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        Arimaa >> General Discussion >> Game nearest to perfect play
        
(Message started by: BlakeD on Jul 1^st, 2014, 11:25pm)

Title: Game nearest to perfect play
Post by BlakeD on Jul 1^st, 2014, 11:25pm

I'm interested in opinions on which Arimaa game to date is nearest to perfect play. My definition of nearest to perfect play would be the game with the worst move that is better than the worst move of any other game. There could also be an argument for the game with highest percentage of perfect moves regardless of the worst moves, but since this is theoretical anyway I'm open to any definition.

I would suspect that one of the Mob games would be closest. I believe the game with the highest combined player rating is a 2010 postal game between chessandgo vs. Fritzlein (149900) so that would be a candidate. Any other nominations?

Title: Re: Game nearest to perfect play
Post by Fritzlein on Jul 2^nd, 2014, 1:26am

From the perspective of computer evaluation, you could say that the badness of a move is how many rabbits it is below the best move. For example, if the best move has an evaluation of +0.78 and the played move is +0.59, it is a mistake of magnitude 0.19.

Now, if you need to get down to an evaluation of, say, -10 for a lost game, without any big jumps downward, then your best bet is a long game, say 100 moves that each lose 0.1 in evaluation. A game between a very cautious and precise human and a passive bot would fit that bill. The human might not make any mistakes of significant magnitude, whereas the passive bot would be making only minor mistakes on every move.

But although this type of game seems closest to your definition of best worst move, it may not be what you had in mind for being close to perfection. A clearly losing strategy that loses very slowly could be considered inferior to a move that holds some promise of winning even though it loses quickly when it does lose.

An alternative definition of the badness of a move would be in terms of winning percentages. If the best move gives a 63% chance of winning, a move that gives only 59% chance of winning is a mistake of magnitude 4%. One could get from a starting position of 50-50 chances to the ending of 100-0 in 100 moves with the winner making no mistakes and the loser making mistakes of merely 0.5% on each move.

The very notion of "winning chances", however, is somehow at odds with the notion of perfect play. Let's say there is an endgame where I am lost and must allow goal in at most six, assuming my opponent plays optimally, and even to extend the game this long requires me to abandon any counter-attacking moves. To say it is closer to perfection for me to play a move allows goal in four with perfect play from my opponent but might confuse him with 25% probability into allowing me to win in five is to say that perfect play requires imperfect play, or at least the possibility thereof.

Instead of trying to find a mistake-free game, I think it would be more interesting to find a brilliant game, which I define as one in which all the "bad" moves by either side are difficult to refute, and require resourcefulness and ingenuity by the opponent to be punished. Thus it is OK for there to big mistakes in a brilliant game, just not mistakes where the refutation is obvious. Does that make any sense?

Title: Re: Game nearest to perfect play
Post by chessandgo on Jul 2^nd, 2014, 8:13am

It does, good stuff Fritz.

Title: Re: Game nearest to perfect play
Post by BlakeD on Jul 3^rd, 2014, 9:04pm

on 07/02/14 at 01:26:14, Fritzlein wrote:

But although this type of game seems closest to your definition of best worst move, it may not be what you had in mind for being close to perfection.

That is more or less what I had in mind. I tend to think that this type of game is inevitable in high level play as strategy matures.

on 07/02/14 at 01:26:14, Fritzlein wrote:

A clearly losing strategy that loses very slowly could be considered inferior to a move that holds some promise of winning even though it loses quickly when it does lose.

Granted, but in either case winning depends on an opponent's mistake. The question is whether the opponent is more likely to make a mistake from a short term complication or from fatigue from a long drawn out game. I think that depends on the opponent.

on 07/02/14 at 01:26:14, Fritzlein wrote:

Instead of trying to find a mistake-free game, I think it would be more interesting to find a brilliant game, which I define as one in which all the "bad" moves by either side are difficult to refute, and require resourcefulness and ingenuity by the opponent to be punished. Thus it is OK for there to big mistakes in a brilliant game, just not mistakes where the refutation is obvious. Does that make any sense?

I definitely agree that this would be more interesting, but it would be hard to identify games like this because in hindsight the mistake would probably seem obvious (even if it wasn't at the time).

The purpose of my initial question was to get some ideas of consensus gold standards for a winning strategies as shown on the board. Basically being able to beat the best games by players who ended up losing. Thinking about it now, perhaps I'm not giving end game tactics enough importance vs. a winning strategy.

I guess as an addendum to my original question, I would ask what game(s) has anyone played that they thought were their best in a losing effort?

Title: Re: Game nearest to perfect play
Post by chessandgo on Jul 15^th, 2014, 3:44pm

on 07/03/14 at 21:04:14, BlakeD wrote:

That is more or less what I had in mind. I tend to think that this type of game is inevitable in high level play as strategy matures.

This is quite the opposite of what we have witnessed in the evolution of arimaa, from long and passive to quick and aggressive.