optimal number of goes in game to maximize return

[jessica123]

A game has two outcomes: winning or losing. The probability of winning is 1/3 and the probability of losing is 2/3. If I win, I will receive 3 units, but if I lose, I will lose 1 unit.

I've calculated that the average rate of return on this game as 33.3%. Over time, it becomes more likely that i will recieve my 33% return. My question is this: If I play the game 1000 times, which go would give me the best bang for my buck? In other words, what is the optimal number of times Ishould play to get the best value for money?

P.S. I hope someone can help. I'd be eternally grateful!

 

[stapel]

Unless there is some manner (unstated) in which one game/round affects the next, I don't see there being any "good" number of games/rounds to play. Each new round/game has the same chance of winning as the next.

I have a feeling I'm missing something in your re-statement of the question. Please reply with the exact wording of the exercise. Thank you!

Eliz.

P.S. Welcome to FreeMathHelp!

 

[jessica123]

If you plot a graph of the situation with probability of getting 33% return on the y-axis(scale 0 to 1) and No of goes on the x-axis(scale 0-1000), it would produce a sigmoid like fuction(http://en.wikipedia.org/wiki/Sigmoid_function) with the optimal number being at the point of inflection but i want to know how do i find that point!

Thanks for your reply Eliz

P.S. The question was verbally given at work, i apologize for my
poor interpretation

P.P.S. But I feel very welcome thanks

 

[JakeD]

If you plot a graph of the situation with probability of getting 33% return on the y-axis(scale 0 to 1) and No of goes on the x-axis(scale 0-1000), it would produce a sigmoid like fuction(http://en.wikipedia.org/wiki/Sigmoid_function) with the optimal number being at the point of inflection but i want to know how do i find that point!

Thanks for your reply Eliz

P.S. The question was verbally given at work, i apologize for my
poor interpretation

P.P.S. But I feel very welcome thanks

If you play \(\displaystyle \L 3n\) times, you will get exactly a 33 1/3% return if you win \(\displaystyle \L n\) times. The probability of this is the binomial \(\displaystyle \L P(n) = { 3n \choose n } (1/3)^n (2/3)^{2n}\). \(\displaystyle \L P(n)\) does not look a sigmoid-like function to me, but suppose it is. In what sense is a point of inflection of this function optimal? How are you measuring "bang for the buck" or "value for the money"?