Introduction to Probability with Texas Hold’em Example #4

Question

Suppose in a tournament with only three players left, first place receives $6,000, second place receives $3,000, and third place receives $500. You have a 32% chance of winning first place, 30% chance of winning second place, and 38% chance of winning third place.

a. What would be your expected winnings in this tournament?

b. The tournament organizer gives you the option to continue playing or stop and split the total prize money, proportional to your current standings. If you currently have 700 of the 1800 chips currently in play, how much would you win if you stopped playing and split the winnings?

c. Based on parts a and b, should you continue playing or stop and split the money? Why?

Answer 1

This question seems more appropriate for math.se, but nevertheless, I will answer the question here.

Expected value can be calculated by taking the sum of the products of each payout and probability for each place. So we can sum 32% of $6,000, 30% of $3,000, and 38% of $500, which yields $3,010.

The split would give you 700/1800 or roughly 38.89% of the sum of the payouts ($6500), which comes to $2527.78.

Obviously, you would want to take the higher amount. But from a poker standpoint, holding 700 out of the 1800 chips in play means you are second in chips at the very worst. If one more player busts, you would instantly be guaranteed $3,000.