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Euchre statistics and odds

How often the good hands and the terrible hands really come along, where a missing bower is likely to be, whether your ace will hold up, and a few numbers from the game's history.

The odds on this page were counted across all 42,504 possible hands, then checked by shuffling a virtual deck two million times. Unless it says otherwise, each one is the chance for one player on one deal, before anybody bids. New to the terms? Read the rules and what the terms mean.

The deck

Twenty-four cards sounds small, but there are 124,672,148,625,024 ways to deal four hands and a kitty. If you dealt one new table every second without stopping, you'd need about 4 million years to get through them all.

Calling trump changes the size of the suits. The left bower moves over, so trump has 7 cards, the other suit of that color has 5, and the two suits of the other color keep 6 each. That means 7 of the 24 cards are trump, and an average hand holds about one and a half of them.

Good hands

Dealt to you	Chance	About 1 hand in
At least one jack	63.5%	2
The right bower of a suit you name	20.8%	5
Both bowers of one suit, any suit	7.2%	14
Both bowers of a suit you name	3.6%	28
Five trump in one suit, any suit	0.2%	506
All four jacks	0.05%	2,125
All four aces	0.05%	2,125
The perfect hand: right, left, ace, king and queen of one suit	0.01%	10,626

The perfect hand can't lose a trick if you call that suit, but don't wait up for it. At a hand every few minutes, most players will never see one dealt.

Bad hands

Dealt to you	Chance	About 1 hand in
No aces	36.5%	3
No jacks and no aces	10.3%	10
No jack, queen or king	1.9%	54
Ace, no face: one ace and four 9s or 10s	0.66%	152
Farmer's hand: nothing but 9s and 10s	0.13%	759

If your club allows a redeal on either of the last two, somebody at the table will hold one about once in every 32 deals, so the rule won't come up much. Clubs define a farmer's hand differently, and the numbers change with the definition.

Counting trump

Here's how many trump you'll hold in a suit named ahead of time. Three or more happens only about once in eight hands.

Trump in your hand	Chance
None	14.6%
1	39.2%
2	33.6%
3	11.2%
4	1.4%
5	0.05%

Things look better when you can pick the suit. Every hand has at least two cards in its best suit, counting the left bower. About 48% have three or more, 5.8% have four or more, and 0.2% have all five.

The color of your hand can surprise you too. Five cards all of one color happen about once in 27 hands, and five cards with the same printed suit about once in 1,771. Most hands, 58%, show three suits. About 30% show all four.

Where's the bower?

Say hearts are trump, you don't have the left bower, and it wasn't the turn-up. You can't see 18 cards, and before anybody bids it's equally likely to be any one of them:

Where it is	Chance
With your partner	27.8%
With the opponent on your left	27.8%
With the opponent on your right	27.8%
Buried in the kitty	16.7%

So it's against you about 56% of the time and with your partner about 28%. These numbers shift as soon as anyone bids, because a call or a pass tells you something about that player's hand.

Your partnership holds both bowers of a given suit on about 16% of deals, and so do your opponents. The turn-up is a jack on one deal in six.

Can you count on your partner?

Say you call trump in the second round, so the turn-up isn't in your suit. Here's how likely your partner is to help, before anyone plays a card:

Trump in your hand	Partner has at least one	Partner has two or more
2	85%	43%
3	77%	30%
4	65%	17%

The more trump you hold, the fewer are left for your partner. With four in your hand, there's about a one in three chance your partner has none.

Will your ace hold up?

Off-suit aces are worth less the more of that suit you hold, because the rest of the suit runs out sooner. This is the chance that both opponents can follow when you lead an ace in a suit of the other color from trump:

Cards of that suit in your hand	Both opponents can follow
The ace alone	71%
Ace and one more	56%
Ace and two more	37%
Ace and three more	16%

This assumes it's the first time the suit has been led and the turn-up wasn't in it. An opponent who can't follow doesn't always hurt you, since they still need a trump to take the trick. The suit of trump's own color is shorter, so an ace there is at more risk.

How good can you get?

Euchre has plenty of skill, but the cards still have a say. In 2015, the online card site World of Card Games looked at its euchre players with at least 100 games. Most won 40 to 50% of the time, only 15 won 60 to 70%, and just one topped 70%. The site said its numbers fit a common belief that about 66% is the best anybody can do.

That's one site, so take it as a rough guide. We haven't included a figure for how often the team that calls trump makes it. That depends on how boldly the table bids, and we didn't find a number we'd stand behind.

A little history

1810s to 1820s

Euchre reaches America, most likely with German-speaking immigrants, from an Alsatian game called Jucker. A memoir describes people playing "Uker" on a steamboat from Louisville to New Orleans in 1829.

1844

The earliest rules that survive are printed in Thomas Mathews's The Whist Player's Hand-book. An American Hoyle describes the game a year later.

1850s and 1860s

Euchre gives the world the joker. American card makers add an extra top trump to the pack for euchre, and poker borrows it later. The name itself may come from "Jucker" or "euchre."

Sources: David Parlett's history of euchre and Wikipedia on the joker.