
Re: (difficult)Theoretical gambling puzzle (solution?)
Posted:
Jul 25, 2006 8:09 AM


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, JoÃ£o 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

