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Re: (difficult)Theoretical gambling puzzle (solution?)
Posted:
Jul 25, 2006 8:09 AM
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Hi,
Very fun problem!
My strategy gives an expected gain of
805867616040669 / 281474976710656 = 2.863016903...
Small numbers of cards can be checked by hand (P is a +1 card, N is a -1 card).
1+1 cards:
P: stop => 1 (1/2)
N: continue => NP 0 (1/2)
=> 1/2
2+2 cards:
P: continue =>
PP: stop 2 (1/4)
PN: continue =>
PNP: stop 1 (1/8)
PNN: continue => PNNP 0 (1/8)
N: continue =>
NP: continue =>
NPP: stop 1 (1/8)
NPN: continue => NPNP 0 (1/8)
NN: continue => NNPP 0 (1/4)
=> 3/4
-- Eric
At 03:00 25/07/2006, João Pedro Afonso wrote:
>Hi to all.
>
>Nigel wrote:
> > You have 52 playing cards (26 red, 26 black). You
> > draw cards one by one. A red card pays you a dollar.
> > A black one fines you a dollar. You can stop any time
> > you want. Cards are not returned to the deck after
> > being drawn. What is the optimal stopping rule in
> > terms of maximizing expected payoff? Also, what is
> > the expected payoff following this optimal rule?
>
> As I said in the previous post, I think I
> achieved the solution for this problem. This is
> a very interesting puzzle and I don't want to
> spoil the solution for anybody in case I'm
> right, so, for now, I'll only present the expected value for my strategy:
>
> E[v]= 1269479634238379/495918532948104 =
>
> ~ 2.55986...
>
> Can someone confirm this value or present a best one?
>
>
> Cheers,
>Joao Pedro Afonso
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