Euchre Odds & Probabilities
The exact math behind the deal: how often you hold the bowers, how much trump to expect, where the card you can’t see probably is, and how likely your ace is to be trumped.
Updated
How much trump will you get?
Trump is seven cards: the named suit’s six plus the left bower. When a suit is named that you didn’t pick — the up-card’s suit in round one, or someone else’s call — here’s how many of those seven you’ll hold:
| In your hand | Hands | Chance | About |
|---|---|---|---|
| 0 trumps | 6,188 | 14.6% | 1 in 7 |
| 1 trump | 16,660 | 39.2% | 2 in 5 |
| 2 trumps | 14,280 | 33.6% | 1 in 3 |
| 3 trumps | 4,760 | 11.2% | 1 in 9 |
| 4 trumps | 595 | 1.4% | 1 in 71 |
| 5 trumps | 21 | 0.05% | 1 in 2,024 |
72.8% of the time you hold one or two. Three or more — the usual floor for a call in when to order up — turns up only 12.6% of the time in a given suit, which is why most turns in the bidding are passes.
Your best suit
Round two lets you name any suit but the turned-down one, so what matters there is your best suit: the one that would give you the most trumps. Across all 42,504 hands:
| In your best suit | Hands | Chance | About |
|---|---|---|---|
| 2 trumps | 22,200 | 52.2% | 1 in 2 |
| 3 trumps | 17,840 | 42.0% | 2 in 5 |
| 4 trumps | 2,380 | 5.6% | 1 in 18 |
| 5 trumps | 84 | 0.20% | 1 in 506 |
Every hand has at least two trumps in its best suit: five cards across four suits put two in one of them, and a jack counts in two suits. Nearly half, 47.8%, have three or more. A hand that’s five trumps in its best suit — every card trump — comes up 1 in 506. The catch in round two is that your best suit might be the one that was turned down.
The bowers
| You’re dealt… | Chance | About |
|---|---|---|
| The right bower of a given suit | 20.8% | 1 in 5 |
| At least one of that suit’s two bowers | 38.0% | 2 in 5 |
| Both bowers of a given suit | 3.6% | 1 in 28 |
| Both jacks of one color (both bowers, if either suit is named) | 7.2% | 1 in 14 |
| At least one jack of any suit | 63.5% | 2 in 3 |
Holding both bowers is rare — 1 in 28 for a given suit — so when it happens, it’s worth a look at the going-alone guide.
Where is the card you can’t see?
Once the cards are dealt you’ve seen six: your five and the up-card. The other 18 are five in each of the other three hands and three face down in the kitty. So any card you haven’t seen is:
- in your partner’s hand 27.8% of the time,
- with one of the two opponents 55.6% of the time, and
- buried in the kitty, never to be played, 16.7% of the time.
For the bowers: if you hold neither bower of the named suit and neither is the up-card, your partner has at least one 49.0% of the time and both 6.5%, while at least one is with an opponent 81.7% of the time. Call without a bower and you should expect to see one played against you.
Will your ace get trumped?
An ace in a side suit only wins if nobody trumps it, and nobody can trump it unless they’re void in the suit. The fewer cards of the suit are out, the likelier a void. Here are the odds that an opponent holds none of the suit you lead, by how many of its cards you can’t see:
| Cards of the suit out | When | A given opponent is void | Either opponent is void |
|---|---|---|---|
| 5 | You hold one card of a six-card side suit — say, a lone ace | 15.0% | 29.4% |
| 4 | You hold two of a six-card suit, or one of the five-card same-color suit | 23.4% | 44.4% |
| 3 | You hold three of a six-card suit, or two of the same-color suit | 35.0% | 63.2% |
| 2 | Only two of the suit are out | 51.0% | 83.7% |
- Cash side aces early. The first round of a suit is its safest; every round played takes cards out and makes a void likelier.
- The same-color suit is riskier. It lost its jack to the left bower, so it has only five cards. A lone ace there meets a void 44.4% of the time, against 29.4% in a six-card suit.
- A void isn’t a trump. These are the odds an opponent can trump your ace. They also need a trump left, and the choice to use it. See how to defend for that side of it.
