How many games of chess will it take for me to beat my friend 50 times?

[DeanCain]

[Solved] How many games of chess will it take for me to beat my friend 50 times?

I have an 86% win rate against my friend in chess.
How games of chess will it take for me to beat my friend 50 times? And what was the algorithm used to solve?

No, this is not for homework. The reason it's written like a homework question is because that's the best way I could explain it.

I need this for a program I'm creating that will tell you how many games of Hearthstone you'll need to play to achieve the golden version of selected hero.

 

[Ishuda]

I have an 86% win rate against my friend in chess.
How games of chess will it take for me to beat my friend 50 times? And what was the algorithm used to solve?

No, this is not for homework. The reason it's written like a homework question is because that's the best way I could explain it.

I need this for a program I'm creating that will tell you how many games of Hearthstone you'll need to play to achieve the golden version of selected hero.

Allowing for 'partial games', if you play 1 game, you will win 1*0.86 games; if you play 2 games you will win 2*0.86 games, ..., if you play x games, you will win 50=x*0.86 games.

 

[DeanCain]

Allowing for 'partial games', if you play 1 game, you will win 1*0.86 games; if you play 2 games you will win 2*0.86 games, ..., if you play x games, you will win 50=x*0.86 games.

Thank you VERY much! It works perfectly.

 

[Steven G]

I have an 86% win rate against my friend in chess.
How games of chess will it take for me to beat my friend 50 times? And what was the algorithm used to solve?

No, this is not for homework. The reason it's written like a homework question is because that's the best way I could explain it.

I need this for a program I'm creating that will tell you how many games of Hearthstone you'll need to play to achieve the golden version of selected hero.

Hi, I do not think that this is a valid problem. Suppose we simplify it a bit. How many times do I have to toss a fair coin in order to get 50 heads. In theory it could be 9,284 tosses. Not very likely to be that many tosses but it is certainly possible. A better question is how many tosses do I have to make in order to EXPECT 50 heads. That answer would be 100---just solve 50%*x=50

 

[pka]

I do not think that this is a valid problem.

I absolutely agree, but because it is ill-posed.
I do not see this as a closed-outcome problem.
If DeanCain means that he will be the first to win fifty matches in a series of games, then it is well-posed. The minimum is fifty games and maximum is ninety-nine( assuming no draws). The probabilities are well known: See the problem of points.

I would like to know what well-posed question was intended.

 

[Ishuda]

Hi, I do not think that this is a valid problem. Suppose we simplify it a bit. How many times do I have to toss a fair coin in order to get 50 heads. In theory it could be 9,284 tosses. Not very likely to be that many tosses but it is certainly possible. A better question is how many tosses do I have to make in order to EXPECT 50 heads. That answer would be 100---just solve 50%*x=50

Hey Jomo,

The difference in the two problems is that one is presented as a win rate and in the other it is presented as a win probability. In the 'rate' situation you have the derivative of the 'win function' is 0.86 [and assumed initial condition of 0 games 0 wins], i.e. W(n)=0.86 n. In the other situation, you don't even have a 'win function'.

 

[pka]

The difference in the two problems is that one is presented as a win rate and in the other it is presented as a win probability. In the 'rate' situation you have the derivative of the 'win function' is 0.86 [and assumed initial condition of 0 games 0 wins], i.e. W(n)=0.86 n. In the other situation, you don't even have a 'win function'.

@Ishuda. Please do point me to text material where these concepts are discussed. I must say even after teaching probability theory on several levels, I have never encountered these. What is a win rate? What is a win function?

 

[Ishuda]

@Ishuda. Please do point me to text material where these concepts are discussed. I must say even after teaching probability theory on several levels, I have never encountered these. What is a win rate? What is a win function?

The win rate was in context of the problem as stated "I have an 86% win rate against my friend in chess." Notice that this is stated as a rate which is typical word problem language for stating a derivative.

The win function is the number of wins W as a function of the games played n or, given the derivative of W [and assuming 0 wins for 0 games played] we obtain
W(n) = 0.86 n.

W(n) is the inverse function of one which can be used to answer the initial question of "How games of chess will it take for me to beat ...", i.e.
n = W / 0.86.

 

[pka]

The win rate was in context of the problem as stated "I have an 86% win rate against my friend in chess." Notice that this is stated as a rate which is typical word problem language for stating a derivative.
The win function is the number of wins W as a function of the games played n or, given the derivative of W [and assuming 0 wins for 0 games played] we obtain
W(n) = 0.86 n.
W(n) is the inverse function of one which can be used to answer the initial question of "How games of chess will it take for me to beat ...", i.e. n = W / 0.86.

Well thank you. But I did ask for an authoritative reference.
Short of having that, I must agree with Jomo: As stated this is a totally meaningless question.
Maybe as mathematicians we expect too much.

 

[Otis]

Maybe as mathematicians we expect too much.

I don't know about Jomo, but you certainly do!

 

[Ishuda]

Well thank you. But I did ask for an authoritative reference.
Short of having that, I must agree with Jomo: As stated this is a totally meaningless question.
Maybe as mathematicians we expect too much.

O.K. You didn't say by whose authority so I feel free to use my own. There is a little known text by Ishuda which states in its entirety "Everything Ishuda says is correct unless, of course, it isn't. However, even then, it may be partially correct but then again, maybe not."

If you like, you can quote me.