A Hand Best Suited

Euchre players dream of being one suited to go alone, but most of the time, they are enjoy being two suited to win a hand. Sometimes euchre players are thankful enough to have a semi-playable hand holding 3 suits.

What is normal?  How many times should a player be 1, 2, 3, or 4 suited?

There are 42,504 euchre hands a player will see. With a little help from Microsoft Excel, these hands can be dissected for further analysis.  The table below breaks downs the total possible hands a player will see with out trump being declared.  Nearly, 90% of the time, a player will be 3 or 4 suited.  Only about 1 out of every 10 hands, a player will enjoy hold a 2 suited hand or better to call trump.

4 Suited 3 Suited 2 Suited 1 Suited Total
Hands 12,960 24,840 4,680 24 42,504
Percent 30.5% 58.4% 11.0% 0.1% 100%

Those mysterious jacks seem to always complicate matters, but this time the numbers don’t really reflect it. If at any one time, trump is declared generically, players will still see a 3 or 4 suited hand nearly 90% of the time.

4 Suited 3 Suited 2 Suited 1 Suited Total
Hands 12,600 2,4890 4,980 34 42,504
Percent 29.6% 58.6% 11.7% 0.1% 100%

It should go without saying these numbers do not reflect when a dealer could improve his or her hand.

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