Rare hands
| Hand | Chance | About |
|---|---|---|
| Five trumps in a suit someone else names | 0.05% | 1 in 2,024 |
| Every card a trump in your best suit | 0.20% | 1 in 506 |
| A farmer’s hand: nothing but 9s and 10s | 0.13% | 1 in 759 |
| “Ace no face”: an ace, but no jack, queen or king | 1.73% | 1 in 58 |
Farmer’s hands and “ace no face” only matter at tables that play them as house rules — see variations and house rules.
What happens after trump is made
The math above is exact; this part is measured. We dealt 200,000 hands and let the same Monte-Carlo AI that plays at our tables fill all four seats, then counted how its calls turned out.
- Trump was made in the first round 65.0% of the time, and the dealer was stuck with the call 10.7% of the time.
- With a partner, the makers took three or more tricks 87.0% of the time and swept all five 19.4%; they were euchred 13.0%.
- Loners — 10.3% of all hands — swept for 4 points 54.0% of the time, settled for 1 point 42.7%, and were euchred 3.3%.
| Maker’s trumps when play began | Hands | Made it | Took all 5 | Euchred |
|---|---|---|---|---|
| 2 trumps | 24,566 | 79.8% | 14.2% | 20.2% |
| 3 trumps | 54,366 | 91.2% | 16.9% | 8.8% |
| 4 trumps | 15,971 | 97.6% | 25.3% | 2.4% |
| 5 trumps | 430 | 100.0% | 34.9% | 0.0% |
Counts the maker’s own trumps once play began (a dealer’s after picking up and discarding). Calls where the dealer’s partner ordered the card into the dealer’s hand are counted separately below, as are stuck dealers.
| Bowers in the maker’s hand | Hands | Made it | Euchred |
|---|---|---|---|
| Both bowers | 18,654 | 95.4% | 4.6% |
| Right bower only | 45,797 | 88.2% | 11.8% |
| Left bower only | 22,906 | 87.7% | 12.3% |
| Neither bower | 8,811 | 85.2% | 14.8% |
| Special cases | Hands | Made it | Euchred |
|---|---|---|---|
| The dealer’s partner orders it up | 62,732 | 87.9% | 12.1% |
| The dealer is stuck | 20,442 | 73.6% | 26.4% |
| Going alone | Hands | Took all 5 | Euchred |
|---|---|---|---|
| Loner with 3 trumps | 12,066 | 47.4% | 4.4% |
| Loner with 4 trumps | 6,480 | 61.4% | 0.3% |
| Loner with 5 trumps | 1,267 | 94.0% | 0.0% |
| Loner with both bowers | 8,459 | 68.5% | 0.5% |
| Loner with the right bower only | 12,199 | 43.8% | 5.3% |
How these numbers are worked out
Standard four-player Euchre: 24 cards, five to each player, four in the kitty with one turned up. Each figure is exact — counted over all 42,504 possible hands, or over the 18 cards you can’t see once you’ve looked at your hand and the up-card — and the page’s code checks them against 200,000 simulated deals.
Two simplifications: the void odds assume the up-card isn’t in the suit you lead, and they leave out the dealer’s pickup and discard, which moves one card after the deal. Neither changes the picture.
The measured section comes from 200,000 hands dealt from fixed seeds and played with stick the dealer on, every seat run by the same AI as our tables (40 simulated playouts per decision). The deals are fixed, so the run can be repeated exactly.
Common questions
What are the odds of being dealt the right bower?
20.8% for any one suit — five of the 24 cards are yours, so about 1 in 5. The odds you hold at least one of that suit’s two bowers are 38.0%, and both of them 3.6% (1 in 28).
What are the odds my partner has the right bower?
If you don’t hold it and it isn’t the up-card, 27.8%. The 18 cards you can’t see are five in each other hand and three in the kitty, so each opponent also holds it 27.8% of the time and the kitty 16.7%.
How many different Euchre hands are there?
42,504 five-card hands from the 24-card deck, and about 499 trillion different deals once you count all four hands, the kitty and the up-card.
How often do the makers get euchred?
In 200,000 hands of our AI playing all four seats, makers with a partner were euchred 13.0% of the time, a stuck dealer 26.4%, and a player going alone 3.3%. Those are the AI’s own calls, so they measure how well its calls hold up rather than the odds for any one hand.
What are the odds of a farmer’s hand?
A hand of nothing but 9s and 10s comes up 0.13% of the time — 1 in 759 hands.
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