This is a simple 2 player game on which each player has an individual "pool" of finite money or points, and every round they must decide how many points they want to risk for a chance to get a directly proportional reward. I've been trying to solve this problem for a while, but I still know very little about game theory and I can't seem to even find the proper place to start. I'd be thankful if anyone could help me.
The Game:
Two players, A and B, start the game with \$500 each.
In every round, a single, 6 faced die is tossed. Both players have to gamble an integer value from \$1 to \$99 (inclusive). If the die shows the number one, both players get their respective bets back and earn 5x the amount they gambled. All earnings are added to the amount available for gambling.
If the die rolls any other number, both players lose the amount they gambled.
The amount of money remaining for each player is revealed to their opponent at the end of every round.
The game ends when one of the players has no money left, or after 1000 rounds. The winner is the player with the most money.
Example:
- Round 1 begins
- Player A bets \$1, Player B bets \$2
- Die rolls a 5
- Player A now has \$499, Player B now has \$498
- Round 1 ends
- Round 2 begins
- Player A bets \$1, Player B bets \$2
- Die rolls a 1
- Player A gets his \$1 back, plus another \$5. He now has \$504. Player B gets her \$2 back, plus another \$10. She now has \$508.
- Round 2 ends
What is the best strategy the players can play to win the game?
Any help is appreciated.