This is a project to visualize the optimal strategy to play a betting game with a 20-sided die. The game consists of 100 turns, and every turn the player has two options: to roll the die or to take the money from the casino. The goal is to maximize the player's profit in each game session. Visit the linke below for the entire problem statement.
- Video Statement: From Jane Street via YouTube (https://www.youtube.com/watch?v=NT_I1MjckaU)
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Scenario 1: Take money or roll the dice, if you take money the dice stays fixed (you can keep the number on the table between rolls).
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Scenario 2: Take money or roll the dice, if you take money the dice disappears and must be re-rolled next turn.
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Scenario 3: (Variant of Scenario 1). If you take the $, the casino can choose to reroll the die. The casino aims to minimize your earnings.
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Gradient Descent to find the optimal player threshold for a given casino threshold.
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Future Game Theory Exploration
- Studying the game from an interaction level
- Analyzing the optimal punishment/reward strategies for each player to maximize their average gains over multiple runs
- Finding Nash and Stackelberg equilibria regarding the strategic decisions each level of player can make