Metagame analysis - Match Win % - Gambling and Probability

Two Plus Two Forums Other Topics Probability

Metagame analysis - Match Win %

Post Reply Subscribe

...

10-18-2010 , 12:52 PM

qeloton

centurion

Join Date: Jan 2008 Posts: 127

I'm making an excel spreadsheet for a friend and I realized how horribly rusty I am at basic probabilities.

Problem:

3 games in a match. Best 2 of 3. Each game has a different win%.

Just gonna refer to the games as g1, g2, and g3.

What is the probability that you'll win at least 2 games?

The example that I was asked was:

g1: 70% chance to win
g2: 40%
g3: 40%

Looking for a general formula where I can just plug in the changing #s for g1-3.

Thanks in advance.

Quote

10-18-2010 , 02:57 PM

halftilt

veteran

Join Date: Jul 2010 Posts: 2,396

What are the ways in which you can win at least two games? (I.e., what sets of games can you win in order to win at least two games?)

For each of those, what is the probability? (You must find the probability of winning each game that is won in that set, and also losing each game that is lost.)

Quote

10-18-2010 , 03:45 PM

qeloton

centurion

Join Date: Jan 2008 Posts: 127

The match is best of 3 so it could be:
WLW
LWW
WWX 3rd game isn't played

and thats in order of g1,g2,g3.

Your chance of winning each game doesn't change based on previous wins/loses so chance of winning the games are:

g1: 70% chance to win
g2: 40% chance to win
g3: 40% chance to win.

I hope thats all the info needed to get a % chance to win the hole match.

Quote

10-18-2010 , 05:01 PM

Sherman

Carpal \'Tunnel

Join Date: Jun 2005 Posts: 7,766

Yes, but it is really:

WLW
LWW
WWL
WWW

for all possible combinations of "at least 2" wins.

To compute the probability of each of these sequences occurring, you just multiply the probability of winning each one:

WLW = .7 * .6 * .4 = .168
LWW = .3 * .4 * .4 = .048
WWL = .7 * .4 * .6 = .168
WWW = .7 * .4 * .4 = .112

Adding up these four probabilities we get the final probability of winning at least 2 out of 3 games:

.168 + .048 + .168 + .112 = .496.

Quote

10-18-2010 , 05:14 PM

qeloton

centurion

Join Date: Jan 2008 Posts: 127

Appreciate it!

I was trying to do something where I was multiplying by the # of combos...felt wrong-ish

Quote

Post Reply Subscribe

...