Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: (difficult)Theoretical gambling puzzle
Replies: 29   Last Post: Jul 31, 2006 5:54 AM

 Messages: [ Previous | Next ]
 Eric Bainville Posts: 10 Registered: 12/6/04
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

Date Subject Author
7/21/06 nigel
7/21/06 Mary Krimmel
7/21/06 João Pedro Afonso
7/21/06 Earle Jones
7/23/06 João Pedro Afonso
7/24/06 Earle Jones
7/24/06 João Pedro Afonso
7/23/06 João Pedro Afonso
7/24/06 João Pedro Afonso
7/25/06 Eric Bainville
7/25/06 João Pedro Afonso
7/25/06 Eric Bainville
7/25/06 João Pedro Afonso
7/26/06 Eric Bainville
7/26/06 João Pedro Afonso
7/26/06 Eric Bainville
7/25/06 Eric Bainville
7/25/06 cuthbert
7/25/06 João Pedro Afonso
7/26/06 cuthbert
7/26/06 João Pedro Afonso
7/31/06 cuthbert1
7/25/06 Eamon
7/25/06 Eamon
7/28/06 João Pedro Afonso
7/28/06 mark
7/28/06 João Pedro Afonso
7/28/06 mark
7/28/06 João Pedro Afonso
7/28/06 mark