## Tuesday, October 24, 2006

### Ruffing the leader - euchre end-play strategy

There was an interesting question posed in the Euchre Science group that prompted me to do a little mathematical figuring to come to an answer. It involves the following scenario that comes up often in euchre.

Scenario
Your side has ordered it up.

You need to win the last two tricks to make either a sweep or to prevent a euchre.

The first three tricks have been played and your partner was good enough to win the last trick with a trump. Now, you have the lone trump remaining and you also have a King of an off-suit that has yet to be led.

Your partner leads an off-suit King of another suit that was never led. The opponent on your right follows with the Queen of that suit.

Now it's your turn to decide, should you ruff (play trump) or should you play your off-suit King and hope that your partner's King will win the trick?

Mathematics
To find the answer you need to figure out the probability of two events and do the one that has the highest chance of winning.

Event 1: Letting your partner's King win the trick.

To figure out the chances in this case, let's review the overall situation at trick 4.

Your partner has 1 card left
Your right hand opponent has 1 card left
You have 2 cards left
Your left hand opponent has 2 cards left
The talon (kitty) has 3 unknown cards

There is only 1 card that can beat your partner's king.

There are 5 unknown cards that are relavant (2 in left hand opponent's hand and 3 in the talon)
There is a 40% chance that the Ace lies in left hand opponent's hand and a 60% chance it's in the talon.

So, mathematics would say if you let it go you have a 60% chance or winning and a 40% chance of losing.

In this situation everyone has 1 card left.

You, the off-king of a suit that hasn't been led
Left and right opponents - 1 card
Partner - 1 card
Talon - 3 unknown cards

Again, your opponents have 2 chances to hold the card and the talon has 3 chances. We assume your partner doesn't have the Ace else he would've led it.

That means the chances of you winning with the King is 60%. And the chances of you losing is 40%.

Bottom line...Mathematically, there is no difference. However, if you can pick up on some psychological clues about who might be holding a high card, then you can adjust your play accordingly.

That's all for today from The Euchre Universe.
Sorry about the sparse posts, I've been training hard and focusing on my efforts to joggle the Chicago Marathon