Handicaps Beyond Nine Stones/ Discussion

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Another 25 Handicap stone placement

HotIce: Hi, once I saw a 25 Handicap as:

[Diagram]
Handicaps up to 25  

Now what is the correct answer for 25 Stones?

Sequence

Robert Pauli: Here's at least the "correct" sequence, HotIce ;-)

[Diagram]
Generalized handicap sequence  


41 stone sequence

(Original (Over nine stones handicap) page by WillerZ)

For the sake of completeness, I wondered what a 41-stone handicap should be (41 stones is about right for a 30kyu playing a 9dan pro). I reckon what I came up with is about right, but the question I couldn't answer was: in what order should the stones be added from 10 through 40?


[Diagram]
41-stone handicap  


[Diagram]
41-stone handicap (alternative, not so good for Black IMO)  

How many various symmetrical 41-handicap-stone-placements are there?

That depends if you ask only for central symmetry or, as in the two diagrams above, for symmetry when you flip the board 90 as well. In any case, notice there must be one stone on the tengen.

[Diagram]
Relevant area for central symmetry  

In the first case, we can restrict the choice to putting 20 stones in the left half of the board, the other stones being placed by symmetry. Hence, this is choosing 20 stones among 180 positions, for a grand total of 175142105857592248012292655 possibilities.

[Diagram]
Relevant area for full symmetry  

In the second case, we can restrict the choice to putting 10 stones in a quarter of the board, the other being forced by symmetry. Hence, this is choosing 10 stones among 90 positions, or 5720645481903 possibilities.

The same calculus could be easily extended if you want some diagonal symmetry too.

- Jhyn


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Handicaps Beyond Nine Stones/ Discussion last edited by Jhyn on March 28, 2012 - 01:36
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