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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 26, 2006 7:42 AM

Hi,

Here are the initial values given by my method:

2+2 => 2/3
3+3 => 17/20
4+4 => 1
5+5 => 47/42
6+6 => 284/231
7+7 => 4583/3432
8+8 => 18457/12870
9+9 => 74131/48620
10+10 => 26995/16796

-- Eric

At 08:13 26/07/2006, JoÃ£o Pedro Afonso wrote:
>Hi Eric,
>
> My method is very similar to yours (but not
> exactly equal) and I don't understand why it
> doesn't give the same values, yet. But I
> didn't found any problems in the reasoning, so,
> maybe the small diferences are significative
> and you have a better stop criteria. Can you
> send the expected values for 2+2, 3+3, and 4+4.
> To 2+2, it is easy to see it must be 2/3.
>
>
> Cheers,
>Joao Pedro Afonso
>
>
>Eric Wrote:

> > Hi again and again :-)
> >
> > Well, maybe I should stick to geometry...
> > My current value is 2.6244755... (seems to converge
> > towards yours :-)
> >
> > I assumed that the expected gain E(P,N) depends only
> > on the quantities
> > of red (P for positive) /black (N for negative) cards
> > remaining in the deck.
> >
> > E(0,N) is N (no more positive, stop now)
> > E(P,0) is 0 (no more negative, draw all remaining
> >
> > In the general case, we compare the current gain S =
> > (N-P) if we stop now
> > to the expected gain if we continue C =
> > E(P-1,N)*P/(N+P) + E(P,N-1)*N/(N+P).
> > Here I have a little doubt about the probability of
> > picking a P or a N, then
> > E(P,N) = max(S,C)
> >
> > -- Eric
> >
> > At 12:39 25/07/2006, Joao Pedro Afonso wrote:
> >

> > > Hi Eric, :-)
> > >
> > > I think you escaped from a good one. Now I have

> > > mapple script, but look what I was preparing to
> > send in reply to
> > > your first message, in the moment it arrived to the
> > MathOrg (where
> > > it is probably waiting now for the moderators
> > approval):
> > >
> > >:-)
> > >
> > >Eric Bainville wrote:

> > >>Hi,
> > >>Very fun problem!
> > >>My strategy gives an expected gain of
> > >>805867616040669 / 281474976710656 = 2.863016903...

> > >
> > > Grrrr! Your expected gain is bigger than mine!!!
> > >-(
> > >

> > >>Small numbers of cards can be checked by hand (P is
> > a +1 card, N is
> > >>a -1 card).
> > >...
> > >>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

> > >
> > > Hufff! Look careful the way you are doing your

> > probabilities. :-)
> > >
> > >
> > > 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