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        riddles >> medium >> RPS, Spock, Lizard. One player without Spock
        
(Message started by: Elegance on Sep 15^th, 2011, 7:52am)

Title: RPS, Spock, Lizard. One player without Spock
Post by Elegance on Sep 15^th, 2011, 7:52am

in the 5 choice Rock Paper Scissors type game popularised on The Big Bang Theory they introduce RPSSL with 2 additions: Spock who is defeated by paper and lizard and wins against rock and scissors; and Lizard who is defeated by Rock and scissors and wins against Spock and paper.

I'm curious, if John, who is unable to do the Spock sign, were to play this game against Gary, how often would John win, ignoring ties, assuming Gary knows John's limitation and each player were to play a perfect Game Theory strategy.

Note: this is not any kind of homework. I do not know the answer. I am just curious.

Title: Re: RPS, Spock, Lizard. One player without Spock
Post by rmsgrey on Sep 16^th, 2011, 7:40am

My immediate intuition (so definitely not a reliable answer) is that it makes no difference to the win record - no matter what Gary plays, there's still a move available to John that beats it.

If John knows Gary's best strategy, then, if that strategy has Gary play moves from the pair that loses to a given non-Spock move more often than moves from the pair that beats it, John can win more than lose by playing only that move. That puts some fairly significant constraints on Gary's best strategy...

Title: Re: RPS, Spock, Lizard. One player without Spock
Post by Hippo on Sep 19^th, 2011, 10:01am

I am sure Gary would win. I have not calculated equilibrium probabilities, but 0,2,4,6,3 is a bet against which John loses.

(Guess which bets belong to what ;))

OK optimal play for John will be 3,6,4,2,0 as well. This gives 1/15 by each game to Gary and none could improve his position. (The only change from 1/15 would be Gary playing lizard giving 4/15 of lizard probability back to John).

Coordinates are lizard, rock, paper, scisors, spock.

Title: Re: RPS, Spock, Lizard. One player without Spock
Post by Elegance on Sep 20^th, 2011, 3:44am

on 09/19/11 at 10:01:42, Hippo wrote:

Thanks

Title: Re: RPS, Spock, Lizard. One player without Spock
Post by fizyka on Sep 20^th, 2011, 12:22pm

That was one of the funniest thing that they made up in the whole "Big Bang Theory"
Me and my friends played that game on some of our lectures :)
That was sooo funny ;D

Title: Re: RPS, Spock, Lizard. One player without Spock
Post by towr on Sep 20^th, 2011, 12:42pm

on 09/20/11 at 12:22:38, fizyka wrote:

That was one of the funniest thing that they made up in the whole "Big Bang Theory"

It already existed way before "The Big Bang Theory".