Talk:Pig the dice game/Player: Difference between revisions

Assuming this instability will exist: We can dampen that instability by adding randomness to our choices: we can start with the "best deterministic strategy" determined above, and grant our opponent complete knowledge that we will use that strategy and give them the right to make one choice differently (at any game state) based on that knowledge, and let the opponent iterate until they find a new best strategy. Then we set up a new strategy where we pick (with even odds) from either our first strategy or this new strategy that our opponent would have picked, and let our opponent pick a new best strategy again, iterating... Here, we converge not to a single deterministic Roll/Hold choice for each game state but to a distribution function for each game state (or odds of picking "Roll" for example, in each game state).