How Many Euchre Hands are There?

Euchre’s popularity is driven by the game’s simplicity.  After all, euchre only uses 24 cards instead of a standard 52 card deck.  Despite the vastly reduce number of possible card combinations, euchre is every bit as difficult to master as any 52 card game.

In Euchre, every player gets 5 cards, and by doing a little math, there are 42,504 possible combination that any one player will hold in their hand.

(24*23*22*21*20)/5! = 42,504

That 42,504 is not very big.  In fact that number could be simplified down, because the 4 suits tend to repeat themselves. Despite the simple number, euchre players still debate if one should call a hand.

What About the Up-card?

Many euchre players consider the dealer to hold 6 cards because of the up-card.  Not to mention, the up-card is very instrumental to any player declaring trump.  With a little bit more math, there are 134,596 possible combinations that any one player will see including the up-card.

(24*23*22*21*20*19)/6! = 134,596

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