Finite Go variant: Loose

[HermanHiddema]

The problem with the pie rule in go, IMO, is that there are no viable first moves. Any move on the second line or higher favors black significantly, any move on the first line favors white significantly. Ergo, you cannot compensate for the first move advantage in go with the pie rule, because there is no suitable move to do so. Now you could probably find some balanced position after 3, 4 or 5 moves, but why bother when there is already a perfectly fair and extremely elegant solution in the form of komi?

Even 2-7 or 2-10? There's a thread elsewhere on this topic, btw.

Yes. I would take black in a no komi game with 2-7 or 2-10, or any other 2nd line move as the opening move. Of course, I can offer no proof for this assertion, only that it is how I feel about it at my current playing strength.

[luigi]

Don't buckle under on the pie/komi issue. Komi is an aesthetic Hiroshima.

Pie Go is simply uncharted territory. Not bad, bugged or odd territory. The first move doesn't have to be awful - just bad enough that you don't care if you get pied.

Mark, I think Herman is right: komi is much more precise than the pie rule. Also, since the winner is already decided on points, isn't it natural enough to make it balanced by giving the second player some extra points? I think this is about as elegant or inelegant as the pie rule.

[HermanHiddema]

You're actually proving me right. You're saying that 25 komi in 5x5 Go is only fair for perfect players, and that everyone else should use a lower komi. Ergo, fair komi (or, more precisely, "balanced komi") depends on the playing strength of the players.

(It shouldn't be that hard to be a perfect 5x5 Go player, by the way.)

Although perfect play for 5x5 is known (solved by Erik van der Werf some time ago), there are no human players that can play it. The tree is just too large. Strong players will, no doubt, have no trouble winning by 25 points, bu their play is not perfect.

[illluck]

Using 5x5 to show that komi should be different for different strength players is a bit strange. Komi acts as a balancing tool and doesn't quite work when a game is solved.

I would believe the claim that komi should differ for different strength if you can provide data to support it. http://www.online-go.com/forums/thread. ... eadID=1296 has some data to 2007, and a preliminary inspection suggests that 6.5 isn't very far from even (about 49% winrate for black). Of course, even games between unequal players with randomly assigned colours will drift the winrate towards 50%, so the statistics aren't completely solid.

[luigi]

Although perfect play for 5x5 is known (solved by Erik van der Werf some time ago), there are no human players that can play it. The tree is just too large. Strong players will, no doubt, have no trouble winning by 25 points, bu their play is not perfect.

If a player has no trouble winning always by 25 points as Black, then he is displaying perfect play. Every line of play with a forced 25 points win is perfect play.

[luigi]

Using 5x5 to show that komi should be different for different strength players is a bit strange. Komi acts as a balancing tool and doesn't quite work when a game is solved.

illluck, it doesn't matter if it's solved or not. A 25 komi for 5x5 Go would be balanced for all dan players, regardless of whether they know the solution or not. They would draw every time, whereas if two complete newbies play 5x5 Go, it's obvious that a 25 komi won't balance the game.

[topazg]

illluck, it doesn't matter if it's solved or not. A 25 komi for 5x5 Go would be balanced for all dan players, regardless of whether they know the solution or not. They would draw every time, whereas if two complete newbies play 5x5 Go, it's obvious that a 25 komi won't balance the game.

I disagree. A game being balanced doesn't mean a draw every time. A game being balanced means both players should draw with perfect play. 25 komi balances the game even for beginners, it's just unlikely that games would finish in a draw. If I play a 3 stone handicap game against a 10k, the game is balanced against me, but I'll still win every time. Balancing in the sense of komi just means that neither player should have an advantage at the beginning, not that the outcome is a foregone conclusion.

FWIW generally, I don't think komi is an unpleasant hack, and I think it has pros and cons just as the pie rule does. Komi isn't an option in a lot of games, such as hex, chess, shogi etc, because the result isn't decided on a score basis - there is no score. Komi only makes sense in score based games.

