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Subject: Hex rule to end in a tie rss

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marco maier
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Since I like games that allow ties I would propose the following for hex: If a player wins with the last stone it's a tie. What do you think about it? Other ideas?
 
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Craig Duncan
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I assume you mean a case where there is only one empty cell left, and the player connects his sides by playing to that cell. Right?

I think that would be a VERY rare case indeed.

Or are you imagining a case where players have a limited supply of stones to play with, and they exhaust the supply?
 
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David Bush
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The ONLY way a game of Hex would use up all the cells on the board would be if both players cooperate to arrive at such a position. I suggest you try Twixt.
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marco maier
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I mean, when there are only two stones left (one for each player)the game is a tie.
 
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marco maier
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I assumed that if both players play perfectly they use all pieces, and if they don't the best player wins.
 
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Russ Williams
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marcoms wrote:
I assumed that if both players play perfectly they use all pieces

Well, there's your mistake.
 
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Craig Duncan
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marcoms wrote:
I mean, when there are only two stones left (one for each player)the game is a tie.


Online games of Hex have, so far as I know, unlimited stones. Commercial games of Hex tend to come with enough stones to fill all cells (or all but one cell). E.g. the two commercial versions of 11x11 Hex that I know of come with 60 stones in each color -- enough to fill all but one cell.

http://nestorgames.com/#hexset_detail

https://www.thegamecrafter.com/games/hex

As David implies above, for practical purposes that many stones will produce a winner every time, unless players collude to engineer a winless board containing 120 stones.

It's open to you to create a scarcity of stones -- say, 30 for each player -- and declare it a draw if stones run out with no winner. Even then, however, my sense is that nearly every game would finish. I haven't got a lot of experience at Hex myself, but I've seen a number of final game boards from games by experienced players and it's striking how few cells are filled. So draws might be rarer than you think, even if you limit the number of stones available per player.
 
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David Bush
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You can see for yourself the most complicated possible game on a 9x9 grid, in this thread. PV means principal variation, the most difficult line for both sides. Less than half the board is filled up. With enough stones to fill about 70% of the grid, whatever size that grid is, players are unlikely to ever run out.

BTW the diagram on the left is not a game, it's a map.

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marco maier
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I meant there are only two stones and only two cells to fill
 
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marco maier
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russ wrote:
marcoms wrote:
I assumed that if both players play perfectly they use all pieces

Well, there's your mistake.


Cannot the board be filled?
 
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Russ Williams
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marcoms wrote:
russ wrote:
marcoms wrote:
I assumed that if both players play perfectly they use all pieces

Well, there's your mistake.


Cannot the board be filled?

It can, but AFAIK perfect play will not cause that to happen. (Suboptimal play intentionally trying to fill the board instead of trying to win can make it happen.)

E.g. look at simple smaller board cases. Optimal play by both sides will reach a winning connection before the board is filled, unless I'm deeply confused.
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Craig Duncan
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marcoms wrote:
I meant there are only two stones and only two cells to fill


I assume that in theory it's possible to fill the board except for two empty cells without either player winning. But there will surely only be a handful of board arrangements fulfilling that condition, compared with a galaxy of other board arrangements. I'm no mathematician but I wouldn't be surprised if the fraction is one out of millions. Of course, many of those millions of board states in the denominator would never result from rational play. But even assuming rational play it is astronomically unlikely that the board would fill except for two empty cells.
 
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marco maier
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russ wrote:


Look at simple smaller board cases. Optimal play by both sides will reach a winning connection before the board is filled, unless I'm deeply confused.


I see, I should have played at least with small boards.
 
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marco maier
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What about the following (I hope it's not another stupid idea):
If it's first player turn and both players need only a stone to connect their respective sides, it's a draw.
With this rule, would the game be fair?
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Russ Williams
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marcoms wrote:
What about the following (I hope it's not another stupid idea):
If it's first player turn and both players need only a stone to connect their respective sides, it's a draw.
With this rule, would the game be fair?

What if the first player's single stone to connect makes the second player's single stone to connect impossible (i.e. they would both win by playing on the same hex)? Would your variant make that a tie or a first player win?
 
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Craig Duncan
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russ wrote:
What if the first player's single stone to connect makes the second player's single stone to connect impossible (i.e. they would both win by playing on the same hex)? Would your variant make that a tie or a first player win?


Wouldn't this HAVE to be the case, Russ, since in Hex a win by one player necessarily blocks the other player from a win? So there is no way one player could place a piece and win, and leave the board such that, were the second player to be given an extra turn, he'd connect too. The only way both players could be one away from a win is if the same hex is the winning hex for both. Right?


. x x x
o . . .
o . . .
o . . .

or

. . o .
. . o .
x x . x
. . o .

etc.
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marco maier
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It would be a tie
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Russ Williams
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cdunc123 wrote:
Wouldn't this HAVE to be the case, Russ, since in Hex a win by one player necessarily blocks the other player from a win?

Hmm, yes... I plead late-night sleepiness!
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Craig Duncan
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marcoms wrote:
It would be a tie


Yes that is a more workable tie rule than the initial proposal.
 
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Joseph DiMuro
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marcoms wrote:
Since I like games that allow ties


Try Havannah.
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Virginia Milne
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And TwixT as already noted above. I have actually had about two draws in TwixT, spread over many years of play.

Why desire a draw option in a game?
Put me right if I guess wrong, but I think some people expect that equally skilled players, playing with equal skill on the day, should end the game with a draw.

With no draw, one of the equally skilled players, playing with equal skill on the day, must win, which looks like a matter of luck.

So games with no draws will manufacture a win, when a win does not reflect the respective strengths of the players.

Have you ever witnessed equally skilled players (what ever that means) who
played a game with no draw, with equal skill on the day, and the wrong player won? How would you measure that they actually played with equal skill on that day?

Now I will stand up a pin balancing on its sharp point, it is possible you know, at least in theory--- ha ha
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Craig Duncan
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Virginia, you might find this old post of mine (from a forum on Hive) relevant:

https://boardgamegeek.com/article/9638711#9638711
 
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Virginia Milne
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Yes, that was an interesting article on draws in the Hive forum

Now let's step down from matters of high philosophy and descend to mundane practical matters.

Hex is a game where one player connecting means the other player getting a forced disconnection. So, unlike Havannah, Hex does not have a racing component. You can find a study of forced potential connections in Hex. To get started just google "hex edge templates".

What does this mean in practical terms? Most games end, in resignation, when one player can show that they have a set of forced potential connections that connect the two boarders of their colour.

Potential connections imply unfilled hexagons. Usually many more than one.
So in answer to the suggestion of the artificial imposition a drawing rule when empty hexagons are close to running out, my suggestion is "Just forget about it! The situation you foresee is too unlikely in a normal game for anyone to waste their time considering it" soblue
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Cameron Browne
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Hi Marco,

marcoms wrote:
If it's first player turn and both players need only a stone to connect their respective sides, it's a draw.

That's an interesting idea, sort of like moving the first move equaliser from the start of the game to the end.

If it works in practice and gives the trailing player (who would otherwise lose by a move) something to continue fighting for, that could be a good thing.

And the obvious variant: if any cell gives both players the win then neither player can play there. This could provide a balancing mechanism that artificially extends some games, though you'd have to check that this did not make most games end in a tie!

Regards,
Cameron
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Benedikt Rosenau
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marcoms wrote:
Since I like games that allow ties I would propose the following for hex: If a player wins with the last stone it's a tie. What do you think about it? Other ideas?


For misère Hex, there is a proof that, given perfect play, the last move is winning. You might apply your rule there.
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