I have the following problem: Suppose I have a 10 level game. You start at level 0, your direction is upwards (this will be of importance later). At each timestep you can ascend or descend a Level. The probability of you going into the direction you are currently heading is T. The probability of you going into the opposite direction you are heading is (1-T), in this case you swap directions. You win if you reach level 10, game over when you "reach level -1".
I am now interested in distribution of the players winning the game by timx x: How many of k players do win the game in 10 steps of time, how many in 11, in 42, ...
I thank everyone of you tries to help me! Cheers Rucki