Mark, I'd really recommend hitting about 10k or so before feeling that the pie rule wouldn't have a fundamental change to the nature of a Go game that may make it less elegant to play. Sure, I have no doubt it could be a balanced game with the pie rule, but the opening would feel very different to play. I wouldn't be keen on that, and that's primarily down to a subjective dislike having gained a reasonable understanding for aiming for optimal moves from the outset. Fiddling my opening to make the most of a single suboptimal stone would feel rather more of a hack to balance the game than a score modification a la komi. I could equally see players advocating the pie rule, particularly those who haven't already been accustomed to Go, it's just not my cup of tea and I don't see anything fundamentally wrong or flawed about using komi (at least, nothing clearly more flawed than other solutions such as the pie rule).

[HermanHiddema]

The 5x5 example does not generalize, because with the correct komi, black cannot win. As such, it has no implications for larger sizes.

Lets talk about 5x6 go instead. With perfect play, it is a 4 point win for black. Can you show that a 4 point komi is wrong for weaker players?

[MarkSteere]

Mark, I'd really recommend hitting about 10k or so before feeling that the pie rule wouldn't have a fundamental change to the nature of a Go game that may make it less elegant to play.

The pie rule is inelegant. A poorly placed first stone is inelegant. Does pie make Go less elegant to play, overall? No. I don't need to play Go 500 times to realize that. Go isn't fragile. It wouldn't have survived the millennia if it were overly sensitive to the opening move. The innocuous pie rule won't harm Go in a general sense. An ugly, though more balanced, first move should actually improve the gameplay overall. Go is every bit as much of a contest with the pie rule as without.

The question is, "Is the pie rule less elegant than komi?" No, it isn't.

1. Komi makes Go an unequal goals game, first off. Black has to totally whomp White, beyond the komi offset, and White has to make that not happen. White has no chance of winning outright. All by itself that makes komi an aesthetic Hiroshima.

2. Komi is variable. The higher the level of play, the closer the final score. Choosing the right komi value is essential to fair play. What if the komi value isn't obvious? How many times have you lost and said, "If only the komi was set right…."?

No rule is uglier than superko, not even komi. But komi holds a distant second place.

[hyperpape]

1. Komi makes Go an unequal goals game, first off. Black has to totally whomp White, beyond the komi offset, and White has to make that not happen. White has no chance of winning outright.

Prior to komi, the game was played using alternation of who went first. White often won. Today, White often wins by more than the value of komi.

Komi is variable. The higher the level of play, the closer the final score. Choosing the right komi value is essential to fair play. What if the komi value isn't obvious? How many times have you lost and said, "If only the komi was set right…."?

Think about this statistically. The variance of the margin of victory may be higher without the advantage for Black being any different. As Herman asks: can anyone actually demonstrate that komi should be higher for weaker players? It's true that there are more games decided by lopsided scores at lower levels, but that includes more games where white wins by 30 points as well. Do they balance out? It's an empirical question, and not one that I'm sure we've properly answered.

No rule is uglier than superko, not even komi. But komi holds a distant second place.

Yeah, well, y'know, that's just like, your opinion, man.

[luigi]

illluck, it doesn't matter if it's solved or not. A 25 komi for 5x5 Go would be balanced for all dan players, regardless of whether they know the solution or not. They would draw every time, whereas if two complete newbies play 5x5 Go, it's obvious that a 25 komi won't balance the game.

I disagree. A game being balanced doesn't mean a draw every time. A game being balanced means both players should draw with perfect play. 25 komi balances the game even for beginners, it's just unlikely that games would finish in a draw. If I play a 3 stone handicap game against a 10k, the game is balanced against me, but I'll still win every time. Balancing in the sense of komi just means that neither player should have an advantage at the beginning, not that the outcome is a foregone conclusion.

I think we're not understanding each other. Let's define:

a) "Fair komi" as the komi which ensures a draw with perfect play, and
b) "Balanced komi" as the komi which ensures that Black and White have the same chance of winning, provided that both players are equally skilled.

