Games, decision theory and puzzles
Optimal stopping
Prices any game with an option to keep playing, from a die re-roll to an American option.
Where
- Value of continuing optimally — and therefore the accept threshold.
Assumptions
- With finitely many rounds, work backwards from the last.
- With infinitely many, the equation is self-referential — and you must check that the policy it assumed matches the answer.
Sanity check. The threshold is the continuation value, never the mean of the distribution.
Where this is taught
- Pricing a game: EV, re-rolls and when to stop · GAME · Expected-value games
- Dynamic programming, and why it is the same as an EV recursion · CS · Dynamic programming