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Subject: Why row handicapping doesn't work rss

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David Bush
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Row handicapping might seem like a granular way to compensate for differing player strengths. And, if the weaker player does not know the relatively simple procedure described below, it might work. But by following these steps, the player with less distance to cross will always win, even if the other player moves first (without the swap rule, of course.)

We use here a 14x13 grid, but the process can be generalized to any grid of unequal dimensions. First, partition the grid into two equilateral triangular regions, as indicated by the purple line. For each cell in one triangular region, define a unique corresponding cell in the other. The three pairs of symbols indicate how the corners are mapped. It's like a mirror image, shifted slightly. If the dimensions of the grid differ by more than one, the excess portion of the grid may be ignored. (In other words, if white plays in the excess region, it does not matter how black responds.)


The strategy is, whenever white plays in a cell in one triangular region, black plays in the corresponding cell in the other region.

In order to win, white would have to create a path which crosses the purple line. That implies white's path must pass through the vertical row of cells from M1 to A13. Consider the "highest" (or closest to M1) white token in this vertical column which is part of this path, connected to the A row, The path shown below is intended to represent an arbitrary path. In order for this path to continue across the purple line, it must pass into the "lower" cell as indicated by the arrow, here G8, because H7 is occupied by black. From G8, there is no way for white to reach row N, because the corresponding path created by black blocks the way.


I'm not saying that during the game, white should construct a path from left to right in such a simple fashion. I'm assuming that the game is over already, and white has won. Any such winning path for white must obey the restrictions described, which leads to a contradiction. So, white cannot win against this simple strategy.
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Max Pfennighaus
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Thanks for this! So what *does* work? Is there an effective handicapping method?
 
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David Bush
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Maybe extra stones for the weaker player (which here we assume would have the black stones) could be placed on the board in specific positions, which is similar to Go handicapping. This initial position could be with white to move. Of course there would be no swapping sides. For example, a one stone handicap where the black stone is in the center would usually be a stronger handicap than a one stone handicap where the black stone is near (but probably not on) an edge. There could be several ways to arrange two black handicap stones at the start of the game, for various levels of two stone handicap. The players could experiment with different initial configurations of different numbers of black stones until they find an arrangement from which both players win approximately the same number of times.
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