[ykcirT]

I was recently playing some Hold ?em at a casino where they were offering a basketball pool to the seated poker players. I?m sure most of you are familiar with these, but this is how it works: In the first half of a college hoops game, each player is given a card with 2 numbers on it... one representing the home team?s score and one representing the visitor?s score. If, at the end of the first half, the last digit of the score of each team matches what you have on the card, you win (payoffs for both correct and reverse scores). In the second half, they give you another 2 tickets. One is just like the first half (forward and reverse wins) and the other has to be exactly correct. The first half card is also good in the second half. Payouts are as follows: Correct on the ?any way? card = $500, reverse on the ?any way? card = $250, and correct on the ?correct only? card = $300.

A young man sitting at our table starting spouting off statistics, and I just know he was wrong. He said you are a 5:1 dog against winning something in the game, and your EV per hour is $50. Here are my calculations? what do you think?

- First of all, assume that all two digit scores are equally probable of coming up (I think this is probably true in hoops, but definitely not in football)
- There are 100 possible unique combinations on your card
- In the first half, you have a 1/100 chance of winning $500 and a 1/100 chance of winning $250. That means your overall odds of winning something are 1/50, and your EV for the first half is $7.50 (1% x $500 = $5 and 1% x $250 = $2.50)
- In the second half, you now have 5 possible combinations of numbers, assuming you have no duplicate cards (2 each on the two ?any way? cards and 1 on the ?correct only? card).
- Thus, you have a 2/100 chance of winning $500, 2/100 of winning $250, and 1/100 of winning $300. So, your overall odds of winning something are 1/20. Your EV is $18 for that half.
- So, bringing everything together, your overall odds of winning something in the course of the game is 7/100, or 7% chance, or about 13:1 against. Your EV for the entire game is $25.50. Assuming that a game lasts 3 hours, your EV per hour is $8.50

So, how did I do? I am sure that this is not correct, so please correct me.

Thanks,
Rich