As you may know, Hex on Little Golem uses the “swap rule.” After black places the first stone, white has the option to effectively swap sides, if desired. Actually, on LG the first token changes color and moves to a reflected location on the board, but it is essentially the same as swapping sides. This makes Hex much more balanced, since otherwise the advantage of the first move would be very strong. This is also known as the pie rule, as in “I cut the pie, you choose the slice.”

Tim Shih, a 5-dan Go player who is currently playing just Hex here, mentioned that perhaps the swap rule could be applied to Go. This started an extended discussion which I thought I would present to the Go forum.

I don't seriously expect to change the komi system, of course. I would just like to hear what you think of this idea. Instead of any komi, white will have the option to swap sides, or perhaps swap the first stone to white, after black makes the very first move. Sides may be swapped only once during a game. If sides are not swapped immediately after black's first move, then sides may not be swapped at all that game.

The point has been made that in order for this to be fair, there must be some initial move which would lead to “jishogi” with perfect play. I assume jishogi is a tie game. I'm not so sure that would be necessary, but in any event, are there not initial moves which would hand the advantage over to white; 1.A1 for example? If there are initial losing moves as well as initial winning moves (with no komi), then it seems like a natural intuitive conclusion that there would be initial moves on a 19x19 board which are *close enough* to this “perfect jishogi game” as to afford both sides equal practical chances. Maybe a move in the very center would be a good move after all…?

Thanks for your attention.

Here is more of the discussion from the Hex forum:

Rex Moore: Swap rule in Go

Tim said: “The swap rule is really ingenious to me. Perhaps even Go games should adopt this rule. :)”

I thought of the same thing just yesterday! (I'm a slow thinker.) This would eliminate the need for komi, and for trying to figure out which komi is right for different board sizes.

Alternatively, players could bid for the right to go first. The winning bid becomes the other player's komi.

---–

ypercube:

I feel that the swap rule is not appropriate for the game of Go. While Hex has only two outcomes (win or lose), Go has two outcomes but these two come from counting stones. So the real outcome can be 0, +1, +2, … or -1, -2, …

I mean that when the game finishes a player has either a positive or a negative or zero amount of space that is in his territory. This makes it difficult for the swap rule to balance the game. A rule like the one we use here at the Word Game could be far better. Each player should auction for the komi that should be used (including negative ones) before starting playing.

---–

David J Bush:

“I feel that the swap rule is not appropriate for the game of Go. While Hex has only two outcomes (win or lose), Go has two outcomes but these two come from counting stones. So the real outcome can be 0, +1, +2, … or -1, -2, …

I mean that when the game finishes a player has either a positive or a negative or zero amount of space that is in his territory.”

Up to here I think I understand what you mean. You are talking about the difference between the two players' scores right?

“This makes it difficult for the swap rule to balance the game.”

But I don't see how A implies B here. Why would the scoring system in Go make it difficult for the swap rule to balance the game?

---–

Taral:

For the swap rule to be able to balance Go, there should be an opening move which leads to jigo with perfect play. It's not obvious that such an opening move exists.

I read somewhere someone claiming that any move on the first row would lose, while any other move would win.

Some additional thoughts:

“…are there not initial moves which would hand the advantage over to white; 1.A1 for example?”

David, A1 would definitely hand the advantage to white, and would not be swapped.

“If there are initial losing moves as well as initial winning moves (with no komi), then it seems like a natural intuitive conclusion that there would be initial moves on a 19x19 board which are *close enough* to this “perfect jishogi game” as to afford both sides equal practical chances.”

I am no expert (I've been playing Go for only a short time), but I don't think there's talk of winning and losing moves in Go like there is in Hex. (At least with respect to mathematical proofs that certain first moves are theoretical wins.)

“I feel that the swap rule is not appropriate for the game of Go. While Hex has only two outcomes (win or lose), Go has two outcomes but these two come from counting stones. So the real outcome can be 0, +1, +2, … or -1, -2, …

I mean that when the game finishes a player has either a positive or a negative or zero amount of space that is in his territory.”

ypercube, like David, I don't see the connection here to the swap rule. I think that in any two-player game where the first move is an advantage, you could implement the swap rule.

“For the swap rule to be able to balance Go, there should be an opening move which leads to jigo with perfect play. It's not obvious that such an opening move exists.”

Taral, I see what you're getting at here. But I don't think there needs to be a perfectly balanced opening move in order for the swap rule to work. It works in Hex, and to my knowledge there is no universally accepted balanced first move in that game. If you're the first player, you have to think about just how much you can get away with without being swapped, OR you may make a relatively weak move that you hope will be swapped so you can make a strong next move.

Good discussion, even though it will never happen. (Though certainly it could in real face-to-face games.)

Rex

True, in Hex there aren't any balanced first moves, since the game cannot be drawn. But in Go there are ways to make the game perfectly balanced, such as using auction for komi, provided that you are using integer komi. So if the swap rule can't achieve a balanced game, it's an inferior solution.

I agree that the swap rule would not be appropriate for Go. I believe that any initial move on the 1-line should be accepted, and any other move should be swapped.

However Go can be balanced perfectly by the use of komi bidding. Or, of course, by the use of the correct komi; except that no-one knows what this is.

Nick, would you swap an initial move in the very center of the board? I have heard that is a poor first move. Is it still strong enough to win?

How would komi bidding work between a 20 kyu and a 1 kyu player?

I would definitely swap a first move in the centre. I think it would be hard to beat a player who starts in the middle and then mirrors your moves, and furthermore, that handicap stones and/or komi are a necessity for keeping the weaker players from doing this against stronger players.

I would swap a move in the center as well, but I am in doubt regarding 2nd line moves. I think I would have accepted a move on the 2.2 square but accepted others.

It is not obvious that the swapping rule would works well in any game though. At least in GWG it would be very hard to find a decent first move if you had to think about the possibility that it could be swapped:)

ooops

Should be:

I would swap a move in the center as well, but I am in doubt regarding 2nd line moves. I think I would have accepted a move on the 2.2 square but swapped others.

I think it is a good idea to apply the “pie-rule” to Go. But it seems more natural to me to use some kind of komi-bidding, and not a swap rule like in Hex.

A natural way would be that one player sets the komi-value (cuts the pie) and then the other chooses to play white or black (chooses a slice).

This method is simple and I don't see why it should cause any problems. But it has the tiny disatvantage that it is non-symmetric from the very beginning (a player is chosen who has to set the komi). One might think of a more sophisticated method, e. g.:

Both players independently bid a number of komi (any real value). The player who bids higher gets the black stones, and white gets the average value of the bids as komi (rounded to the nearest multiple of 1/2).

Using this method, every player has to think what he considers a fair komi-value to equalize for the first move. If he bids higher, he risks to play black and give too many komi to the opponent, and bidding lower, he might play white and get too few komi. The average value of the bids is equally satisfying both players: white gets more komi and black gives less komi than they, respectively, consider to be fair.