The general idea makes sense to me, I’m a bit confused about the chess example though:
But there’s a very important rule to follow when calculating. Always end your calculations after your opponent has moved. You must never end your calculations after your own move.
Say you’re able to calculate things either to depth 2 (ending after your opponent’s move) or to depth 3 (ending after your own move). Isn’t it still better to calculate things as far out as you can?
Not at all. You may be able to see a positional advantage or capture of a minor piece in your move, and not see that they can respond by capturing your queen. The most apparently valuable moves after your own move are very often close to the worst after theirs, because they are often made with the most powerful pieces and expose them to risk.
I learned that lesson quite well when writing my own poor attempt at a chess playing program years ago. Odd ply searches are generally worse than even ones for this reason.
What’s going on is something like adverse selection in an auction. In reality, chess is a solvable game, so that in perfect play win/loss/draw probabilities are all 0 or 1 for every board state. However, you don’t know what these probabilities are, so you use a model. A naive player might just want to play the action which takes them to the board state they model as having the highest probability of winning. However, this fails to take into account the fact that one’s model can be wrong, and so one will tend to pick actions which lead to board states which one mispredicts as being better than they actually are.
If one can accurately model how inaccurate one’s model tends to be at certain board states, then one can do fine without ending on one’s opponent’s move by discounting board states one models as modelling poorly. This is nontrivial for humans to do correctly, however.
Instead, a heuristic one can use is to just let one’s opponent make the last move in one’s search tree. This gives one a lower bound on how good each board state is (an optimistic guess for one’s opponent is a pessimistic guess for one’s self), so one’s choices of board states will not be catastrophically biased. By catastrophically biased, I mean that in chess it’s much easier to wreck your game than to make a stunningly clever move which causes you to win, so that being too optimistic is much worse than being too pessimistic.
The general idea makes sense to me, I’m a bit confused about the chess example though:
Say you’re able to calculate things either to depth 2 (ending after your opponent’s move) or to depth 3 (ending after your own move). Isn’t it still better to calculate things as far out as you can?
Not at all. You may be able to see a positional advantage or capture of a minor piece in your move, and not see that they can respond by capturing your queen. The most apparently valuable moves after your own move are very often close to the worst after theirs, because they are often made with the most powerful pieces and expose them to risk.
I learned that lesson quite well when writing my own poor attempt at a chess playing program years ago. Odd ply searches are generally worse than even ones for this reason.
What’s going on is something like adverse selection in an auction. In reality, chess is a solvable game, so that in perfect play win/loss/draw probabilities are all 0 or 1 for every board state. However, you don’t know what these probabilities are, so you use a model. A naive player might just want to play the action which takes them to the board state they model as having the highest probability of winning. However, this fails to take into account the fact that one’s model can be wrong, and so one will tend to pick actions which lead to board states which one mispredicts as being better than they actually are.
If one can accurately model how inaccurate one’s model tends to be at certain board states, then one can do fine without ending on one’s opponent’s move by discounting board states one models as modelling poorly. This is nontrivial for humans to do correctly, however.
Instead, a heuristic one can use is to just let one’s opponent make the last move in one’s search tree. This gives one a lower bound on how good each board state is (an optimistic guess for one’s opponent is a pessimistic guess for one’s self), so one’s choices of board states will not be catastrophically biased. By catastrophically biased, I mean that in chess it’s much easier to wreck your game than to make a stunningly clever move which causes you to win, so that being too optimistic is much worse than being too pessimistic.