Variations by Player Count
Euchre is a four-player partnership game, but it adapts. The common adaptation is three-handed Cutthroat, which keeps the trick-taking and the bidding and drops the fixed partnership.
Standard (Four-Player)
Two teams of two, sitting across from each other. Each hand one team names trump and must take at least three of the five tricks to score, and the first team to 10 points wins. Documented in full on the euchre rules page.
Cutthroat (Three-Player)
No partners. Each hand the player who calls trump plays alone against the other two, who defend together for that hand only. Calling is tighter than in the partnership game, not looser: you need three tricks with nobody to supply one, so the hands that are worth a call are a clear step stronger. The full page covers the deal, the dealer pickup that matters more here than at four, scoring (including where tables disagree on the march and euchre payouts), and strategy for calling and defending.
Bidding Modifications
These change how trump gets chosen, usually to kill the dead hand that results when everyone passes through both rounds.
Stick the Dealer
If the second round reaches the dealer with nothing named, the dealer cannot pass and has to name a suit whatever they are holding. No hand is ever thrown in, and a small positional disadvantage lands on whoever is dealing. The full page covers the mechanics, which way each seat's bidding shifts, and what to name when you are the one stuck.
Redeal Rules
These throw a hand back when the cards are too weak to play. The two forms set different thresholds, and many tables run both.
Ace No Face
A hand holding exactly one ace and four cards below the Jack is thrown in and dealt again by the same dealer. The hand is technically playable, which is why the rule has genuine detractors. The full page covers what qualifies, how often it comes up, and the argument on both sides.
Farmer's Hand
A hand of nothing but 9s and 10s, with no ace and no face card, is thrown in and dealt again by the same dealer. The most widely accepted of the redeal rules, and the rarest trigger, at roughly one deal in 759.
Combining Rules
They stack. Stick the Dealer solves passed-out hands, and the redeal rules solve dealt-but-weak ones, so the two categories never collide. All three work in Cutthroat without modification.