Sorenson's Game (Math)

by Andrew Daugherty
High Tech High, San Diego CA

Our casino game is based off of Craps. Our game is a dice game played with two dice. A bet is placed and the player rolls two dice, and the outcome determines if they win or not.

There are twelve options for a player to bet on, these include individual number bets on 4, 5, 6, 7, 8, 9 and 10. The chances of rolling a 4 are 1 in 12, with the possibility of rolling a 3-1, a 1-3 and a 2-2. Those are the same odds as rolling a ten, with combinations of 6-4, 4-6 and 5-5. Since there is a 1 in 12 shot of getting either of these rolls this will be the highest payout of any of the bets since there is such a low chance of rolling these. The chances of rolling a 5 are 1 in 9, with possibilities of rolling 3-2, 2-3, 4-1 and 1-4. Those are the same odds as rolling a 9, with combinations of 6-3, 3-6, 5-4 and 4-5. The payout for these will be a lower percentage since there is a higher shot at rolling 5 or 9. The chances or rolling a 6 are 5 in 36, with possibillities of rolling 5-1, 1-5, 4-2, 2-4, and 3-3. There is the same chance of rolling a 8 with combinations of 6-2, 2-6, 5-3, 3-5 and 4-4.

The payout for these will be less still because there is nearly a 1 in 6 chance of winning, so the payout for rolling either of these is will be 1:5 And then there is a very high chance of rolling a 7, 1 in 6, with combinations of 4-3, 3-4, 5-2, 2-5, 6-1 and 1-6. Since there is a 1 in 6 chance of rolling 7 the payout will only be 1:4. Then there are bets that are not on single numbers, but about multiple rolls. There is a bet of rolling a double. There is a 1 in 6 chance of rolling a double, but we can't payout that high. So the payout for this will be 1:4. There are bets to roll even numbers 4 through 10 and odd numbers 5 through 9. These are a lot higher than any individual number to get, so the payout is higher. The probability of rolling either a 4, 6, 8 or 10 is 16 in 36, which is nearly one half. The payout for this will be 2:1. The chances of rolling a 5, 7 or 9 is 14 in 36 and there will be the same payout as the even number. We can convince our customers they are the same ratio because a 7 is the most common single rolls. The final two bets are odd and even 3 through 11. There is a 5/12 chance of each of these, so the payout will be 1:1.5, our lowest payout total.