Of course, "fair komi" is always the same, since it implies perfect play. My hypothesis is that "balanced komi" varies with skill. Consider these two extreme cases on a 19x19 game:

a) Black and White always choose their moves at random.
b) Black and White are 9p players.
c) Black and White are perfect players.

In the first case, the advantage of playing first is virtually meaningless. Therefore, without komi, the winning chances for both players must be really close to equal. With a 6.5 komi, the average result will be really close to +6.5 for White (maybe +6, since Black will have made on average 0.5 more moves than White).

In the second case, 6.5 is the "balanced komi", but needn't be the "fair komi".

In the third case, the "balanced komi" is equal to the "fair komi", and it can be arbitrarily low or high. It can be the case that some incredibly sophisticated sequence of moves ensures a 32 point win for Black, for instance. We simply don't know.

[HermanHiddema]

a) Black and White always choose their moves at random.

In the first case, the advantage of playing first is virtually meaningless. Therefore, without komi, the winning chances for both players must be really close to equal. With a 6.5 komi, the average result will be really close to +6.5 for White (maybe +6, since Black will have made on average 0.5 more moves than White).

Have you tested this assertion?

[MarkSteere]

I'm just debating, btw. No ill will intended. I hold Go and Go players in high regard, the bgg dustup notwithstanding. That was just masterful debating. Yes, I goof on Go, but that's in the context of Go being a great game in the world. Don't take it personal.

Go got me started in game design (along with Reversi, a lesser game). Now, coming full circle, I've got a Go variant. Arghhh! A genetically mutated offspring.

I took the line "Redstone makes use of the pie rule" out of the rule sheet. I don't want to play the role of pie police if people are more comfortable with komi. I don't think the choice of balancing mechanism really matters in a game of hundreds of moves.

Pie wouldn't affect Go gameplay one iota other than rendering irrelevant "The Big Book of Opening Plays". If there were an iota, it would be a positive iota.

One thing to consider. Minus komi. You might still need komi to augment the pie rule. If the komi would be 7.5, if not for pie, you might need a komi of, for example, -1.5 with pie.

[jts]

Pie wouldn't affect Go gameplay one iota other than rendering irrelevant "The Big Book of Opening Plays". If there were an iota, it would be a positive iota.

What do you take the "Big Book of Opening Plays" to be like? There are a few players who take their prepared openings very seriously (there's an active thread right started by a player who's sad that they don't work), but it's not really that important for go, and most people who enjoy the game put vastly more effort into other areas.

I could go into more detail, but you mentioned elsewhere that you don't really play go, so it will probably be easier for you if you explain what you think the relevance of the Big Book is, and we take that as a starting point.

[luigi]

a) Black and White always choose their moves at random.

In the first case, the advantage of playing first is virtually meaningless. Therefore, without komi, the winning chances for both players must be really close to equal. With a 6.5 komi, the average result will be really close to +6.5 for White (maybe +6, since Black will have made on average 0.5 more moves than White).

Have you tested this assertion?

Now I have. I happen to have a rudimentary Go script handy which I wrote some time ago. I've just used it to run 10000 random 9x9 games with 0.5 komi and other 10000 with 6.5 komi. Here are the results:

0.5 komi, 9x9 board:

