Talk:Handicap

Any suggestions for how handicap play can be implemented are welcome. We need more discussion on this wiki. :)

what about moving some stuff about the winning ways on non symmetrical boards to theory page ? Halladba 21:08, 3 February 2008 (CET)

OK, discussing you will get :-) Regarding fixed starting moves instead of swap as a handicap option, it would be lovely to get some empirical data. For instance, in a game where I place (and get to keep) the first piece at A1, just how much more do I lose than in a game I got to keep B2 instead? Vintermann 12:47, 5 February 2008 (CET)

As a general rule of thumb, c3 and the 2-2 obtuse corner (shown below) give Red approximately a 0.25 move advantage, at least for board sizes 13×13 to 19×19. Is there any evidence to support this? It seems to me to be at most an educated guess. For example, KataHex assigns these openings a winning probability above 94% for 13x13 (which may not translate into an actual probability). 20:43, 30 March 2023 (UTC)

I think the win probability converted to an Elo advantage (or equivalently, log odds) is more useful than win probability itself for measuring the "strength of a stone." Empirically, if you set up various board positions with 2 (1 Red / 1 Blue) or 3 (2 Red / 1 Blue) stones and ask KataHex for its win percentage, it pretty closely approximates the answer you'd get if you simply used Elo to linearly interpolate what "fraction of a full stone" each stone was. (If you're not convinced this is true, I can try to elaborate on why I think so). If you believe that premise, we can make inferences from bot swap maps (which I believe are more reliable than human game statistics, which are subject to tricky biases, like the players being unevenly matched, and the weaker player being more likely to play a questionable opening like c3).

• leela_bot: Looking at leela_bot's swap map, the worst move i1 has a 100%-85.6%=14.4% win rate, which is -310 Elo using the logistic Elo formula. The move a1 is -206 Elo; c3 is +198; b12 is +180. I think we have to make inferences here (which you may not agree with) for what win rate a "pass" move would be. I think -400 is quite appropriate, since it implies a full stone is 800 Elo, and a1 is worth about twice as much as i1. If so, this would imply c3 and b12 are worth about 3/4 of a stone, hence giving Red a 0.25 move advantage. If you think a pass move is -450 or -350 Elo, that implies c3 is worth 72% or 78% of a stone respectively, still close to 3/4.

• We don't have to guess as much with KataHex. It's hard on 13×13 because the probabilities are so close to 100%, leading to huge error bars in Elo terms. But if we consider 15×15, the strongest move is about 97.2% (+616 Elo), so a full move is +1232 Elo. Then c3 is +301 Elo, or 74% of the way between -616 and +616. Similarly for 19×19. Hexanna (talk) 00:08, 31 March 2023 (UTC)