Finite Go variant: Loose

[MarkSteere]

I took the line "Redstone makes use of the pie rule" out of the rule sheet.

Oops, komi can't be used in Redstone because there's no score. Doh!

[Putting pie rule back in rule sheet.]

[luigi]

So how does it decide when to count? When both players happen to pass in succession?

That's right. It's completely random, even at that.

[luigi]

Also, this comparison isn't between weak Go players and strong players, it's between random play and perfect play, which is a _huge_ difference.

Even at 30k, learning that a single stone atari'd on the second line is dead comes almost immediately. By 20 minutes of playing, even a rank beginner will have a strategy and a plan, and be aware of enough things that the play is a long way from random. If for these players 0.5 komi is correct, that becomes really interesting in how komi scales with strength, but I suspect even by 20k the komi should be much closer to 6.5 than 0.5 - that's only my intuition speaking, I don't have data, and anecdotally I know most DDK players I've spoken to about komi consider it almost completely irrelevant to the game result.

I'm not sure how much useful information can be taken from random playout stats.

The only thing that is proved by my random games is that the balanced komi varies with skill. If the balanced komi is 0.5 for some players and 6.5 for some others, there must be a skill level for which the balanced komi is 1, 1.5, 2, 2.5, etc. However, it probably grows very quickly as soon as one leaves random play, and starts to grow very slowly very early in the skill progression, so I agree with you that for any two real players it will always be closer to 6.5 than 0.5.

My intuition is that balanced komi is a function of the logarithm of the player's skill. Maybe something like this:

[jts]

What you may be missing, luigi, is that a skilled player can play conservatively to protect his komi advantage. You can say that each of those skills (skill at using the first stone, skill at conservative play) would grow as a logarithm; since you've made it a monotonic function, that will be an arbitrary consequence of how you scale "skill level". But that doesn't mean that the correct komi grows as a logarithm.

[luigi]

What you may be missing, luigi, is that a skilled player can play conservatively to protect his komi advantage. You can say that each of those skills (skill at using the first stone, skill at conservative play) would grow as a logarithm; since you've made it a monotonic function, that will be an arbitrary consequence of how you scale "skill level". But that doesn't mean that the correct komi grows as a logarithm.

I'm not sure I understand what you're trying to say. Do you mean balanced komi grows even quicker with skill than a logarithmic function because of that? Could you elaborate on that?

[jts]

Say (regardless of whether there is komi or not) W's strategy is not necessarily to win, but to make sure that the gap in territory on the board is smaller than some value, X. You would probably conclude that random players would be incapable of implementing this strategy, beginners would be quite bad (they can't even count the score), and stronger players would be better and better at it. (We'll ignore for a moment that a stronger B player might be getting better and upsetting this strategy.)

Say (regardless of whether there is komi or not) B's strategy is to get the largest point advantage possible from his first move advantage. We'll assume, like you say, that better players get uniformly better at this (and ignore that stronger W players might slow them down).

The first consideration suggests that, all else equal, the correct komi should get smaller and smaller as players get stronger, since W gets better and better at keeping B's lead smaller than X. The second consideration suggests that, all else equal, the correct komi should get bigger and bigger, since B gets better at seizing the flow of the game. But clearly all else is not equal. In order to know which consideration dominates, we need to know the rates at which each skill grows, which we're unlikely to determine.

However, we do know that black wins 50.4% of professional games and 52.6% of games on KGS (at least, according to http://www.lifein19x19.com/forum/viewto ... =10&t=4743 ) -- which suggests that komi should, if anything, be larger for amateurs than for professionals.

[luigi]

Say (regardless of whether there is komi or not) W's strategy is not necessarily to win, but to make sure that the gap in territory on the board is smaller than some value, X. You would probably conclude that random players would be incapable of implementing this strategy, beginners would be quite bad (they can't even count the score), and stronger players would be better and better at it. (We'll ignore for a moment that a stronger B player might be getting better and upsetting this strategy.)

Say (regardless of whether there is komi or not) B's strategy is to get the largest point advantage possible from his first move advantage. We'll assume, like you say, that better players get uniformly better at this (and ignore that stronger W players might slow them down).

The first consideration suggests that, all else equal, the correct komi should get smaller and smaller as players get stronger, since W gets better and better at keeping B's lead smaller than X. The second consideration suggests that, all else equal, the correct komi should get bigger and bigger, since B gets better at seizing the flow of the game. But clearly all else is not equal. In order to know which consideration dominates, we need to know the rates at which each skill grows, which we're unlikely to determine.