0 -> 58 / 114 = 0.50877192982456
1 -> 59 / 137 = 0.43065693430657
2 -> 46 / 131 = 0.35114503816794
3 -> 63 / 125 = 0.504
4 -> 55 / 111 = 0.4954954954955
5 -> 54 / 120 = 0.45
6 -> 57 / 123 = 0.46341463414634
7 -> 62 / 128 = 0.484375
8 -> 50 / 115 = 0.43478260869565
9 -> 61 / 121 = 0.50413223140496
10 -> 55 / 114 = 0.48245614035088
11 -> 55 / 111 = 0.4954954954955
12 -> 55 / 115 = 0.47826086956522
13 -> 64 / 112 = 0.57142857142857
14 -> 55 / 115 = 0.47826086956522
15 -> 54 / 102 = 0.52941176470588
16 -> 52 / 112 = 0.46428571428571
17 -> 56 / 116 = 0.48275862068966
18 -> 65 / 144 = 0.45138888888889
19 -> 61 / 131 = 0.46564885496183
20 -> 56 / 121 = 0.46280991735537
21 -> 61 / 114 = 0.53508771929825
22 -> 79 / 130 = 0.60769230769231
23 -> 64 / 135 = 0.47407407407407
24 -> 81 / 140 = 0.57857142857143
25 -> 65 / 131 = 0.49618320610687
26 -> 70 / 119 = 0.58823529411765
27 -> 61 / 123 = 0.49593495934959
28 -> 65 / 124 = 0.5241935483871
29 -> 56 / 113 = 0.49557522123894
30 -> 60 / 114 = 0.52631578947368
31 -> 62 / 121 = 0.51239669421488
32 -> 74 / 143 = 0.51748251748252
33 -> 60 / 120 = 0.5
34 -> 67 / 114 = 0.58771929824561
35 -> 51 / 105 = 0.48571428571429
36 -> 49 / 110 = 0.44545454545455
37 -> 73 / 136 = 0.53676470588235
38 -> 59 / 128 = 0.4609375
39 -> 71 / 124 = 0.57258064516129
40 -> 68 / 114 = 0.59649122807018
41 -> 63 / 114 = 0.55263157894737
42 -> 64 / 116 = 0.55172413793103
43 -> 72 / 133 = 0.54135338345865
44 -> 68 / 120 = 0.56666666666667
45 -> 69 / 124 = 0.55645161290323
46 -> 63 / 133 = 0.47368421052632
47 -> 67 / 142 = 0.47183098591549
48 -> 71 / 131 = 0.54198473282443
49 -> 66 / 124 = 0.53225806451613
50 -> 68 / 129 = 0.52713178294574
51 -> 60 / 131 = 0.45801526717557
52 -> 57 / 117 = 0.48717948717949
53 -> 64 / 116 = 0.55172413793103
54 -> 62 / 117 = 0.52991452991453
55 -> 57 / 131 = 0.43511450381679
56 -> 60 / 117 = 0.51282051282051
57 -> 67 / 127 = 0.52755905511811
58 -> 69 / 130 = 0.53076923076923
59 -> 74 / 134 = 0.55223880597015
60 -> 69 / 116 = 0.5948275862069
61 -> 86 / 155 = 0.55483870967742
62 -> 68 / 116 = 0.58620689655172
63 -> 61 / 126 = 0.48412698412698
64 -> 52 / 125 = 0.416
65 -> 81 / 143 = 0.56643356643357
66 -> 66 / 129 = 0.51162790697674
67 -> 53 / 111 = 0.47747747747748
68 -> 53 / 119 = 0.4453781512605
69 -> 61 / 102 = 0.59803921568627
70 -> 66 / 134 = 0.49253731343284
71 -> 67 / 115 = 0.58260869565217
72 -> 76 / 141 = 0.53900709219858
73 -> 49 / 112 = 0.4375
74 -> 50 / 110 = 0.45454545454545
75 -> 54 / 120 = 0.45
76 -> 66 / 126 = 0.52380952380952
77 -> 58 / 110 = 0.52727272727273
78 -> 52 / 109 = 0.47706422018349
79 -> 49 / 105 = 0.46666666666667
80 -> 44 / 99 = 0.44444444444444
81 -> 43 / 115 = 0.37391304347826

Total -> 5054 first player wins / 10000 games = 0.5054 winning probability
_____________________________________

6.5 komi, 9x9 board:

