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Subject: Balancing the game without the pie rule rss

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Nick Bentley
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I've recently been playing a modified version of hex, that doesn't seem to suffer from imbalance as much as the original, to the extent that I haven't needed the pie rule. But I am a mediocre player; a good one might be able to find a problem with the idea. In any case, the rule is:

For the first move of the game, the first player places a single stone. From then on, starting with the second player, each player places two stones on his turn.

The important effect of this rule is that at the end of his turn each player always has one more stone on the board than his opponent. In the original rules, it is only the first player enjoys this advantage, and he can exploit this to find winning positions more easily.

I think I can prove that the theoretical winner of this modified version depends on the board size. It seems that, for board sizes with an odd number of spaces along the edge, the 1st player is the theoretical winner. For board sizes with even number along the edge, the second player has the theoretical win.

Comments and criticisms of the idea are welcome. I'd especially like to hear from experienced players who are in a better position to find flaws.


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Patrick Schultz
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This is certainly more balanced than straight Hex, but it is also a very different game. I wouldn't propose this as an alternative to the swap rule, but as a Hex variant. It is for sure a very interesting variant, and I believe has been studied in some depth before. It greatly changes the tactics, and makes for a more tactical game overall. It also creates an interesting situation which can occasionally come up similar to a ko in Go.
 
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Nick Bentley
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cool. Do you know where I could find info about it on the web?
 
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Nick Bentley
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I'm curious as to how a ko-like situation arises here, since this is a finite game. Can you describe it?

 
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Patrick Schultz
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It is not a ko situation in the sense that it could possibly repeat the same board configuration twice, but it does create a situation where players alternate making threats (actually responding to the previous threat and making a new one on the same turn), and whoever runs out of threats first loses the local battle (has their connection cut).

This page describes the situation in the context of the game *Star, but the tactics are mostly the same as Hex:
http://ea.ea.home.mindspring.com/*DoubleStar.html
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Nick Bentley
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thanks. I've read it, and I think I get it.
 
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Tony Chen
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On a related note, a Taiwanese professor used this method to balance Go-Moku, and came up with Connect6.
 
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Rex Moore
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Sorry I'm late to this party.

I would argue that with the swap rule, Hex is not "unbalanced." Almost by definition it becomes about as balanced as a game can be.

Thus, I don't agree "it is only the first player enjoys this advantage, and he can exploit this to find winning positions more easily." Why? Because either his first move was so unhelpful the opponent didn't swap, or he got swapped.

Just sayin'....



 
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Tony Chen
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I think they were saying that hex is unbalanced as is without the swap rule.
 
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Nick Bentley
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drunkenKOALA wrote:
I think they were saying that hex is unbalanced as is without the swap rule.


yup, this is what I meant. Sorry I wasn't more clear.
 
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Harald Korneliussen
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As you've said here, it's really a completely different game if you do that. But there IS another way to balance Hex without the swap rule. A rather obvious one, in fact, used by many early players and implemented in some simple applets. For some reason it is not much talked about.
It's simply to restrict where the first piece can be placed. From playing with the swap rule we know roughly which starting positions make for an even game. Just highlight those positions, and say that the first move has to be on one of them.

The nice thing about this approach is that it can be extended to give Hex something else it sorely needs: a handicap system. By extending the number of (good) legal positions for the first piece, you can balance the game somewhat between unequal opponents.

The downside is that we would have to work out empirically (and agree on!) how much of an advantage various starting positions give - and do it again for each common board size. But IMO, for increasing the pool of challenging players, it's definitively worth it.
 
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Benedikt Rosenau
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milomilo122 wrote:
I think I can prove that the theoretical winner of this modified version depends on the board size. It seems that, for board sizes with an odd number of spaces along the edge, the 1st player is the theoretical winner. For board sizes with even number along the edge, the second player has the theoretical win.


I am curious to see a sketch of this proof.

As for comments, you are well aware that the idea has been used for The Game of Y. Since Y-boards are half the size of Hex-boards with comparable edge length and since more cells of Y boards belong to an edge area, that was not a clever idea at all. The 1-2-2-... pattern at least halves the effective size of the board. I even think it is more like reducing it to a quarter. When you use the move pattern together with a small board size, the game is as pointless as Hex on a 6x6 board.
 
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Tony Chen
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Quote:
I think I can prove that the theoretical winner of this modified version depends on the board size. It seems that, for board sizes with an odd number of spaces along the edge, the 1st player is the theoretical winner. For board sizes with even number along the edge, the second player has the theoretical win.
The winning position probably depends on the board size. I don't think it is as easy as first player on odd, second player on even though. What's the reasoning for that? If it is the first player placed an odd number of pieces at the end of his turns so he wins on boards with odd number of spaces, then that's just wrong.
 
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