to be “working” on the Come Out, you have to ask for it, and the dealers will place a little “working” chip on your bets. If you’ve ever wondered why this is the case, or why “not working” is the default, now you know. Most Place bets are made by right bettors who are also making Pass bets. These are generally smart players and want to avoid this hedging situation, though it’s probably more often due to distaste for have money working against them rather than knowledge of mathematics. But it’s a case where the casino helps you avoid hedging thereby improving your odds without you even having to ask! Some people are understandably suspicious of this and keep their Place bets working out of spite. But the little “working” chip might as well say “sucker” if you’re also betting Pass. On the other hand, if you’re not the shooter and just making Place bets without Pass bets, you’ll probably always want your Place bets working. And there’s a similar case involving your Odds bets and Come/Don’t Come bets that I won’t go into, but also where the conventions of the game help you avoid hedging. The moral, hedging is never smart.

Conclusions

The No Risk Don’t Come system is like all other craps systems of no value to the player looking to gain an edge over the house. Its only value is as a fun way to play that lets you root for sevens to come up (at the cost of not playing optimally). Like most craps systems, it uses hedging and overloading complications to lure you into a false confidence while leaving you at the mercy of the standard house advantages.

Overview

Someone discovered that if you drop some mentos into a bottle of Diet Coke, all the carbonation will be released instantly.There are two basic applications, the Mentos Diet Coke Fountain and the Mentos Diet Coke Rocket. I went to Google Video and YouTube and watched all the videos people posted on the subject (hundreds). And I did a cursory search of web pages that give how-to and design advice. Most have very poor information. Almost all of the videos show only the simplest form of the ‘experiment’, dropping a handful of Mentos into Diet Coke, often with dissappointing results. I only found a few mentions of the rocket concept, but no good ideas on how to control it – which was fine because it meant that the coolest application needed some work…

Fountains

The best fountain advice I found was here:

http://www.youtube.com/watch?v=GAHGz2reXsU&search=diet%20coke%20mentos

I have only one thing to add to that advice. Caps from actual Diet Coke bottles are brittle and tend to shatter if you try to poke a hole in them. Drilling a 1/8″ to 1/4″ hole in a plastic cap is difficult. Instead, I used caps from WalMart water bottles which are the same size and less brittle. To make the holes I bought a set of decorative hole punches made for scrapbooking (shown to right). These are available at Micheals and JoAnns. They look like little staplers and come in various designs (circle, star, flower, spiral). The hole sizes were just right, the circle being 1/4″, and other shapes having less area. You can rip these punches apart and extract the ‘die’ – a piece of sharp metal of the proper shape. Then just place the die on top of a bottle cap (oriented opening down is fine), then hit it with a hammer to punch the hole. The star shape worked best.

The crown-effect fountain is extra cool, but I didn’t play with it for a couple reasons. Obviously it spreads the mess over a wide area. The remote firing concept from the above video helps but I still didn’t want my whole yard covered in soda. It also requires that holes be drilled or punched into the bottle after it is opened, but immediately prior to doing the fountain – you cannot prepare it in advance, and you can’t pour the soda into another prepared bottled without losing too much carbonation. A good solution to that would involve some kind of pre-drilled extended cap that you could screw onto the freshly opened bottle, but I didn’t work on that.

Rockets

I couldn’t locate a single example of the ‘rocket’ being done properly. All the videos showed people dropping mentos into the bottle, capping it, and slamming it into the ground hoping it would break just right and launch into the air – not reliable at all, and a huge mess, maybe even a minor hazard. Just plain not worth trying. Improvement ideas that people posted ranged from laughable to complex and expensive.

My final solution is very satisfactory. It’s simple, free, safer, predictable, and works just about every time. Click on the picture to the left for complete instructions. It’s very basic so it’s probably not a unique idea. But working it out, refining, testing, and documenting it was rewarding. I recently demonstrated this twice at a party and both flew 30 or 40 feet high without a hitch (sorry no video available here – you might be able to find it on http://www.happaymommay.blogspot.com/ July 2006).

