The pie rule

[hyperpape]

This started in Luigi's thread, but I think it's an interesting curiousity.

Many board games in the same category as go (deterministic, perfect information, abstract, deep) use a pie rule (Hex does). Player A makes the first move, then B has a choice. He may either play second, or he may take the move on the board as his first move, letting A make the next move as White. From there the game continues as normal. In practice, A should choose a move that's balanced, so that his opponent can't make his position immediately inferior, and/or a move that he knows the intricacies of.

For the reasons I laid out there, I don't like that rule for go. But what would be an even move? (Leave aside the fact that you can prepare trick plays. Let's say that whatever move you choose, A and B will be equally familiar with it).

$$c You'd obviously choose Black.
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Click Here To Show Diagram Code

[go]$$c You'd obviously choose Black.
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$$c Obviously White.
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Click Here To Show Diagram Code

[go]$$c Obviously White.
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$$c Maybe good for Black? I'm not sure.
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Click Here To Show Diagram Code

[go]$$c Maybe good for Black? I'm not sure.
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[shapenaji]

I could actually see the 2x2 point being played there, it's playable, but usually small and overly tricky.

As a balancing move though, I think it's ideal.

I'd also consider 5x5, 6x6, 7x7, and depending on the opponent, Tengen

[tchan001]

In an H9 game, what are the odds that Player B would take the move on the board as his first move?

[jts]

More interesting than finding a 7.5 point move, in my opinion, is why you would use a pie rule at all.

There are lots of different ways to resolve the first-mover advantage* in games. The most obvious is to play sets; bidding for the right to play a certain side is used in a many card games and war games; something like komi is basically just a community-approved bid for the favored side; other games, especially multiplayer games, build balancing mechanics into the rules of the game.

So why would you use a pie rule? I think the most obvious reason would some combination of the following: (i) The game is solved. The pie rule is necessary to move it out of the solution set. (ii) The first-mover advantage is so large that the game is essentially solved. (iii) The game does not have any equivalent to points, so bidding is impossible. (iv) The game is too boring for anyone to want to play a set.

But if a game is solved (or the first player inevitably wins with good play) or {it doesn't have a point-equivalent, and isn't worth playing more than once}, there's a problem with the game. Decent games shouldn't need the pie rule.

I think we can see how unsatisfying the pie rule is by thinking about how its application would work in a game like tennis. Good tennis players spend years perfecting their serve: learning to place it precisely, getting power and spin, and thinking about how the game will develop from the initial serve. Likewise, they spend a lot of time practicing returning serves, and getting good at that. The game of tennis is built around the player with first-move advantage trying to use that advantage to the hilt, and the other player trying to resist it, and the kinetic ballet that develops from that interaction.

So then if someone comes to me and tells me that playing sets has disadvantages, and he has a way to stop time immediately after the serve so that the second player can decide whether he would rather return the serve or let his opponent return it, and that henceforth tennis will be about having the most mediocre serve possible, so that neither player has any advantage... what do you think I would say about that? What would you say? What would serious tennis players say?

I guess in go there are certain players who don't enjoy the opening and, when two of them play often, they'll have one particular opening that they always use, which they think is fair for both of them and saves them some tedium. People like that might want to consider the pie rule. But it seems to me that in general, the pie rule is designed for games that aren't well designed, and only adds to a game for people who don't like the start of the game anyway.


*Loosely speaking. In some games the first player to pick a side will pick the side that (in the game) moves second; in other games, moves are simultaneous, etc.

[hyperpape]

Shapenaji, that means you think that a 5x5 move is only doing half the work of a normal corner move. Or alterantely, that

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Click Here To Show Diagram Code

[go]$$c
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This game is even, without komi (I guess it could be even/uneven because I made silly plays in the other corners. I don't know 5-5 opening theory). I'm quite surprised by that.

6-6 or 7-7 seem more plausible. But tengen, I'm really surprised about. I mean... http://senseis.xmp.net/?KitaniGoFirstGame, http://senseis.xmp.net/?GameOfTheCentury.

[luigi]

Decent games shouldn't need the pie rule.

Corollary: Hex is not a decent game.

[shapenaji]

Shapenaji, that means you think that a 5x5 move is only doing half the work of a normal corner move. Or alterantely, that

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Click Here To Show Diagram Code

[go]$$c
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This game is even, without komi (I guess it could be even/uneven because I made silly plays in the other corners. I don't know 5-5 opening theory). I'm quite surprised by that.

6-6 or 7-7 seem more plausible. But tengen, I'm really surprised about. I mean... http://senseis.xmp.net/?KitaniGoFirstGame, http://senseis.xmp.net/?GameOfTheCentury.

I think it's more that against certain territorial players, I would trust them to have very little experience with center openings. For them, a 5x5, 6x6, 7x7 or Tengen is worth a lot less, whereas for me, it's worth a lot more (since they don't get komi).

I guess that's the one thing I like about the pie rule, is that there is strategy involved depending on who you play.

[hyperpape]

Corollary: Hex is not a decent game.

Yeah, not just Hex, but several other games that either look interesting to me or are attested to be interesting by quite a lot of the people who like the same sorts of games that I like use the pie rule for me to dismiss it.

