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Re: Simple Card Game Of Ups and Downs
Posted:
Dec 14, 2009 10:20 AM
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On Dec 14, 9:44 am, Leroy Quet <qqq...@mindspring.com> wrote:
> Is there any pure strategy to playing this game, or is it totally a
> psychological game -- trying to guess in what order your opponent will
> play their cards?
>
> By the way. More of my games (many of which are more interesting than
> this game) at:http://gamesconceived.blogspot.com/
>
> Thanks,
> Leroy Quet
Interesting game. In effect, each deal specifies a two player zero sum
game which in principle has an optimal strategy (though perhaps
mixed). Some deals make the game blatantly unfair (with the extreme
case of one player getting the top half of the deck).
Suppose that player 1 recieves cards 1,3,5, ..., 2n-1 and player 2
recieves cards 2,4,...,2n. It is obvious that any pure strategy that
player 1 adopts is defeated by one of player 2's (the one in which
player 2 happens to always play the successor of the card that player
1 plays - this assures player 2 will get at least n of the 2n-1 total
points. It is irrelevant that player 2 is unlikely to know what this
strategy actually is - its existence demonstrates that player 1 has no
optimal pure strategy). Player 1 can almost do something similar to
player 2 - but not quite since their 1 always loses and player 2's 2n
always wins when placed down. Thus most pure strategies of player 2
are defeated by some strategy of player 1. I suspect that all of
player 2's are defeated by at least 1 of player 1's (at least for n
sufficiently large) - but I haven't bothered to prove it. I suspect
that this deal is (slightly) unfair to player 1. Does *any* deal lead
to a fair game?
The game reminds me of a modification to the card game war called
Napolean's War that I read about here: http://www.pagat.com/invented/war_vars.html
-scattered
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