
Re: (difficult)Theoretical gambling puzzle
Posted:
Jul 23, 2006 4:37 AM


wrote Nigel: > I have the solution to a puzzle i've been working on > for a while that i think you might like: > > 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?
Hi Nigel!
VERY nice problem. Beautiful with unexpected surprises. I think I have found yesterday an optimal strategy too, but it is going to be computational intensive, either to play it, either to calculate the expected values, unless there are another big surprises ahead. I still have to program it, so, don't put already your solution in the site, please.
It's a shame we don't have some kind of simulator at hand (at least, I don't know none) capable of be programmed with player strategies, to test the ideas. I don't think this is the kind of problem we are going to be totally convinced, by looking at the candidate solutions. If we reach that stage of discussion, I can do one (unless other want to do that). We could do some nice contests like that.
> whilst you're there any help with #s 1&2 wouldn't go > amiss ;)
I didn't have the courage to see any solution yet (first I have to solve them). Are you saying that what is in the "solution" page is not the solution yet?
Cheers, Joao Pedro Afonso