The part about tennis nicely captures why I don't like the pie rule for go. I think the key to the pie rule is that there have to be plays that are only somewhat useful while not being obnoxious. My limited acquaintance with Hex makes it seem like that is probably true. My sense of go is that it is decidedly false.

[shapenaji]

Also, following up that thought,

I don't think the pie rule is an even trade. If I know anything about my opponent, it will cease to be a balance, because I can play a move that I know works well with my style, but poorly with my opponent's.

As a result, there is still an advantage to the first move.

[Kirby]

Also, following up that thought,

I don't think the pie rule is an even trade. If I know anything about my opponent, it will cease to be a balance, because I can play a move that I know works well with my style, but poorly with my opponent's.

As a result, there is still an advantage to the first move.

In my opinion, this is probably just because go is complicated enough that styles make a difference from person to person.

If we could all play optimally, the pie rule should still work with go. If you play tengen, it is worth some value, regardless of style. I think style and psychological factors of the game expose human irrationality, and are part of what makes go interesting.

If we could all play rationally and optimally, there would be no reason that tengen would be a good first move for you and not for me.

Here, I think the game of go is a pie, but we're all wearing different glassesthat let us look at that pie a different way. You can cut the pie in such a way that a particular piece looks big to you, and small to me, but in reality it's the same piece of pie.

It's just that our irrational glasses skew the way that we look at the pie.

[shapenaji]

Also, following up that thought,

I don't think the pie rule is an even trade. If I know anything about my opponent, it will cease to be a balance, because I can play a move that I know works well with my style, but poorly with my opponent's.

As a result, there is still an advantage to the first move.

In my opinion, this is probably just because go is complicated enough that styles make a difference from person to person.

If we could all play optimally, the pie rule should still work with go. If you play tengen, it is worth some value, regardless of style. I think style and psychological factors of the game expose human irrationality, and are part of what makes go interesting.

If we could all play rationally and optimally, there would be no reason that tengen would be a good first move for you and not for me.

Here, I think the game of go is a pie, but we're all wearing different glassesthat let us look at that pie a different way. You can cut the pie in such a way that a particular piece looks big to you, and small to me, but in reality it's the same piece of pie.

It's just that our irrational glasses skew the way that we look at the pie.

Good luck taking off the irrational glasses

[Kirby]

Mine are the size of bottlecaps, as you can probably tell if you've seen any of my malkovich games.

[jts]

Decent games shouldn't need the pie rule.

Corollary: Hex is not a decent game.

Decency has different aspects. When I was in preschool, tic-tac-toe seemed to be a decent game. I was still having fun with it when I was 13 (writing out the game tree by hand). I don't want to ban tic tac toe from the family of games just because I don't play it anymore. Lots of people derive pleasure from it. Nonetheless - wouldn't use "it's even better than tic-tac-toe!" to praise a game that I admired.

[jts]

Yeah, not just Hex, but several other games that either look interesting to me or are attested to be interesting by quite a lot of the people who like the same sorts of games that I like use the pie rule for me to dismiss it.

The part about tennis nicely captures why I don't like the pie rule for go. I think the key to the pie rule is that there have to be plays that are only somewhat useful while not being obnoxious. My limited acquaintance with Hex makes it seem like that is probably true. My sense of go is that it is decidedly false.

You mention games that seem interesting, and games that are attested by others to be interesting. Are there any games that you yourself enjoy for which the pie rule is an integral mechanic? I definitely want to think seriously about games you'll vouch for, but am reluctant to do so for games that people for whom you will vouch for will vouch for.

I think when you worry that a move is "obnoxious" what you mean is "it would be really irritating to study (possibly tricky) opening sequences that arise from an intentionally mediocre move." That is, it's obnoxious to try to be really good at being mediocre; it would be really obnoxious to forced to come up with the most healthy lard pie, or to figure out the most attractive way to arrange a week's worth of dirty dishes, or to look at all the songs that glorify pimps and decide which one is least misogynist.

If you care enough about a game to admire excellent play, I think you will (to some degree) find playing a strong opening fun, and find figuring out the best way to proceed from a mediocre opening obnoxious. If you think it's fun to start a game from a mediocre opening, that probably means you don't care for the game very much.

[ez4u]

Also, following up that thought,

I don't think the pie rule is an even trade. If I know anything about my opponent, it will cease to be a balance, because I can play a move that I know works well with my style, but poorly with my opponent's.

As a result, there is still an advantage to the first move.

Are you assuming an information asymmetry? Assuming your opponent knows your style as well as you know theirs, it still comes down to judging the relative value of the allowing you or denying you the use of the first move that you chose. If there actually is a "heads I win, tails you lose" condition in, for example, center-oriented first plays against a particular opponent, there is presumably a symmetrical "tails I win, heads you lose" condition when that opponent plays first.

As far as I can see, a pie rule reduces to starting the game with a willfully inferior move (with or without internal gamesmanship), followed by a decision on whose move it is, and then followed by reversion to playing as well as possible in order to win. I think it would spoil the beauty of the game for me.