Two Plus Two Older Archives  

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

 
 
Thread Tools Display Modes
Prev Previous Post   Next Post Next
  #1  
Old 04-04-2003, 01:58 AM
2ndGoat 2ndGoat is offline
Senior Member
 
Join Date: Sep 2002
Location: DC Area
Posts: 147
Default creating a 2:1 shot with a fair coin

so here's a probability curiosity I've been pondering. I imagine there may be a very trivial way to do this, but I can't figure it:

You've got a *finite* number of fair coins (Pr(H) = Pr(T) = .5). Any number you like, but not infinite. How do you define a test, with any *finite* number of coin flips using any combination of the coins, that have a Pr(Success) of exactly 1/3?

Basically, I'm saying you and your buddy have a handful of pennies, and you want to create an even-money game based entirely on coin flips where one player lays the other 2:1 odds.

Obviously, to create an even-money game, one player could place two coins facing heads up, one tails, and have the other try to pick tails. But that wasn't a random coin flip. No using infinite series either, obviously one can create a situation with a Probability arbitrarily close to 1/3 by adding more coin flips and picking the binomial expiriment with the probability closest to 1/3. We're talking finite numbers here.

Is this possible? I can't get away from probabilities that are sums of powers of two, I'm starting to believe it can't be done.

Goat
Reply With Quote
 

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 08:22 AM.


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