I couldn’t find any rules for the variation of Euchre for two players anywhere on the web, so here are the rules I learned. If you’ve never played this card game before, you can read up on normal, four-handed Euchre in many places online — here are a couple:
All the cards are the same as in normal Euchre: 9, 10, J, Q, K, A of each suit.
Deal 4 face-down, 4 face-up on top of the face-down cards, and 4 in the hand to each person. The resulting table looks like this:
Euchre is a trick-taking game. The non-dealer has the opportunity to call trump or pass. If they pass, the dealer is forced to choose (like in “screw the dealer” in normal Euchre).
Once trump is chosen, the non-dealer leads normal play. To reiterate, it doesn't matter who chose trump — the non-dealer always leads. Each player must follow suit, playing from the face-up cards in front of them on the table or in their hand. When a card on the table is played, the card below it (if there is one) is turned over once the trick is complete.
There are twelve tricks to be played. To win the hand, you must take 7 of the 12 tricks. Each player gets one point for each trick they took. If the trump-caller fails to take 7 tricks, they have been “Euchred”, and the other person gets all 12 points.
The game is over when one player reaches 31 points.
Reneging. If you, or your opponent, realizes that one of you has played out of turn, played a card that they shouldn’t have, or made some other similar error, it is called reneging (it’s pronounced like renegging, with a short e or short i sound). When that happens, the player who made the mistake loses the hand immediately, and the opposing player gets 12 points. In other words, it’s the same as getting Euchred. Don’t do it!
Remember that you have cards in your hand that the other player can’t see. That sometimes will determine who wins.
Readers have informed me of many variations on the deal. Any of these will work nicely:
There's also a variation on scoring that's more like regular Euchre (where you use 2 five cards). Instead of 31 points, you play to 10 with the following point assignments: take 7 tricks, get 1 point; 8 tricks, 2 points; 9 tricks, 3 points; 10 or more; 4 points. The person who calls trump is the only one who can earn points unless he is Euchred. If that happens, the other player wins two points for that round. This scoring method doesn't require paper, which is nice, although it does require remembering something slightly more complicated than 1 trick equals 1 point.
This page has gotten a fair amount of attention from people who can't always scare up enough others to play four-handed Euchre, and while I'm glad to offer it, I've had some help.