I tried to solve this game (no removal effect, the input is the frequencies of dealt cards) and it's far from easy.
The game (both player can either bet or check, fold or call) has 4^3 * 3^3 = 1728 unique pure strategies. This can be represented by a matrix of strategy vs. strategy values (this is called a normal form game).
The first step is to eliminate strategies that are dominated by other strategies (obvious stuff like never fold an ace), this very easy to implement and reduces the game to like 1/15th of the original game.
The difficult part is to solve the rest, in fact solving any non-trivial normal form games that are larger than 2*2 requires some kind of linear programming. One of the most powerful algorithms is simplex algorithm, it's not very easy to implement, but there are multiple solvers online, so you can just plug the matrix here (http://levine.sscnet.ucla.edu/games/zerosum.htm