gaius wrote:Also, whether it's by 50.5 points or 0.5 points, a win is a win. Therefore, questions like "could a 10.5 pt loss be reduced to a 0.5 pt loss" or "could the 10.5 point win be stretched to a 15.5 point win" are irrelevant to strong endgame play. What matters is taking home the win; counting the value of moves is merely an imperfect tool to help the imperfect human brain work towards that goal.
I disagree.
If you assume perfect play by your opponent, then yes, it's irrelevant. But in practice, if I'm 10.5 pt behind and I see a chance to reduce it to a 0.5 pt loss, it may still be a better strategy to try that. Let me elaborate:
Let's say on the board I'm behind, with a few good endgame points left. Now I have two strategies:
a) Play a solid endgame and reduce it to 0.5 pts behind with a high probability. I'm good at endgame, so let's say 90%. I'm not playing risky, in the worst case I'll lose by 5 pts.
b) Play a risky endgame (overplay) and make it a 5 pt win. It's risky, let's say the probability to pull it off is 30%, but if it fails it will be a 30 pt loss.
Current MC bots use strategy b). It would just see that a) has a very low probability to win, and b) has a 30% probability to win.
But I argue that there is another factor, namely the probability of a mistake by the opponent:
Let's say the probability that the opponent makes another 1 pt mistake is 40%, for a 5 pt mistake it's 5% and a 30 pt mistake just won't happen.
Suddenly strategy a) looks a lot more appealing: In 90% of the cases, I just need a 1 pt mistake from the opponent (40% chance), at worst case (10%) I need a 5 pt mistake (still 5%). This still gives a total win probability of 36.5%, assuming a just small mistake by the opponent.
Strategy b) has just 30% chance, and it's also assuming a mistake by the opponent (namely falling for the overplay).
Of course all these numbers are just made up on the spot to demonstrate a point.
Sure, you could argue that my strategy is not theoretically best play but exploiting mistakes by the other player. Against a hypothetical "perfect opponent", my strategy would be worse. That's true, but that argument is flawed: The assumption of mistakes by the opponent is already there in the MC method itself by assuming a win probability instead of a fixed final score.