Ok. We are doing a poor man’s version of the NCAA basketball square pool seen here:

1k March Madness squares

My buddy and I got to talking, and he wanted to know if there was a way to figure out an “optimal” number of squares to purchase based on odds and probabilities. After he brought it up, I kinda started to wonder the same thing.

There are 100 squares. There are 63 total games that payout on an increasing scale. Each square costs $20 and the payouts are as follows:

• 2nd Round – 32 games * $15/game = $480
• 3rd Round – 16 games * $25/game = $400
• Sweet Sixteen – 8 games * $40/game = $320
• Elite Eight – 4 games * $65/game = $260
• Final Four – 2 games * $125/game = $250
• Championship – 1 game * $250 = $250

For these small stakes, it will most likely boil down to what we are willing to spend, but thought the problem was fun anyways. Any advice on how to figure it out?

assuming that each square is picked randomly, and there's no vig, they are all 0 EV. there is no "optimal" number of squares. the only question is how much gamble you want.