Craps: A Game of Chance

I am at a casino in California, and I am thinking about playing a game or two of craps. This is my first time ever playing craps and for the first three or four rolls I sit down and watch. Finally I feel like I am ready to play. So I stepped up and placed my first bet. Winner is announced. Shocked I gathered my winnings and kept playing. After winning a few more times I was given the opportunity to be the shooter. By now I have figured out that if I roll a seven or eleven we’ll automatically win. However if I roll a 2, 3 or twelve we all lose automatically. So I rolled. To my astonishment I roll a ten. Well I had never seen this and don’t know what to do. A nice gentleman explains to me that now I have to roll a ten again before rolling 7, 2, 3 or twelve. Nervous I roll. What are the odds of rolling the ten and not rule and a seven, two, three, or twelve?

In the following few pages I will analyze statistically the chance of winning or losing on your first roll. This game is played with two dice each of which have six sides this means that there are 36 possible combinations that can occur when a rolling these two dice. Also because of the nature of this game the odds of rolling a certain number are reset at the beginning of each roll. Therefore before even beginning to analyze this game of chance I already know that the chance of rolling at ten on the first roll is the same as rolling a ten on every role thereafter. This little bit of knowledge will make all of my calculations tremendously more simple. The first time you ever get to a craps table, make a small bet on the pass line. The pass line is the strip that runs all around the craps table's layout.

This small bet that you just made on the pass line is called a come-bet. That's because the first throw of the dice is a come-out roll. At this point, you're hoping to roll a 7 or an 11 if you're the shooter, or hope that the person who is throwing the dice rolls a 7 or an 11. On the come-out roll, a 7 or an 11 is a winner automatically, so if that happens, you're already a winner.

On the other hand, if the shooter rolls a 2, a 3, or a 12, then he's rolled "craps", which is an automatic loss.

Any other number establishes a pass-line point. The shooter's goal at this point is to roll this number again before rolling a 7. If he does roll the pass-line point before rolling a 7, then again, you win. But if he rolls a 7 before rolling the pass-line point, then you lose, and the hand ends. In this case, the dice move to another player, who becomes the new shooter.

So if the shooter doesn't roll craps, and the shooter doesn't roll a 7 or an 11, he's rolled a point number. When he rolls a point number, you should put another small bet behind your original bet. (Roughly twice the original amount would be an appropriate amount to bet.) This extra bet is called a free-odds bet or just an odds bet.

Your original bet (the pass line bet you made) gets paid out as even money if you win. Your odds bet, on the other hand, gets paid out as a true-odds money. So even though you have to put extra money up for this wager, it's a great bet, because the house edge on this bet is exactly 0. (Any time the house pays out money in a true odds fashion, the house edge is exactly 0. Almost all casino game bets pay out at less than their true odds, which is why a casino is a profitable business to run.)

This bet isn't even shown on the layout of the craps table. That's because it's such a great bet for the player, and not such a good bet for the casino.

Free-Odds Bet Payouts

Pass-line point House Odds Payout

4 or 10 2 to 1 2 to 1

5