/sci/ - Science & Math

>>11672870
Essentially, the geometric sum is *almost correct*, but you forgot to account for permutations (or multiple routes, so to say).
So there's a [math]0.5^3[/math] chance of it finishing in three steps, that's correct, because the route is unique.
But there are quite a few routes for it finishing in five turns. It can start with a ball going from A to B, and then B gives A four balls in a row, which has [math]0.5^5[/math] probability of happening, or B can give A a ball, A gives a ball back, and then B gives all three of its balls to A, which also has [math]0.5^5[/math] chance of happening, and so on.