Possibly. Do you have any additional conditions on ? For instance, is a probability? Is the number of successes and the number of failures (or replace the words successes and failures with whatever game terms make sense)? Knowing a little more of the specifics might help.
Anyway, we can start with the Binomial Theorem.
This gives you a polynomial of degree . There are many techniques for finding real solutions of polynomials. Knowing if is a probability would help generate bounds when looking for solutions. Additionally, knowing more about the problem may help generate another formula that could lead to the same solution (potentially).
Please let me know if I used any notation you don't understand.