I am attempting to determine two variables in this game:
- The optimum strategy: (What number the bettor should stay at)
- The expected value given perfect play: (The percent return on a bet when using the optimum strategy)
Here is how the game works: There are two players. One is the "dealer" and the other is the bettor. A bet is placed, and the "dealer" rolls a 100-sided die, having the numbers 1-100. The bettor wants to get close to or at 100, without going over. If they go over 100, they "bust" and lose the game. The first roll(s) are for the bettor, and they have the option to hit or stay until they either bust or choose to stay. Each time a player hits, the numbers are added together. After the bettor stays, the dealer rolls until they beat the bettor's score, draw, or bust. In the case of a draw, the bettor will have their money returned to them.
Example game: The dealer rolls for the bettor and the 100-sided die shows a 60. The bettor decides to stay. Now, the dealer rolls for them self and the 100-sided die shows a 3. The dealer hits, rolling an 8. The dealer adds these numbers, and is at 11. The dealer rolls again and the die shows a 50. The dealer adds 50 and 11, making 61. The dealer has beat the bettor without going over 100, winning the game.
Additional info: I have tried my best to determine the optimum strategy and return on investment for this game, but the math is too complex for me. There are too many variables involved and when multiple rolls come into play it becomes overwhelming to fully understand. I only have basic knowledge of statistics and probability. Help is greatly appreciated.