Tuesday, March 13, 2007

The ultimate euchre equation

Euchre is a finite game. That is to say there are a limited number of situations that one will face. In fact, there are only 42,504 unique euchre hands possible. (combination of 24 things taken 5 at a time).

Because of this, euchre is a game that can succumb to the rigors of mathematics and game theory. The point system for evaluating your euchre hand that we use here in the Euchre Universe relies on the finite nature of the game to work.

It is interesting to note that any strategy you use in euchre can be described by one equation, The Ultimate Euchre Equation. If someone can figure out all the factors in this equation than the perfect euchre strategy can be created. The perfect strategy would be the one that results in the highest value for the equation.

Here is the The Ultimate Euchre Equation.

Expectation = 4 x p1 + 2 x p2 + 2 x p3 + 1 x p4 - 4 x p5 - 2 x p6 - 2 x p7 - 1 x p8

p1 = Probability of scoring a loner
p2 = Probability of marching
p3 = Probability of euchering opponents
p4 = Probability of making your point
p5 = Probability of opponents scoring a loner
p6 = Probability of opponents marching
p7 = Probability of opponents euchreing you
p8 = Probability of opponents making their point

Figuring out the values for all the different probabilities and which strategy leads to the highest value of the Ultimate Euchre Equation is one of the main topics of this blog.


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Anonymous said...

Funnily enough I started on working on an equation to work out the probability of a Euchre game last night. I have so far worked out the odds of who has what suits and now going through bowers and all the other fun stuff. Afterwards I'll be settling an argument with my partner. Leading Trumps. T_T It's going to be a long haul.