How to Bet on Anything (If you want to win)

Introduction

You’re in Las Vegas for a business convention when you’re approached by a funny-looking guy on the street.

It’s me, and I’m holding an ordinary, 6-sided die. I propose a game, as follows:

You roll the die, and either:

1. Receive the amount shown on the die in dollars, or
2. Roll the die again, and forfeit this roll

You can roll the die at most 3 times, and you only get to keep your last roll. If you re-roll, you…