Timeline for A Nim game variant
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 18, 2011 at 13:37 | comment | added | Jean-Pierre | Thank you for your comments. Quantumelixir said:"the first player will always win ". Are you sure? For example: How do you play and win if you are the first player and have to play the position (2,2,1)? | |
| Apr 18, 2011 at 7:31 | history | edited | quantumelixir | CC BY-SA 3.0 | gap in proof |
| Apr 18, 2011 at 4:30 | history | edited | quantumelixir | CC BY-SA 3.0 | updated answer to reflect changed question |
| Apr 18, 2011 at 4:24 | comment | added | quantumelixir | Well, in that case too, the first player will always win but for a different reason. See the updated answer; hope this helps answer your question. | |
| Apr 17, 2011 at 22:30 | comment | added | Jean-Pierre | In this problem, only one in the game, a player may pass his turn. There is only ONE pass available for BOTH players .Once one player has passed, no other player can pass. For example, if I give my opponent the position (1,1), if my opponent -uses the PASS, I let him with (1) and I win -plays (1), I use the PASS and I win Other example, if I give my opponent the position (2,2,1), if my opponent: -uses his pass, I let him with (2,2) and I win -plays (2,2), I pass and I win -plays (1,2), I let him with 1 and I win -plays (1,2,1), I give my opponent the position (1,1) and I win | |
| Apr 17, 2011 at 17:54 | comment | added | quantumelixir | I've divided the set of positions into winning and losing ones and from that the conclusions regarding the variants with a pass move follow. I don't understand why my conclusion is not true for the reason I give. (You can check my previous edit for this question where I explain the strategy, which is the same as the one pointed out by @thomas-andrew above later) | |
| Apr 17, 2011 at 17:44 | comment | added | whuber | "Zero-sum" is not a relevant adjective for this game. We're really working with Conway/Berlekamp/Guy's partizan games. A pass gives a move to one side, to be sure, but this guarantees a win only when the value of the game for that person was already greater than -1. Because the values of Nim are extremely close to 0, your conclusion is indeed true, but not for the reason you give. | |
| Apr 17, 2011 at 16:22 | history | edited | quantumelixir | CC BY-SA 3.0 | correct definition |
| Apr 17, 2011 at 16:02 | history | answered | quantumelixir | CC BY-SA 3.0 |