Timeline for Algorithm on winning strategy of Winner (Simplified card game)
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2012 at 23:45 | comment | added | Barry Cipra | @Zsban, if A holds 1,2,3 and B holds 1,2,4 (and you're starting the game at 0), then A can win by playing 2, but loses if he plays 3. | |
| Jan 31, 2012 at 18:49 | comment | added | Zsbán Ambrus | Is it ever worth not to play the highest card you have when the rules allow you that? | |
| Jan 31, 2012 at 3:28 | comment | added | user20948 | @Barry Cipra: I only meant that the game is finite. @Guilaume Brunerie: I think that it's not obvious that if the player has cards to play, the decision of pass will be worse. I'll rewrite the problem more formal. | |
| Jan 30, 2012 at 16:34 | comment | added | Guillaume Brunerie | @Barry Well, yes B should play his 2, but passing is not better than playing 1 (if B pass or play 1, A will always be able to play 2 and win). I’m not saying that you should always play your smallest card, but that it cannot be worse than passing. | |
| Jan 30, 2012 at 14:57 | comment | added | Barry Cipra | @Guillaume, it's not quite true that it's "always" better to respond to a pass by playing your smallest card. Suppose A and B are both holding a 1 and a 2. If A (foolishly) passes, then B should play his 2, not his 1. But I think the basic principle is correct: You should always play something (if you can) rather than nothing. (@Frank, I wasn't suggesting a scenario where one player always passes no matter what the other player does. I was suggesting the conceivability of a scenario where the first player to make an active move loses.) | |
| Jan 29, 2012 at 15:26 | comment | added | Guillaume Brunerie | @Barry Cipra : If one player pass, it is always better for the other player to play its smallest card than to pass | |
| Jan 29, 2012 at 2:29 | comment | added | user20948 | Thanks. Because it is finite with perfect information, the game is determined. I think that it is a mathematical game. Not like chess, which is also a finite game with perfect information, my game seems to be easier. I want a analysis of the game to find out an effective algorithm to the game, as Nim is solved (en.wikipedia.org/wiki/Nim). There's another case that we can prove it to be NPC for $n$. (en.wikipedia.org/wiki/…) Barray Cipra: If one player wants to throw "pass" forever, the other one can win. | |
| Jan 28, 2012 at 13:02 | comment | added | Barry Cipra | It's not a hundred percent clear (to me) that this game doesn't admit situations where each player's only way of avoiding a loss is to throw the game to the other player -- i.e., situations where the game toggles back and forth between $w(0,A,B)$ and $w(0,B,A)$ and never ends. | |
| Jan 28, 2012 at 12:41 | comment | added | Guillaume Brunerie | I updated my answer. | |
| Jan 28, 2012 at 12:41 | history | edited | Guillaume Brunerie | CC BY-SA 3.0 |
Added the case when both player know both hands
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| Jan 28, 2012 at 8:08 | comment | added | user20948 | Thanks. I meant that when the player received a situation, he not only knew the set $A$ which meant his cards but also knew the set $B$ which meant the other player's cards. As I've written in the postscript in the text, $B$ is known to the player. In other words, either player always knows the cards in his hand and in the other player's hand. Thank you for your comment. | |
| Jan 28, 2012 at 7:37 | history | answered | Guillaume Brunerie | CC BY-SA 3.0 |