Tips

• Concentrate on making 3-letter words. 3-letter words are the most efficient way to score, the easiest to see, and the fastest to type. Longer words don’t help very much except in a few special cases.
• At the end of the first two rounds, make sure your second-to-last word gets you to exactly 74 (or 98) letters. For example, in round one, you’ll get to 74 letters by using all 3-letter words except two 4-letter words. Watch the letter meter and get to 74 or 98 as quickly as possible. Then take your time to form the longest word possible (10, 11, or even 12 letters long). This will be your last word and will end your turn, but you can use a lot of left over time to find a huge word. The bonus time is not nearly as valuable as the score for the long word.
• In the first two rounds, set up prefixes and suffixes that will help make a long final word. For example, leave some INGs at one end of the screen or the other and try to use up difficult letters like F, K, Z, Q, V, W, J, and X so your final letters are easier. It’s also helpful to remove the two golden balls before the final word. This leaves more flexibility and adds to your score.
• In the bonus round, concentrate on making rapid-fire 3-letter words, as many as possible. Always try to remove as many of the golden blocker balls as possible. Don’t slow down to use the bonus letter, but if you can use it without hesitating, try to use it as much as possible. The bonus letter is best ignored when it is an unusual letter (like Q) because they appear so infrequently on the screen. But when it’s an N, T, R, S, and so on, you can use it to inflate your score quickly.

Advanced Tips

• In the first two rounds, the method of forming all short words, then one long word to end the round can actually be improved by very advanced players. The key is to form several words longer than 8-letters during the round, the more the better. 8-letters is the hot spot in the scoring algorithm where very long words really pay off. 5-7 letter words are not very helpful.

Scoring Algorithm

Below is the Word Dojo scoring algorithm (which is also common to Wordster). Following are some conclusions that can be drawn from this information.

Letter values (from help screen):
a=3 b=10 c=7 d=9 e=1 f=10 g=9 h=9 i=4 j=12 k=6 l=2 m=9 n=5 o=5 p=9 q=12 r=4 s=6 t=5 u=8 v=11 w=11 x=12 y=10 z=12

There are two variables used to calculate a word’s score.
n = the number of letters in the word (for ‘sunshine’ n=8)
s = the sum of all letter values in the word (for ‘sunshine’ s=6+8+5+6+9+4+5+1=44)

In round three, the bonus letter multiplier affects the individual letter score and therefore the value of s (for ‘sunshine’ if ‘s’ is the bonus letter with a multiplier of 5x, s=(6*5)+8+5+(6*5)+9+4+5+1=92)

The algorithm changes based on how many letters are in the word (or partially formed word):

1-letter, score = s
2-letter, score = (1000*n+20*s)
3-letter, score = 10*s*(n+0)+2*(1000*n+20*s)+1000
4-letter, score = 10*s*(n+0)+2*(1000*n+20*s)
5-letter, score = 10*s*(n+1)+2*(1000*n+20*s)
6-letter, score = 10*s*(n+2)+2*(1000*n+20*s)
7-letter, score = 10*s*(n+2)+2*(1000*n+20*s)+1*(1000+10*s)
8-letter, score = 10*s*(n+2)+2*(1000*n+20*s)+4*(1000+10*s)
9-letter, score = 10*s*(n+2)+2*(1000*n+20*s)+7*(1000+10*s)
10-letter, score = 10*s*(n+2)+2*(1000*n+20*s)+10*(1000+10*s)
11-letter, score = 10*s*(n+2)+2*(1000*n+20*s)+18*(1000+10*s)
12-letter, score = 10*s*(n+2)+2*(1000*n+20*s)+26*(1000+10*s)

After finding the score of a word using the formula above, there is one more adjustment to make. If the word is more than 2 letters long and s equals any of the following values: 5,6,17,30,31,32,57,58,59 subtract one from the score.

