Can negamax use an asymmetric scoring function?
TL; DR: I have an asymmetric scoring function to implement non-gamax - is this acceptable? Or do I need to make it symmetrical?
Longer: I'm writing an AI game (for the chess board game "Hive") that used a minimax with an alpha-beta clipping and an asymmetric scoring function.
But I was having trouble adding the transposition tables correctly and was losing confidence in my minimax implementation, so I decided to switch to negamax using the pseudocode here: https://en.wikipedia.org/wiki/Negamax#Negamax_with_alpha_beta_pruning_and_transposition_tables
I have everything that "works" and AFAIK following the pseudocode exactly, but my AI is now doing a few different moves than before and games that usually end after 10-15 turns now take 30+, and I am not I'm sure the AI is really playing better than before. I am concerned that having an asymmetric scoring function means I am clogging the nodes in a different way than before (due to the flip-flopping negation).
I don't want to change the symmetric function unless I really need to - I tried to experimentally create an optimal function (AI vs AI battles) and put hundreds, if not thousands of computational hours into production, a strong scoring function.
source to share
Negamax supports asymmetric scoring functions, but this does not lead to optimal play (unless you have knowledge of your opponent).
I don't know enough about Hive, but in computer chess, there is usually a bug for the asymmetric evaluation function. The reasons for this should be the same for chess and hive.
For example, take the starting position (chess). White is approaching, and suppose your scoring function gives a position with a result of +0.08.
Now change the position so that black has to move first. Everything is the same, the roles of white and black have just changed. Assuming that +0.08 was the optimal bar for White's position, why shouldn't Black's position also be rated as +0.08?
The same argument applies to any position. If you cancel everything, you have no good reason to play differently.
There is only one exception to this rule. If one opponent is clearly stronger than the other, there are arguments for an asymmetric assessment. For example, take a fully extended position like this:
FEN: 4k3/8/8/p1p1p1p1/PpPpPpPp/1P1P1P1P/8/4K3 b - - 0 1
This position can be evaluated as 0. Now create a starting position, but white will start without one knight. This should be a strong advantage for black.
Suppose you are Magnus Carlsen and you are playing against an opponent who does not even know the chess rules. Which position would you prefer? Here I would argue that an asymmetric scoring might make sense (for example, gauging a likely draw similar to a loss). Carlsen should avoid the drawn position, while the beginner should prefer it.
The chances that a rookie can hold their own against a world champion, even on the same knight's field, are practically nil. On the other hand, in a drawn position, the skill advantage is irrelevant, since no single move of steps can lead to victory or loss.
In computer chess, Rebel had a function that favored tactical positions when playing against humans (see ANTI GRANDMASTER PLAY ). There is also the general concept of "contempt", which is the rating the engines give for a remix.
But note that in both of my examples, this is not an optimal game. Magnus Carlsen did not choose a position without a knight, playing a strong (or unknown) opponent. Also, the rebels would not use an anti-human strategy against other machines that also succeed in tactical battles. (Despite the fact that depending on the position, the Rebel 10 used ANTI GRANDMASTER PLAY against computers .)
source to share