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Arimaa >> General Discussion >> Harlog vs Winning probability
(Message started by: lightvector on Oct 2nd, 2014, 8:48pm)

Title: Harlog vs Winning probability
Post by lightvector on Oct 2nd, 2014, 8:48pm
Just for fun, I took all rated games from 2008-01 to 2014-06 where both players had a gameroom rating of 2000 or better and looked at the probability that a player won the game conditioned on the material score at that point according to HarLog.

Specifically, for every position in every game that had a winner, I computed the HarLog score in millirabbits from the perspective of the current player (prior to that player's move), and then counted a 1 ifthat player won that game and a 0 otherwise. I made no attempt to adjust for any biases, such as the bias here towards longer games, or identify any causality, such as material loss being a symptom of a crumbling position as opposed to the cause of it.

Here are the results, bucketed every 500 millirabbits:

Code:
Lower Upper Mid Wins Total Prob
-1000000 -9751 -10000 1342 50039 0.0268191
-9750 -9251 -9500 284 4852 0.0585326
-9250 -8751 -9000 237 4547 0.0521223
-8750 -8251 -8500 572 6079 0.0940944
-8250 -7751 -8000 383 6122 0.0625613
-7750 -7251 -7500 617 6888 0.0895761
-7250 -6751 -7000 1037 8342 0.124311
-6750 -6251 -6500 1021 8123 0.125692
-6250 -5751 -6000 1519 11196 0.135673
-5750 -5251 -5500 1629 8443 0.192941
-5250 -4751 -5000 2402 13050 0.184061
-4750 -4251 -4500 2709 13254 0.204391
-4250 -3751 -4000 2513 11947 0.210346
-3750 -3251 -3500 5942 24142 0.246127
-3250 -2751 -3000 4125 15987 0.258022
-2750 -2251 -2500 6397 21642 0.295583
-2250 -1751 -2000 11447 36385 0.314608
-1750 -1251 -1500 11486 30064 0.382052
-1250 -751 -1000 26814 64343 0.416735
-750 -251 -500 10052 21560 0.466234
-250 250 0 220567 438537 0.502961
251 750 500 11936 21368 0.558592
751 1250 1000 37191 61753 0.602254
1251 1750 1500 18191 28391 0.640731
1751 2250 2000 24327 34279 0.709676
2251 2750 2500 14888 20482 0.726882
2751 3250 3000 11703 15236 0.768115
3251 3750 3500 17036 21807 0.781217
3751 4250 4000 9210 11277 0.816707
4251 4750 4500 10101 12405 0.814268
4751 5250 5000 10203 12111 0.842457
5251 5750 5500 6554 7898 0.82983
5751 6250 6000 9158 10345 0.885259
6251 6750 6500 6534 7178 0.910281
6751 7250 7000 7023 7900 0.888987
7251 7750 7500 5939 6422 0.92479
7751 8250 8000 5424 5718 0.948583
8251 8750 8500 5335 5838 0.91384
8751 9250 9000 4078 4255 0.958402
9251 9750 9500 4402 4635 0.94973
9751 1000000 10000 47770 48896 0.976972



Title: Re: Harlog vs Winning probability
Post by Fritzlein on Oct 4th, 2014, 1:01pm
Does that make Harlog more or less predictive than FAME?  One way to compare them would be to find the best-fit conversion of material into winning probability for each (perhaps linear, perhaps logistic?), and see which has the lesser prediction error.



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