Tuesday, December 19, 2006

Should you count on your euchre partner to win one?

You often hear the euchre advice that you should "count on your partner to win one." Ever wonder why this should be or whether it's even true?

We can find the answer by looking at the euchre point ordering strategy. The point system is derived from euchre probabilities. That is the chances that a card will win a trick. We can only approximate these probabilities because it is highly dependant on the other cards at the table. However, by simulating a large number of hands we can see patterns start to emerge. For example, an off-Ace (in the Next suit) will win about 44% of the time. In a green suit it is about 50% of the time that an Ace wins.

Now, if we can figure out the average value for any card by taking the average of all the probabilities. This turns out to be about 24.8%.

Since you have 5 cards in your hand, you can simply multiple that probability by 5 to get the average expectation. This turns out to be about 124%. Therefore, you should expect the average euchre hand to win 1.24 tricks thus this validation of the idea that you should "always count on your partner to win a trick."

Of course, this is all very rough mathematics. It is quite variable in any specific case. For example, if your hand is better than average someone else's hand will be worse than average and will not be able to win a single trick.

So, if your partner doesn't happen to win her trick don't be too hard on her. Sometimes you're on the wrong side of average.

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