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You have created 2 scenarios with very small actions spaces. Most games have enormous action spaces, so you can't easily compute a probability. Take Chess for

You have created 2 scenarios with very small actions spaces. Most games have enormous action spaces, so you can't easily compute a probability. Take Chess for example. Chess engines evaluate millions of scenarios for every move. They don't generate a "win probability" value though, they evaluate board positions.

anonymoushn 6y ago
> Most games have enormous action spaces, so you can't easily compute a probability. Saying you can't compute something by hand on a single sheet of paper is different from saying it doesn't exist. In Chess, your win probability is either 0 or 1 (you either can force a win or you cannot), but most chess engines have a real-valued estimate of their equity in the game that is between 0 and 1.
- ZephyrBlu 6y ago
  > but most chess engines have a real-valued estimate of their equity in the game that is between 0 and 1 My understanding is that Chess engines do not evaluate a 0-1 value to representing chance to win. They evaluate the perceived material advantage from the current board position. See: https://www.chess.com/blog/ChessMN16/how-to-read-engine-evaluations https://www.chess.com/blog/ChessMN16/how-to-read-engine-eval...
  - deleted 6y ago
    [deleted]
  - TylerLives 6y ago
    Why do you think it's unreasonable to interpret the value function as probability? I think chess engines don't do it because of draws, but you could look at a chess position and estimate what are your chances of winning/drawing/losing.
    - ZephyrBlu 6y ago
      If the probability of winning was static I would agree that the evaluation function is (Or can be) a prediction of win probability. However, because the probability of winning is clearly dynamic over time, trying to predict that probability is inherently a future prediction of the outcome (I.e. a forecast) rather than the prediction of a value. In that case, it does not make sense to view the evaluation function as probability because a forecast is not the same thing as a probability. I'm looking at this from the perspective of the game. From the perspective of any given state in isolation I agree that it makes perfect sense, but in the context of a game it doesn't. This is why I think that plotting all these values on a chart together and calling it "win probability" is non-sensical. It does give you an idea of the game state, but it's not a probability.

anonymoushn 6y ago

> Most games have enormous action spaces, so you can't easily compute a probability. Saying you can't compute something by hand on a single sheet of paper is different from saying it doesn't exist. In Chess, your win probability is either 0 or 1 (you either can force a win or you cannot), but most chess engines have a real-valued estimate of their equity in the game that is between 0 and 1.

ZephyrBlu 6y ago
> but most chess engines have a real-valued estimate of their equity in the game that is between 0 and 1 My understanding is that Chess engines do not evaluate a 0-1 value to representing chance to win. They evaluate the perceived material advantage from the current board position. See: https://www.chess.com/blog/ChessMN16/how-to-read-engine-evaluations https://www.chess.com/blog/ChessMN16/how-to-read-engine-eval...
- deleted 6y ago
  [deleted]
- TylerLives 6y ago
  Why do you think it's unreasonable to interpret the value function as probability? I think chess engines don't do it because of draws, but you could look at a chess position and estimate what are your chances of winning/drawing/losing.
  - ZephyrBlu 6y ago
    If the probability of winning was static I would agree that the evaluation function is (Or can be) a prediction of win probability. However, because the probability of winning is clearly dynamic over time, trying to predict that probability is inherently a future prediction of the outcome (I.e. a forecast) rather than the prediction of a value. In that case, it does not make sense to view the evaluation function as probability because a forecast is not the same thing as a probability. I'm looking at this from the perspective of the game. From the perspective of any given state in isolation I agree that it makes perfect sense, but in the context of a game it doesn't. This is why I think that plotting all these values on a chart together and calling it "win probability" is non-sensical. It does give you an idea of the game state, but it's not a probability.