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#1
08-06-2005, 05:39 AM
 Izverg04 Member Join Date: Mar 2004 Posts: 55
Random walk question

What average number of fair coin flips does it take to lose N bets?
#2
08-06-2005, 06:50 AM
 SumZero Member Join Date: Jul 2004 Posts: 73
Re: Random walk question

[ QUOTE ]
What average number of fair coin flips does it take to lose N bets?

[/ QUOTE ]

The expected number of flips of a fair coin to lose N bets is 2N.

But I suspect based on the subject you meant what is the expected number of flips to be -N bets in a running total of equally sized bets about flips of a fair coin. For large M number of flips the expected value of the absolute value of the running total is around sqrt(2M/pi). For smaller M the expected value of the absolute value is ((M-1)!!)/((M-2)!!) when M is even and ((M!!)/((M-1)!!)) for M being odd. Of course half the time the distance is positive, so this may not be quite what you are looking for.
#3
08-06-2005, 07:13 AM
 BruceZ Senior Member Join Date: Sep 2002 Posts: 1,636
Re: Random walk question

[ QUOTE ]
What average number of fair coin flips does it take to lose N bets?

[/ QUOTE ]

If you play until you lose N bets or bust your opponent, the average duration is N*(opponent's bankroll). If your opponent is infinitely wealthy so he can't be busted, then the average duration is infinite.

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