Two Plus Two Older Archives  

Go Back   Two Plus Two Older Archives > General Gambling > Probability

Reply
 
Thread Tools Display Modes
  #1  
Old 08-06-2005, 05:39 AM
Izverg04 Izverg04 is offline
Member
 
Join Date: Mar 2004
Posts: 55
Default Random walk question

What average number of fair coin flips does it take to lose N bets?
Reply With Quote
  #2  
Old 08-06-2005, 06:50 AM
SumZero SumZero is offline
Member
 
Join Date: Jul 2004
Posts: 73
Default 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.
Reply With Quote
  #3  
Old 08-06-2005, 07:13 AM
BruceZ BruceZ is offline
Senior Member
 
Join Date: Sep 2002
Posts: 1,636
Default 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.
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT -4. The time now is 08:09 PM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, vBulletin Solutions Inc.