0 -> 48 / 124 = 0.38709677419355
1 -> 50 / 133 = 0.37593984962406
2 -> 44 / 123 = 0.35772357723577
3 -> 47 / 116 = 0.4051724137931
4 -> 56 / 125 = 0.448
5 -> 49 / 124 = 0.39516129032258
6 -> 49 / 131 = 0.37404580152672
7 -> 51 / 127 = 0.40157480314961
8 -> 43 / 127 = 0.33858267716535
9 -> 46 / 122 = 0.37704918032787
10 -> 39 / 115 = 0.33913043478261
11 -> 38 / 103 = 0.36893203883495
12 -> 48 / 125 = 0.384
13 -> 53 / 130 = 0.40769230769231
14 -> 39 / 112 = 0.34821428571429
15 -> 51 / 137 = 0.37226277372263
16 -> 39 / 112 = 0.34821428571429
17 -> 53 / 108 = 0.49074074074074
18 -> 51 / 119 = 0.42857142857143
19 -> 51 / 129 = 0.3953488372093
20 -> 37 / 92 = 0.40217391304348
21 -> 48 / 113 = 0.42477876106195
22 -> 58 / 122 = 0.47540983606557
23 -> 37 / 109 = 0.3394495412844
24 -> 46 / 132 = 0.34848484848485
25 -> 62 / 128 = 0.484375
26 -> 46 / 131 = 0.35114503816794
27 -> 51 / 141 = 0.36170212765957
28 -> 50 / 117 = 0.42735042735043
29 -> 46 / 129 = 0.35658914728682
30 -> 49 / 121 = 0.40495867768595
31 -> 45 / 122 = 0.36885245901639
32 -> 53 / 122 = 0.4344262295082
33 -> 56 / 119 = 0.47058823529412
34 -> 40 / 95 = 0.42105263157895
35 -> 43 / 109 = 0.39449541284404
36 -> 45 / 118 = 0.38135593220339
37 -> 42 / 116 = 0.36206896551724
38 -> 43 / 122 = 0.35245901639344
39 -> 49 / 129 = 0.37984496124031
40 -> 50 / 117 = 0.42735042735043
41 -> 39 / 113 = 0.34513274336283
42 -> 45 / 121 = 0.37190082644628
43 -> 58 / 122 = 0.47540983606557
44 -> 56 / 138 = 0.40579710144928
45 -> 54 / 115 = 0.4695652173913
46 -> 49 / 142 = 0.34507042253521
47 -> 36 / 100 = 0.36
48 -> 48 / 118 = 0.40677966101695
49 -> 55 / 128 = 0.4296875
50 -> 52 / 125 = 0.416
51 -> 54 / 135 = 0.4
52 -> 63 / 121 = 0.52066115702479
53 -> 53 / 130 = 0.40769230769231
54 -> 47 / 132 = 0.35606060606061
55 -> 42 / 109 = 0.38532110091743
56 -> 51 / 126 = 0.4047619047619
57 -> 42 / 91 = 0.46153846153846
58 -> 48 / 127 = 0.37795275590551
59 -> 46 / 108 = 0.42592592592593
60 -> 60 / 132 = 0.45454545454545
61 -> 49 / 127 = 0.38582677165354
62 -> 52 / 113 = 0.46017699115044
63 -> 46 / 115 = 0.4
64 -> 52 / 132 = 0.39393939393939
65 -> 43 / 120 = 0.35833333333333
66 -> 60 / 124 = 0.48387096774194
67 -> 38 / 116 = 0.32758620689655
68 -> 64 / 145 = 0.44137931034483
69 -> 57 / 119 = 0.47899159663866
70 -> 59 / 136 = 0.43382352941176
71 -> 49 / 137 = 0.35766423357664
72 -> 50 / 118 = 0.42372881355932
73 -> 46 / 131 = 0.35114503816794
74 -> 40 / 123 = 0.32520325203252
75 -> 64 / 140 = 0.45714285714286
76 -> 38 / 91 = 0.41758241758242
77 -> 35 / 124 = 0.28225806451613
78 -> 50 / 132 = 0.37878787878788
79 -> 47 / 141 = 0.33333333333333
80 -> 32 / 104 = 0.30769230769231
81 -> 41 / 133 = 0.30827067669173

Total -> 3951 first player wins / 10000 games = 0.3951 winning probability

The first column represents where the first stone was placed. 1 is a1, 81 is j9 and 0 is a pass. Not surprisingly (for me), 0.5 seems to be the ideal komi for random players, whereas 6.5 komi results in an unbalanced game.

(Rules used: area scoring, no suicide, positional superko.)