# Average number of points and wins given a win rate.

#### quake004

##### New Member
I'm playing a game in which there is an event that I can keep playing until I reach 3 loses or 7 wins. You get points for every win. 0 wins 5 points, 1 wins 10 points, 2 wins 20 points... 7 wins 95 points.

I'd like to know given my win rate what is the average number of wins and points that I'm getting.

#### quake004

##### New Member
Ok I found the solution somewhere at least for the points. We have the probability of wining pw, and of losing pl. We get the probability of going 0-3, 1-3, ..., 7-2, 7-1, 7-0 like:
Probability of going 0-3: pw^0 * pl^3
Probability of going 1-3: pw^1 * pl^3
Probability of going 2-3: pw^2 * pl^3
Then we get the probability of getting each point by multiplying the points by the probability
Probability of getting 5 points: (pw^0 + pl^3) * 5
Then we sum all the probabilities of getting each of the points to get the average points for or win rate. Am I correct?

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#### fed2

##### Active Member
i think you is goin' to haf too use a negative binomial distribution to reckon the number of trials to your third loss. keep in mind that if the number of trials is >= 10 then you got 7 wins. the part about 'Then we get the probability of getting each point by multiplying the points by the probability' is right way to expectation/average i be thinkin tho.

keep it crunchy!

#### quake004

##### New Member
Mmm so I have to count the number of possible ways in which I can end up getting a given result? For example to go 1-3 it could be WLLL, LWLL, LLWL, LLLW. So probability of going 1-3 is 4*pw^1*pl^3?

#### fed2

##### Active Member
So probability of going 1-3 is 4*pw^1*pl^3?
Problem is that is only if there are exactly 4 trials ya know. jest googles 'negative binomial distribution' and use that formulas in excel.

You actually might be able solve it using something close to what you iz doing above, but will be more tedious.

Q: How will you know if you are right or not, once you got a solutione. Ask internet? I recommend simulation.