Spoiler for It's easier than that.
Well then, I hope Morty's is very, very spacious, or that most of Davey's friends are very, very small! :P
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Posted 05 August 2008 - 06:55 PM
Spoiler for It's easier than that.Davey just gathers 52C26 of his drinking buddies - he's been drinking for a while - and has each of them bet a different one of the 52C26 possible red-card distributions. They agree to work for half their earnings. That is, the winner splits his take with Davey, the others just drink and play.
Davey and one of his buddies get about $4, Alex gets $1,
and Morty's closes at the normal time.
Posted 13 August 2013 - 10:55 PM
Starting with r reds and b blacks, the expected return is
V(r,b) = 2r+b/(r+bCr)
Note that this satisfies
V(r,b) = (r/r+b)*V(r-1,b) + (b/r+b)*V(r,b-1)
Therefore V is a martingale! This means that ANY rational strategy will yield the same expected return. 'Rational' here just means never betting on the rarer colour, and always betting everything when only one colour remains.
Moreover, there exists a risk-free strategy of always betting a proportion (r-b)/(r+b) of current wealth (or likewise (b-r)/(r+b) if there are more blacks remaining), such that one is GUARANTEED a return of $9.08.
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