Why Craps Will Always Beat You

Statistically, it is impossible to obtain the expected average rolling one die .

Probability of rolling a “1” is 1 x 1/6
Probability of rolling a “2” is 2 x 1/6
Probability of rolling a “3” is 3 x 1/6…

If you multiply the probabilities of rolling all six sides together and add the results the expected average is 3.5(an impossible number to roll).

BUT… if you roll two dice the expected average is “7”, statistically you will roll a “7” more than any other number… why is this important?

Las Vegas has perfected this Statistical truth in a very popular casino game. Craps.

Rules of Craps – Copied and Pasted from Wikipedia:

“First, the shooter makes a "come-out roll" (First roll) with the intention of establishing a point. If the shooter's come-out roll is a 2, 3 or 12, it is called "craps" (the shooter is said to "crap out"), and the round ends with players losing their pass line bets.

“A come-out roll of 7 or 11 is called a "natural," resulting in a win for pass line bets.

“Either way, the come-out roll continues for the same shooter until a point is established. If the point numbers 4, 5, 6, 8, 9, or 10 are rolled on the come-out, this number becomes the "point" and the come-out roll is now over. The dealers will move an "On" button to the point number which identifies the point number to all players at the table. The shooter now continues rolling for either the point number or a seven. If the shooter is successful in rolling the point number, the result is a win for the pass line. If the shooter rolls a seven (called a "seven-out"), the pass line loses. A seven-out ends the round with the dice being passed clockwise to the next player who wishes to become the new shooter.”


Dice Roll Possible Dice Combination
Roll a 2 : 1-1
Roll a 3 : 1-2, 2-1
Roll a 4 : 1-3, 2-2, 3-1
Roll a 5 : 1-4, 2-3, 3-2, 4-1
Roll a 6 : 1-5, 2-4, 3-3, 4-2, 5-1
Roll a 7 : 1-6, 2-5, 3-4, 4-3, 5-2, 6-1
Roll a 8 : 2-6, 3-5, 4-4, 5-3, 6-2
Roll a 9 : 3-6, 4-5, 5-4, 6-3
Roll a 10: 4-6, 5-5, 6-4
Roll a 11: 5-6, 6-5
Roll a 12: 6-6

Rolling a 2, 3, or 12 to “crap out” is very unlikely, where as rolling a “natural” ( 7 or 11) is much more likely.

If you roll a point: 4, 5, 6, 8, 9, or 10 on the “come-out roll” then you are much much more likely to roll a 7 than one of those point numbers again.

So the Casino has the probability of winning on its side with this game. As our professor says, “no matter how many times the cute cocktail waitress blows on the dice or how many times you beg for new shoes, you can’t beat the statistical truth of the game.”

Interesting that this highly “unwinnable” game is one of the most popular in casinos.

“Las Vegas’ goal is to take all of your money while making you think you had a great time while they did it”.