Saturday, February 04, 2006

More on points

Euchre QOD: Count on your partner for 1 trick…shoot him if he doesn’t get it.

I once read a book by John McGervey called Probabilities in Everyday Life. This is a great book and ever since then I try to find any excuse to figure out probabilities. I also now use a coin flip to make decisions whenever I’m uncertain.

Anyway, using some of the principals in that book I tried to figure out the most mathematically sound strategy for euchre. The point system was the result.

To figure it out, I created a computer program that played euchre. At first, I made all the players follow the Pinochle rule that if you can win a trick, you have to win the trick. The computer then played 10,000 games and kept track of all the times that each card won.

For example, the Right bower won 100% of the time. Since it’s the highest card it never loses.

The Left bower won about 70% of the time. It can only get beat by the Right bower and that is only if it is in someone else’s hand.

It turns out that the Ace of trump wins about 60% of the time, the King 50%, etc.

I figured that you could use these probabilities to figure out the value of your hand. To make it a little easier, I just divided everything by 10. So, the Left bower is worth 7 points because it has a 70% chance of winning. The Ace of trump is a 6 because it has a 60% chance of winning.

Cards that are worth 0 points had a probability of winning that was less than 10.

The nice thing about this experiment is that it verified that the strong suit off-Aces were worth more than the weak suit off-Ace. The former win about 50% of the time while the latter win about 40% of the time.

Why 21?

The thing about the point system is that the number of tricks you might expect to win can be figured out by further dividing your points by 10. So, if your hand adds up to 30 points, you could expect to win 3 tricks. When your hand adds up to 21, you can expect to win 2.1 tricks. The more points you have, the more tricks you’re likely to get.

There’s an old adage in euchre that says you should count on your partner for 1 trick. So, if you can get 2.1 tricks, your partner gets 1, you’ve got it made.

It turns out in my euchre simulator, 21 points was the lowest number of points you want to have in order to guarantee that you and your partner win 2 out of every 3 times you order it up. Next time, we’ll see why 2 out of every 3 times is important.

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