Game Theory number of ways to win in a sequential game

26 Views Asked by At

two players start with a and b points. In each set of the game, they can score a point from -k to k (both including). if s set are played, the number of ways the first player can win the game.

So in every set there are 4*k^2 ways, for example in the first set point can end up in for the first player [a-k, a+k] and for second player [b-k,b+k]