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Topic: RPS, Spock, Lizard. One player without Spock (Read 1438 times) |
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Elegance
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RPS, Spock, Lizard. One player without Spock
« on: Sep 15th, 2011, 7:52am » |
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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.
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rmsgrey
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Re: RPS, Spock, Lizard. One player without Spock
« Reply #1 on: Sep 16th, 2011, 7:40am » |
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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...
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Hippo
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Re: RPS, Spock, Lizard. One player without Spock
« Reply #2 on: Sep 19th, 2011, 10:01am » |
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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.
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| « Last Edit: Sep 19th, 2011, 12:43pm by Hippo » |
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Elegance
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Re: RPS, Spock, Lizard. One player without Spock
« Reply #3 on: Sep 20th, 2011, 3:44am » |
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on Sep 19th, 2011, 10:01am, Hippo wrote: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. |
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Thanks
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fizyka
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Re: RPS, Spock, Lizard. One player without Spock
« Reply #4 on: Sep 20th, 2011, 12:22pm » |
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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 
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fizyka , karta wzorów fizyka , książki z fizyki
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towr
wu::riddles Moderator
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Re: RPS, Spock, Lizard. One player without Spock
« Reply #5 on: Sep 20th, 2011, 12:42pm » |
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on Sep 20th, 2011, 12:22pm, fizyka wrote:| That was one of the funniest thing that they made up in the whole "Big Bang Theory" |
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It already existed way before "The Big Bang Theory".
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