However, we do know that black wins 50.4% of professional games and 52.6% of games on KGS (at least, according to http://www.lifein19x19.com/forum/viewto ... =10&t=4743 ) -- which suggests that komi should, if anything, be larger for amateurs than for professionals.

Nicely explained. So, after all, the apropriate komi seems to be different for different players.

[Bill Spight]

Komi for no pass go.

You can implement komi by giving White some number of passes. (See Mathematical Go by Wolfe and Berlekamp.) You can even implement a half point komi. For instance, say that komi is 2.5. White gets 3 passes. Black gets 1 pass, but only if she passes first.

[speedchase]

I think that Half point komi is just so white wins ties. since no pass go can't have ties anyway I see no point in adding a more complicated rule

[luigi]

I think that Half point komi is just so white wins ties. since no pass go can't have ties anyway I see no point in adding a more complicated rule

The implication of half point komi in No Pass Go is that, if White wants to make use of all his passes, he must pass before Black does. Therefore, his extra pass is not worth as much as a normal pass, and in fact its value converges to half a pass. Since the balanced komi is very low in No Pass Go, it seems convenient to double its granularity with this rule.

[Bill Spight]

I've often heard the claim that fair komi (here used in the sense of giving both players equal chances) depends on the playing strength of the players, but I've never seen anyone provide even a shred of evidence for this assertion. Your example doesn't work, because a 25 komi game on 5x5 has only two possible outcomes: it's either a tie, or white wins. Black can never win. Under those conditions, any non-perfect black player is at a disadvantage with 25 komi.

Well, it's not go, but here is a game where komi depends upon the skill of the players. Let's call the game Grab Coupon. There are a number of coupons, each worth some value to the player who grabs it. The players take turns grabbing a coupon, until there are none left to grab. The player with the larger score wins. Suppose that there are 20 coupons, with integer values of 1, 2, ... , 20. With perfect play by both sides, the correct komi is 10. With random play, the correct komi is 0.

[Bill Spight]

On komi vs. the pie rule

In Grab Coupon with coupons worth 1 and 2, proper komi is 1. Using the pie rule it is a second player win.

Edit: In fact, with coupons worth 1, 2, ..., M, it seems that the pie rule works only when M = 4*N or M = 4*N - 1, but not when M = 4*N + 1 or M = 4*N + 2.

For instance, when M = 5, if the first player takes the coupon worth 3, the second player can take the coupon. Then the first player gets 5 - 4 + 2 - 1, for 2 points, and loses. If the first player takes the coupon worth 2, the second player continues and gets 5 - 4 + 3 - 1 = 3 points, and wins.

But when M = 4, the first player can take the coupon worth 2, for a tie.

[lightvector]

luigi: I'm guessing that the random players in your experiment may fill their own eyes, even to the point of killing their own group and letting the opponent capture?

If that's the case, then if you wouldn't mind, could you make a quick tweak to your script to see what happens for players who play randomly except that they don't fill their own single point eyes? Specifically, ban a move from being chosen by a player if all adjacent points are already stones of that player's color and none of them are in atari. (This will occasionally ban a move that's worth something, but it should be close enough). With these slightly smarter players, who will actually play until their territory is secure and no further, you should also be able to remove "pass" as a possible random move, and instead pass only when every legal move is eye-filling.

It would be interesting to see if komi 0.5 is still ideal, or if a value like 1 or 1.5 is better.

[luigi]

luigi: I'm guessing that the random players in your experiment may fill their own eyes, even to the point of killing their own group and letting the opponent capture?

Yes, that's right.

If that's the case, then if you wouldn't mind, could you make a quick tweak to your script to see what happens for players who play randomly except that they don't fill their own single point eyes? Specifically, ban a move from being chosen by a player if all adjacent points are already stones of that player's color and none of them are in atari. (This will occasionally ban a move that's worth something, but it should be close enough). With these slightly smarter players, who will actually play until their territory is secure and no further, you should also be able to remove "pass" as a possible random move, and instead pass only when every legal move is eye-filling.

It would be interesting to see if komi 0.5 is still ideal, or if a value like 1 or 1.5 is better.

Yes, that had occurred to me. The ideal komi would be somewhat higher that way, indeed. I'll try to do it.

To avoid occasionally banning useful moves, I think I'll make it just a little closer to random play by allowing eye filling whenever the surrounding stones aren't part of the same group yet. This will cause the death of living groups every now and then, but occasionally allowing bad moves seems somehow more apropriate than occasionally banning good moves, since random play is far closer to the former anyway. What do you think?

[luigi]

There was a small mistake in the last move of the sample game I included in my original post. I've replaced it with a fixed version.