Calculating Craps Probabilities

Even if it sounds difficult, calculating craps odds can actually be quite simple. Before we get started, lets look at a few assumptions we must make.

  • We need to assume that we are using two identical six-sided dice.
  • We need to assume that each roll of the dice is perfectly random.

Even though some people might disagree with these assumptions in a 'real world' environment, we are going to say that each side of the dice is as likely to appear as any other side of the dice.

Gathering The Info

The first step is figuring out how man possible outcomes any roll of the dice could have. Each die has six sides, and thus six outcomes. Because each of the outcomes of one die can coincide with any outcome of the other, we multiply six by six, which is thirty-six. This is how many total outcomes there are in a craps roll. In the table below all of the dice combinations and odds are displayed.

Dice Combinations and Odds
Dice Total # of Combo's Odds All Combinations
2 1 35:1 (1,1)
3 2 17:1 (2,1) (1,2)
4 3 11:1 (3,1) (1,3) (2,2)
5 4 8:1 (4,1) (1,4) (3,2) (2,3)
6 5 6.2:1 (5,1) (1,5) (4,2) (2,4) (3,3)
7 6 5:1 (6,1) (1,6) (5,2) (2,5) (4,3) (3,4)
8 5 6.2:1 (6,2) (2,6) (5,3) (3,5) (4,4)
9 4 8:1 (6,3) (3,6) (5,4) (4,5)
10 3 11:1 (6,4) (4,6) (5,5)
11 2 17:1 (6,5) (5,6)
12 1 35:1 (6,6)

So we now know that there are a total of 36 combinations, and we know the number of combinations that can make up each specific number from 2-12. This is all of the information we need to calculate the odds.

Crunching The Numbers

There is not too much math involved in calculating the odds for a specific number. You just take the number of possible outcomes (36), and divide it by the total number of possible combinations. Simplify the result and subtract one from the value. Set this number before a colon and a '1' and you are done. For example, the odds a seven appearing would be calculated like this...

  • There are 6 ways to roll a 7. [(6,1) (1,6) (5,2) (2,5) (4,3) (3,4)]
  • There are a total 36 possible outcomes.
  • 36 / 6 = 6
  • 6 - 1 = 5.
  • Thus odds are 5:1

It really is that simple. In the example above, the odds would be read "The chances that a seven will appear is five to one." This means that for every way to roll a seven, there are five ways not to roll a seven.

The Connection Between Odds And Edge

When casinos designed the game of craps, they used this same basic calculation to figure out how likely any single event was. To guarantee a long term profit, casinos payout slightly less than the fair odds that would be normally expected, and this discrepancy is where the house edge is formed.

For instance, there are 35:1 odds that a 2 or 12 will be rolled in any given toss. If the casinos were perfectly fair, you would receive $35 for a $1 winning one-roll bet on 2, or 12. Because casinos expect to make a profit though, they would really only payout $30 (30:1). In the long run, for ever $35 they receive, they will only have to pay out $30. This difference is the house edge, and the smaller the difference, the smarter the bet.

House Edge on Multiple Bets

When you use a betting system like the Iron Cross you are usually combining multiple craps bets. You can take the odds for each specific bet though, and combine their house edges to find the overall house edge. To do this you have to take the weighted average of all of the house edges. Here is the formula and an example to show you how it is done.

[(x1)(e1) + (x2)(e2) + (x3)(e3)...] / (Σe); x=bet amount; e = house edge.

  • You make a $5 pass line bet, a $10 place bet on 4, and a $8 one roll bet on 7.
  • Passline's house edge is 1.41%, the Place Bet's is 6.67%, and the one roll bet carries a 16.67%.
  • We need to multiply each of these edges by the amount of money bet on them; then add all of these numbers together.
  • (5 x .0141 = .0705) + (10 x .0667 = .667) + (8 x 16.67% = 1.3336) = 2.0711
  • Then take this number and divide it by the total amount of money wagered.
  • 2.0711 / 23 = .090 or 9% overall house edge

All your doing is putting more weight on the bets with more money, and less weight on the smaller bets.

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