Dice Probabilities and Craps House Edge
There are a lot of decisions that players have to make in a game of craps. These game play decisions, more often than not, relate to which bet they need to make. When making these decisions you'll often hear a lot of myths about which bets to make or a "fool proof" and "sure win" betting strategy. If that were true then most players would be making millions.
Coming back to reality, one thing we'll observe is that the game isn't as structured as any card game, like poker or blackjack, which we find in a casino. Two items of interest that is unique to this game are the randomness of the dice (often relating to probabilities) and the varying degrees of house edge for each bet there are on the table.
Knowing the probability that a certain dice roll turning up helps with our betting decisions. The same goes for the house edge, the lower the house edge the better are the players' chances to cash out on any casino game.
Notice that as you get near to seven you get better probabilities to get that result on the dice. And, as you get past seven the probability of each total on two dice go down. There are only 36 combinations in the game that can be made by a shooter on two dice. Here are the probabilities for each dice roll:
There is a 1/36 chance of getting a two on two dice.
Getting a three is a 2/36 probability.
Getting a four has a 3/36 probability.
Getting a five has a 4/36 probability.
Getting a six has a 5/36 probability.
Getting a seven has a 6/36 probability.
Getting an eight has a 5/36 probability.
Getting a nine has a 4/36 probability.
Getting a ten has a 3/36 probability.
Getting an 11 has a 2/36 probability.
Getting a 12 has a 1/36 probability.
Here are the different bets you can make listed with its corresponding house edge:
Pass Line Bet: house edge at 1.41%
Don't Pass Bet: house edge at 1.40%
Come Bet: house edge at 1.41%
Don't Come Bet: house edge at 1.40%
Field Bet: house edge at 5.6%
Big Six or Big Eight: house edge at 9.1%
Hard Bets: house edge at 12.5%
Craps Two or Craps: house edge at 12 13.9%
Any Seven: house edge at 16.7%
Given the house edge of each bet on the table and the probabilities of each dice roll combination we can decide which numbers to bet on and which bet we're going to make.