*edit: finding the optimal value, not maximum
I've been investigating the optimal strategy for bluffing in a simplified version of poker with only five card 10, J, Q, K, and A. I think this is referred to as a Nash Equilibrium. Player 1 can choose whether or not to bet, and Player can choose whether or not to call, which are the probabilities b and c (with subscripts for each card). Trying to find the expected value gives me the following:
$$E(Player 2)=0.05(c_J (3b_T-b_Q-b_K-1)+c_Q (3b_T-3b_J-b_K-1)+c_K (3b_T-3b_J-3b_Q-1)-5b_T-3b_J-b_Q+b_K)$$
Of course, these are probabilities so they are all constrained to between 0 and 1 inclusive. I want to know how it would be possible to find the maximum value from the function. If it is not feasible or would take far too much work, some assumptions can be made to reduce the variables to (realistically) 4 or 5.
A bit more explanation on the game and idea behind this can be found here: https://plus.maths.org/content/bluffing-and-exploitation-introduction-poker-maths, however their example uses only three cards in which the function has only two variables; this can be modeled with a 3D graph (obviously not possible in my case with several more variables).
Thanks in advance for any input.