THE LAW OF LARGE NUMBERS FOR CRAPS PLAYERS

We’ve talked about several randomness concepts as it relates to craps but this is one that is very important to all forms of gambling. We’ll preface this with a similar introduction that we’ve given to all of these discussions. Despite the fact that there is no shortage of scam artists trying to sell ‘never lose’ craps systems that promise hundreds of dollars of profit daily it is *not* possible to make money at craps dependably over the long term. Other ‘systems’ suggest that a player can turn $10 into $10,000 with ‘no risk’ in just a few hours at the casino craps table. This is also not possible, at least not on a regular basis. In the short term it can happen but it has nothing to do with a ‘system’--it’s simply luck.

This is why the concept of ‘randomness’ and it’s implications are so important to gambling. Once you understand the math that underpins gambling you’ll be able to understand what will work in practice and what won’t. You’ll understand that certain games are ‘beatable’ and can potentially offer long term positive ‘expected value’ and others simply cannot. To be sure, some people don’t want to know this. They prefer to subscribe to concepts like ‘luck’ and think that a rabbits foot or lucky charm can make the difference between success and failure. They’ll argue that knowing the math behind the game ‘takes the fun out of it’. Some people can’t get their head around it while others just don’t want to.

WHY THE MATH IS IMPORTANT

People who don’t understand or don’t want to understand the math behind gambling are at a disadvantage. Our goal with this content at this site is to give you the best shot at the casino. Most people *would* agree that leaving the casino with more money in your pocket than you arrived with is more fun than doing the opposite. In light of this, the amount of fun is directly proportional to how much math you know. This is simply because the more you understand about the math of gambling the more money you’ll win. These concepts are applicable in all forms of gambling–not to mention many other disciplines–so the more you know, the smarter you are at gambling and at life.

Simply put, craps is a negative EV game. This means that in the long term, you should ‘expect’ to lose money. The house edge is very specific in craps and it varies depending on the bet. It works like this–the house derives an edge by paying out on specific rolls at lower odds than the ‘true odds’ at making those rolls. For example, a ‘hard 6’ or ‘hard 8’ pays out 9 to 1 though the ‘true odds’ on hitting these rolls are 10 to 1. This might not seem like much but it translates into a house advantage of 9.09%. The ‘Any 7’ bet pays at 4-1 though the ‘true odds’ are 5-1. This results in a ‘house advantage’ on this wager of 16.90%. The ‘house edge’ in craps ranges from 1.402% (‘Don’t Pass/Don’t Come’ bets) to the aforementioned ‘Any 7’ bet at 16.90%.

THE GAMBLER’S FALLACY AND LAW OF LARGE NUMBERS

These numbers just can’t be overcome in craps. The player simply does not have enough influence to the outcome of the game to do so. No strategy can change the randomness of the dice roll nor can any ‘betting strategy’ overcome the house edge and negative expected value. The ‘scam’ systems are invariably contingent on one of the two–they depend on discredited money management/betting theories (eg: the Martingale System) or the more dubious notion that craps is not truly random. The latter system usually requires that the player ‘keep track‘ of which rolls have appeared and to bet on ones that haven’t appeared in a certain amount of time based on the thinking that they’re ‘due’.

It just doesn’t work that way. This is the ‘Gambler’s Fallacy’–the mistaken belief that random events in the past can have an influence on random events in the future. If two dice are rolled 100 times without ‘snake eyes’ (1-1 = 2) appearing the odds of one appearing on roll 101 doesn’t change (it’s 2.778%). No matter how many rolls you make these odds don’t change. The simple minded gambler would say that if something hasn’t appeared in a certain amount of time that it *has* to appear soon to ‘even out the odds’.

This is also untrue which is where the ‘Law of Large Numbers’ comes into play. This concept suggests that a random event will move closer to the ‘expected value’ as the number of repeated trials increases. This means that the longterm–the time where the odds ‘even out’–is an abstract concept. There’s no defined number that equals ‘the longterm’. What we do know is that an event’s probability of occurance will reflect the ‘expected value’ more closely after 10,000 repetitions than it will after 100. It’ll do so even more after 100,000 or 1,000,000 repetitions. That being said, it is incorrect to label any number of trials as the ‘long term’.