BrainKing - 讨论板 (Chess variants (10x8))

监管者:

Chess variants (10x8)

Sam has closed his piano and gone to bed ... now we can talk about the real stuff of life ... love, liberty and games such as
Janus, Capablanca Random, Embassy Chess & the odd mention of other 10x8 variants is welcome too

For posting:
- invitations to games (you can also use the New Game menu or for particular games: Janus; Capablanca Random; or Embassy)
- information about upcoming tournaments
- disussion of games (please limit this to completed games or discussion on how a game has arrived at a certain position
... speculation on who has an advantage or the benefits of potential moves is not permitted while that particular game is in progress)
- links to interesting related sites (non-promotional)

讨论板列表

状态: 所有人能发表

先显示最旧的消息。

31. 八月 2004, 21:53:43

AbigailII

显示此用户所有帖子 | 链接

题目: Re: Gothic Chess NIM.......(OT)

It's a win for black. It's a game of parity. Let the game consist of N numbers (i = 10 for the first example), x_0 .. x_N-1. Decompose each number in powers of 2: x_i = a_i,0 * 2^0 + a_i,1 * 2^1 + a_i,2 * 2^2 + ..... Now for 0 = j, look at the sums a_i,j, 0 = i < N. Call this sum A_j. A player wins if at the end of his turn, all A_j's are even. For the game 3464334643, we have A_0 = 4, A_1 = 6, A_2 = 6, and A_k for k > 2 is equal to 0. This means the person going second, black, wins.

4444444444 is also a win for black (this is very easy to see, black can always copy what white does). 8888800000 is a win for white - but not if he plays a8. In that case, black plays a1, resulting in 0888800000, which is a win for black.