A game has two outcomes win or lose, 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 is 33.3%. Over time it becomes more likely that i will receive my 33% return. My question is 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 i should play to get the best value for money. Ps. Any help would gratefully be appreciated,my thoughts are that a graph with probability of gething 33% return on the y-axis(scale 0 to 1) and No of goes on the x-axis would produce a sigmoidal like fuction with the optimal number being at the point of inflection but how do i find that point!