THE LAW OF RANDOMNESS FOR CRAPS PLAYERS

Craps is a negative EV game. That means that the house has a theoretical advantage in every bet a player makes (with one exception which we’ll discuss shortly). Many players don’t understand this concept which is why there’s a mistaken notion that it is possible to make money at craps in the long term. That has led to a surprising number of ‘craps systems’ offered for sale online. Most of these systems are predicated on discredited money management/bet structure concepts (eg: The Martingale System) but others are based on even less viable concepts.

There are some craps systems that are based on a simple–if completely erroneous–concept: that all the player has to do to turn a profit is to keep track of the numbers that *have* been rolled and bet on ones that haven’t appeared in some time. For example, if the player’s ‘number tracking’ reveals that the number eight or specifically a ‘hard eight’ hasn’t appeared in awhile he should start betting on it thinking it is ‘due’. It’s surprising that people actually buy into this but it does serve to underscore the need for better education in math and probability among gamblers.

THE HOUSE EDGE IN CRAPS

The house edge in craps varies depending on which bets a player makes. The way the house derives an edge is similar in all wagers. The casino pays out on specific rolls at lower odds than ‘true odds’. 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 exception is the ‘odds bet’ on pass or come bets. This bet allows a player to bet a specific amount at ‘true odds’ which means that the house edge is 0%. This is among the best wagers in the casino but over the long term you’ll do no better than ‘break even’ on this bet. More importantly, you can’t place this bet without placing a previous bet on the ‘come’ or ‘pass’ line. So in reality the ‘odds bet’ has a theoretical ‘house edge’ based on the ‘qualifying’ bet even if the actual bet is at ‘true odds’.

THE DICE ROLL IS RANDOM

For our purposes we’ll dismiss any discussion of dice manipulation. There are gamblers’ stories and ‘urban legends’ about players who can roll certain numbers with great regularity while not attracting the attention of the dealer, pit boss or ‘eye in the sky’ security cameras. Roulette has it’s counterpart in ‘ball manipulation’. The discussion of the validity of these manipulation concepts is beyond the purview of this article. For our purposes, we’ll assume that the dice roll is random. This is not to say that any number has an equal chance of appearing–it doesn’t, simply because some numbers can made ‘made’ in more ways than others. If one six sided die is rolled there *is* an equal chance of every number occurring. Each number 1 through 6 has a 16.667% chance of appearing.

When you roll two dice, however, there are more ways to make a 7 than any other number. For that reason, the number 7 appears 16.667% of the time since there are six ways to make the 7: 1-6, 2-5, 3-4, 4-3, 5-2, 6-1. There are five ways to make a six or eight making the odds of either number appearing 13.889%. There are four ways to make the five or nine (11.111%). There are three ways to make the four or ten (8.333%) and there are two ways to make the 3 or 11 (5.556%). There is only one way to make the number 12 (6-6) or 2 (1-1) making the odds of either number 2.778%.

What many players fail to understand (aka the ‘Gambler’s Fallacy’) is that each roll is independent of the ones before or after it. If the dice are rolled 100 times and the 6-6 = 12 never appears what are the odds it’ll show up on roll #101? If you said 2.778% give yourself a pat on the back. The odds of each roll are correct in theory but might not manifest in reality in the short term. This is where a lot of players get screwed up–there’s no definition of the ‘long term’. It can be hundreds of thousands, millions, or hundreds of millions of rolls.

For more discussion on randomness as it applies to the various casino games read the other articles on the subject on this website. The more you understand these theoretical concepts like probability and randomness theory the better gambler you’ll become, no matter your game.