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I just released v26, which does nothing beyond remove the experimental suited game as an option.
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Explanation: http://cordialminuet.com/incrementensem … 2618#p2618
Canto Delirium: a Twitter bot for CM. Also check out my strategy guide!
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Damn, I was starting to feel that the experimental game had become a guaranteed win for me. Probably a good reason to remove it though, it really doesn't have the same depth as the original.
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I'd be interested in hearing about your strategy with the experimental mode.
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I'll send you an email.
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With the experimental mode it was really easy to get people to bet on poor hands by giving them the illusions of a straight or flush draw. Not so much in the standard mode, since a high or low first number matters so much more.
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There might be a way to make a variant of this game perfectly symmetrical if there are six suits and six ranks. You could make the values one player sees as suits the same ones the other sees as ranks, so a fair board would be one where the transpose of the rank-swapped board was a row and column permutation of the original.
Last edited by redxaxder (2015-05-29 13:22:22)
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Hmm.. interesting idea!
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I was curious whether there would be any fair boards under that rule, so I came up with a classification. Every such board can be row/column permuted into a board that has (1,1), (2,2), (3,3), etc going down the diagonal and the tile in position (i,j) is the pair of the tile in position (j,i). There are on the order of 10^16 distinct boards that look like that.
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This is really mind-bending, so I'm not sure I'm getting this right...
Firstly, there are different ways of comparing the player's hands. There seem to be two obvious ways of doing it.
1. If one player has a pair (of the same rank), the other sees them having a pair of the same suit, which is normally worth nothing. So one solution is to make the rank-suit swap of a hand equal in value to the original (e.g. a flush would rank equal to a triple). However then there's no point doing the rank-suit swap at all, as it would be merely cosmetic.
2. What I am pretty sure you actually meant: each player gets the hand THEY see, so you can give the other player what looks like a pair, knowing it's actually worthless to them. (Assuming hand ranking is done in an asymmetrical way similar to Poker). This seems like it could add a bit more depth to the game.
Such a mirroring of rank and suits isn't a trick specific to the suited game. In general for any game variant defined by a "hand" ordering rule (e.g. sum of values in CM) you could label each square with two "values": what player 1 receives on getting the square, and what player 2 receives on getting it. In your rank-suit swap there is a simple mapping between the two values which makes it easy to represent both of them at once. But I could just as easily combine a normal 6x6 magic square and its transpose into a single, so there is no relation between the two numbers ("us" and "them") in a cell. As long as your transpose-mirror condition holds, this game is completely fair with no bias to either player, unlike CM.
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You're right. Suits aren't necessary to introduce this kind of symmetry. I think we can also do away with the double meaning of the tiles by altering the selection rule.
Imagine if each player sees the same board (not transposed!) and they pick columns for themselves and rows for their opponent, with the restriction that the index of a chosen row can't match the index of a chosen column. This way we don't even need an extra condition on the board generation.
Last edited by redxaxder (2015-06-01 20:00:27)
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Maybe I'm misunderstanding (which is highly likely given this entire conversation), but if both players are playing on the same board, no transposition, and they're picking rows for their opponents, wouldn't it be possible for them to choose the same row for each other?
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Yeah. It would be possible for both players to give themselves the same column and give each other the same row. So they'd gain the same space on that turn. That's pretty unsatisfying.
I think this kind of pitfall is unavoidable if you want perfect symmetry, though. If both players are playing identical games and make identical moves, their outcomes will be identical.
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I guess I'm not entirely sure what you're trying to solve. CM as it is may have some boards with bias, but the trade-off is a game that's simple and easy to learn. Boards that seem against you may actually be in your favor if you understand your opponent better than they understand you. At least, that's how I see it.
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We're just trying to explore the space of possibilities a bit. Certainly none of these ideas are quite as simple as CM.
Yeah. It would be possible for both players to give themselves the same column and give each other the same row. So they'd gain the same space on that turn. That's pretty unsatisfying.
Since that's the case anyway, I don't see the use of the "restriction that the index of a chosen row can't match the index of a chosen column".
(EDIT: OK, I worked out the reason: it's so that you learn something about the column the opponent picked for themselves, in the same way as CM. That makes this variant is very similar to CM.)
I don't think the possibility for such a tie is a problem. CM has ties anyway. We can fairly confidently assume there is no pure strategy which is optimal in any of these variants (which I think Jason or Josh showed for CM?), which makes the possibility of the players making identical moves unimportant.
But those sorts of ties aren't unavoidable in a perfectly symmetric game. Consider rock-paper-scissors. For example if CM was played on a Latin square instead of a magic square then it would be unbiased to either player. But it would also be much more boring.
Magic squares don't always use the numbers 1 ... n*n. I suspect that if every number appeared twice (1,1,3,3,...35,35) then it would be possible for the transpose of the square to be a permutation of the rows and columns of the original. This would require that every four cells forming a square contain both duplicates of two numbers, like:
. . . . . .
. . . . . .
. . . . . .
. 9 . . 3 .
. . . . . .
. 3 . . 9 .And maybe it would then be possible to deduplicate the numbers (change one 1 into a 2, etc) and get a magic square with zero or very low bias?
Last edited by .. (2015-06-03 09:25:03)
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