Additional Conclusions Based on Scoring Algorithm

1. Three-letter words receive a 1000 point bonus. This makes 3-letter words the most efficient way to score quickly. Also consider that 3-letter words will occur most frequently among any random arrangement of letters and are obviously the fastest to enter. So the strategy of forming only 3-letter words is supported. The only exceptions being (a) to get exactly 74 or 98 respectively with the second to last word in the first two rounds (b) to get the highest possible score for the last word in the first two rounds to capitalize on the ‘overshoot’ and of course (c) if a longer word is all you see, it certainly doesn’t pay to delay to find a 3-letter word.
2. Longer words don’t benefit the lengthier data entry time until they are at least eight letters long when some added scoring power takes effect. However, 8-letter+ words are less commonly present, are difficult to see, and are more prone to typing errors. So any strategy that favors using long words is dubious – with the exception of the overshoot in the first two rounds.
3. In the bonus round, bonus letter multipliers contribute to the base score of each occurrence of the letter in the word. Therefore, they do have a substantial effect on the word score when entered quickly while the multiplier is high. The total contribution for a bonus letter is more than the multiplier. For example if a word contains a letter ‘s’ and the ‘s’ is the bonus letter with a multiplier of 10x, the word score actually increases more than 54 points (10*6-6), but more like 50 times that much (for each occurrence of the bonus letter). So using the bonus letters in the third round can make a big difference in your score. But by ‘big’ I do not mean millions, maybe a couple hundred thousand.
4. In round 3, high-scoring bonus letters like J, Q, X, Z could in theory provide the potential for huge scores. However, while these letters come up relatively often as bonus letter, you almost never see these letters ‘drop. The best prospects for high scores based on bonus letters in round three is simply to get common letters, maybe those with a middle value like (l, n, o, p, m, t, s, u, r), and enter lots of three letter words quickly using the bonus letter. This has been suggested by nearly everyone who gets very high scores. It also explains why you can happen on very high scores without even watching the bonus letter.As for 12-letter words… Based on the scoring algorithm, 12-letter words aren’t rewarded nearly well enough to compensate for the rarity and difficulty of finding them. 12-letter words will VERY rarely even appear on the screen, much less would be the chances of detecting them.
5. You can manipulate the letters as they drop to ‘build’ long words. For example, you can encourage and preserve common prefixes and suffixes such as “ING” or “TION” and simultaneously exhaust letters that are less likely to contribute to long words. However, you have a limited number of letters to work with and you rarely even get the opportunity to build a 12-letter word. That said, ‘building’ one huge word to end the first two rounds is certainly the best strategy. It’s fairly easy to consistently end with a word of 8 to 10 letters, with an occasional 11 or 12. If you get the maximum score for rounds one and two, it would not add enough to inflate the overall score to the level of these super high scores that are achieved by cheating (lantern trick). I couldn’t find any credible evidence that there’s any valid ‘trick’ involving forming 12-letter words that would help to get huge scores (over 2M).

High Scores

Scores of 1.2 million are very good. My personal high is just over 1.5 million and credible scores of as high as 1.6 to 1.8 million have been reported. Looking at the scoring algorithm in combination with letter frequencies, there doesn’t seem to be an obvious way to score legitimately above 2 million.

Update: The Lantern Trick has been fixed and no longer works in the newer versions. So it seems that all new scores are legitimate. No more three hour sessions on one quarter. No more  phony claims of ridiculously high scores (over 25 million for example). If you have access to an older game (versions out before 2010 I believe), it might be fun to try to discover for yourself. Anyone claiming to get over 1.6 million or even scoring 12-letter words, I’d love to see video, including proof it’s the new version. It’s still unclear what the top players can score. Post a video on YouTube and I’ll include it on this page.

Btw, comments containing obscenities, rude language, or personal attacks on others will be deleted.