Re: Betting on {0,1} strings ... game theory ?

On Mar 2, 2:48 am, olegtsodi...@xxxxxxxxx wrote:
I may be wrong, but if you bet 1/2 of your money every time than on
average you are multiplying your money by p/2, where
1/p (>1/2) is your ratio. In the long run then, you should be
infinitely rich! This is by no means rigorous, but see if it is still
correct.

You mean bet half your money on zero every time? I don't think that
will work - not in general anyway. If the amount of money you have is
x then a loss takes you to x/2 and a win to 3*x/2. If you consider the
evolution of log(x) then a loss subtracts log(2) and a win adds
log(3/2). If I did my sums correctly then this will in the long run
cause x -> oo only if the probability of a zero is greater than log(2)/
log(3), or about 0.63. If 1/2 < prob. < log(2)/log(3) then x will tend
to zero.



On Mar 1, 1:39 pm, "Bart" <qjohnny2...@xxxxxxxxx> wrote:



Suppose you have an infinite {0,1} sequence where (number of zeros /
number of ones ) approaches a number greater than 1/2 as the sequence
gets longer and longer. ( Limit Exists and is greater than 1/2 ).

Is there a strategy to make money without bound by starting with $1
and betting on the next digit to appear in the sequence. You only
know the initial values of the sequence and must bet on whether next
digit is a 0 or a 1, you can bet any amount that you have in your
pocket or $0 if you choose. You can bet fractional amounts or any
real number amount as long as you have money. Also you can't go
negative or borrow money or anything like that.

I thought about betting 1/2 and halving bet each time you lose - this
will guarantee you will never go to $0 but I don't think it gurantees
you make money without bound.

Is there a strategy where as n->inf the sup{ max money in pocket since
start of game}->inf ?- Hide quoted text -

- Show quoted text -


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