The No Risk Don’t Come system has been known for years under a variety of different names. It claims that the player can establish a Don’t Come point with little or no risk, thereby having a bet that is always to their advantage. Unfortunately, this system, like all craps systems, does not deliver its promise and leaves the player at the mercy of the standard house advantages. Nevertheless this particular system has many avid followers. It has an interesting premise and appeals to seasoned players and their understanding of the game. Reviewing and ultimately debunking this system is a rewarding exercise in probabilities and is also an intriguing demonstration of what makes systems compelling to gamblers. Here I give you for free a system that unscrupulous or ignorant people have sold to millions, and I also give you the explanation of why my price is the right one!
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
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.
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.
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.
When the second roll establishes a new point, remove the Odds on your Don’t Pass bet – eliminating that money from any risk.
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.
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.
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 two catches with this system. The first is minor and relatively simple. It reduces the potential advantage that the player can supposedly achieve over the house. The second is the true flaw of the system. It eliminates the perceived player advantage and restores the house advantage. This second flaw is also more subtle and difficult to explain. Proponents of the system will dismiss both 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.
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.
-
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).
-
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)!
-
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.
December 19, 2008 at 6:41 pm |
Sure no combination of bets beats the house edge. But you incorrectly stated the when a point repeats we loose the DC bet. – The DC bet travels to the number on the second roll and is active, it isn’t lost. This must be factored in. Though Doubt the game will favor the player.
Great job with the math.
December 21, 2008 at 3:27 am |
Thanks for pointing out the error. You’re right, I have corrected the wording of the explanation to properly indicate that the DC wager is not lost in the immediately repeating point case. As you point out, the repeating number does become a new Don’t Come point which may end up being either won or lost depending on what rolls follow. It’s the odds bet that is lost before it can be taken down that accounts for flaw. The event table and the calculated probabilities took the case into account properly, so no results or conclusions were affected. The math is easy compared to the descriptions.
October 7, 2009 at 4:48 pm |
Great job evaluating this system. Even though the system has “flaws”, it still seems like one of the best methods to play craps from the “dark side”. I’ve used this system with good results for a couple of years. I never was smart enough to determine the overall vig for this system (due to the one time lays involved), but it has to be low. My main concern is that my one line lay bet will get picked off when the number repeats.
October 19, 2009 at 6:39 pm |
I faithfully believe in everything you’ve stated. No linear combination of wagers with negative expected value can ever result in a positive expectation.
One factor which almost no one discusses, though, is the variance of wagers – probably because it’s more complicated.
We know that a risk-averse person wouldn’t accept an unfair bet, i.e. one with a negative expected value. Gamblers are, by their nature, risk-lovers so they will take unfair bets. The degree of their risk-loving nature defines which wagers they will accept and which they will not. In that, they will consider not only the expected loss, but the variance of the outcome.
For a given level of risk-loving, there is an optimal wager (with a negative expected value).
What can you say about the variance of different wagers? Are there some wagers among all those with negative expected value which at least give the risk-loving individual a higher probability of session gains? For that matter, why stop at the second moment. Are the distributions of all casino wagers symmetric or are some skewed? Do some have fatter tails (kurtosis)?
Some pundits (like Gary Carson) have mentioned things like variance, skew, and kurtosis, but NONE of them have ever followed up with any advanced analysis. Apparently they just want to be credited for saying things which sound smart from Chapter 2 of a statistics textbook.
Also, have you ever examined poker? At first glance it would seem that in the meta-game of opponent selection, it’s indeed possible to find someone who will surrender their money to you for fun. The only evidence you need is people handing money to beggars on the streets.
I have played poker for 20 years and I have difficulty believing that in an infinite game of incomplete information, there would ever be a winning strategy, especially with the rake. In particular, I lost a lot of money playing tight and aggressive before I learned the books weren’t worth the paper they were written on. I also have my doubts about the ability of people to read tells consistently. My explanation for the seemingly stellar performance of so-called “pros” is that they play a LOT of tournaments funded by sponsors and have non-poker income to keep them afloat.
October 20, 2009 at 1:29 pm |
Good points, completely agree. There’s the variance in the wager amounts themselves and in what some call the volatility of the bet. What bets a gambler will take or prefer is largely a matter of psychology – their thirst for risk and the level of positive feedback they require to keep betting. Too long a drought, no matter the probabilities of the bets, and they’re likely to quit. Good poker players seem to have a feel for that aspect, moreso even than they do for the probabilities of the hands.
I played pool for 25 years and it’s similar. There’s certainly an art in the ‘metagame’, ‘making’ a game that looks attractive to the wagerer but is unfavorable. The actual probability of the outcome is a relatively minor part of the equation. And IMO very little of a proven successful strategy could be articulated in a book. And that’s not because it’s mathematically obscure or mystical in any way. I feel it’s because it’s a matter of picking up on little cues that matter, having a good feel for how much they matter, and knowing how they affect the player when mixed with everything else going on. For example, it’s easy to say that a player who just won a huge bet will be a bit looser with his betting than a player that’s on a prolonged losing streak. But just being aware of that is of little value without the wisdom and experience of knowing how and when to use it to your advantage. Recently (sorry lost the link) poker playing robots have achieved a surprising level of success against humans by recognizing a player’s personality type (one of just four or five different models) and playing optimally against it, adjusting as it changes.
Aside from personality and psychology, I suspect you’re also right that more advanced statistical techniques would reveal measurable affects of the sort you imply. I’ll bet they’ve been done, but the results are buried in scientific journals rather than in statistics textbooks.