This thesis delves into the complex card game of euchre in an effort to display the mathematics behind the game. There are two major elements of euchre where the mathematics will be explored. The first is the shuffling of the 24 cards in the euchre deck. This will entail using normal distribution along with the random number generator and matrix multiplication. The final aspect will be to model how a given hand will be played out assuming the players understand how to play. This will be done using a Monte Carlo system, as there are too many possible ways to play to feasibly model them all. Therefore, the Monte Carlo system will allow the modeling using the random function and one hundred thousand iterations, without contemplating theoretically every possible combination of how the hands could be played.