[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

What about conditional probability?

Posted By: bob koca
Date: Tuesday, 25 March 2008, at 5:26 p.m.

In Response To: What about conditional probability? (Chuck Bower)

The chance of reaching 1 away 1 away after losing the first match is exactly the same as the equity lost by turning a win in the first match into a loss (17.6% to the first d.p..)

There are two ways to look at how much the error affects your match win% (at the time of its occurrence). Both involve realizing that stopping when someone reaches 11 wins and playing the full 21 games and seeing who has more wins are probabilistically equivalent.

1) (This is how I originally calculated the .176) After losing the first match your equity is P(X >= 11) where X is binomial with 20 trials and .5 success probability. The equity lost is twice the difference of .5 and that amount. This gives 2(.5 - .412) = .176

2) a) Suppose that after losing the first match that in the next 19 games you win 10 making the score 10 - 10. This happens with probability .176. If the first game is switched into a win you would now have already won the match instead of needing to win the last game. This saves 1/2 of the .176.

b) Now suppose that after losing the first game that in the next 19 games you win 9 making the score 9 - 11. This also happens with probability .176. If the first game is switched into a win you now have a chance to win the match instead of losing for sure. This saves the other 1/2 of the .176. Any other score after 20 games means that the result of the first match will not swing the match winner.

Bob Koca

Messages In This Thread

 

Post Response
Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:
 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.