Quad Aces: Meaning, Exact Odds and What Beats Them

Quad aces means four of a kind, aces: A♠ A♥ A♦ A♣, plus a fifth card called the kicker. It is the highest possible four-of-a-kind hand in standard high-hand poker. It beats every full house and every lower-ranked four of a kind, but loses to a straight flush—including a royal flush. Those comparisons follow the standard hand rankings and same-rank tiebreaking rules.

How rare it is depends on which cards you are counting. Being dealt four aces in five cards is not the same event as making quad aces by the river in Texas hold’em.

Exact probabilities of quad aces

These calculations assume a uniformly shuffled 52-card deck, no wild cards and no information about opponents’ cards. Hold’em river figures assume all five community cards are dealt, regardless of whether you would fold.

Situation	Exact probability	Percentage, rounded	Frequency, rounded
Four aces in a random five-card hand	1/54,145	0.001847%	1 in 54,145
Four aces among your two hold’em hole cards and five board cards, before any cards are known	1/7,735	0.012928%	1 in 7,735
Flopping quad aces when you hold AA	3/1,225	0.244898%	1 in 408.33
Making quad aces by the river when you hold AA	2/245	0.816327%	1 in 122.5

“1 in” expresses probability, not a schedule: none of these hands becomes due after a particular number of deals.

Five cards versus seven

For five cards, all four aces are fixed, leaving 48 choices for the kicker. There are C(52,5) = 2,598,960 possible five-card hands, so:

P(quad aces) = 48 / 2,598,960 = 1/54,145.

This is the counting method set out in CK-12’s four-aces example. Here, C(n,k) means the number of ways to choose k cards from n, without regard to order.

For seven cards, the four aces leave three other cards to choose:

P(quad aces) = C(48,3) / C(52,7) = 17,296 / 133,784,560 = 1/7,735.

Brian Alspach’s seven-card enumeration gives those counts for a specified quad rank. Multiplying the numerator by 13 counts quads of any rank; it would no longer answer the quad-aces question.

The seven-card figure applies to one hold’em player’s two hole cards plus the completed board. It includes deals with all four aces on the board, not just quads made using a hole card. For the wider comparison, see our exact poker hand probabilities.

Starting with pocket aces

With AA in your hand, both remaining aces must appear on the board.

On the flop, the third board card can be any of the 48 non-aces:

P(flopping quad aces | AA) = 48 / C(50,3) = 48/19,600 = 3/1,225.

By the river, choose both remaining aces and any three non-aces:

P(quad aces by river | AA) = C(48,3) / C(50,5) = 17,296/2,118,760 = 2/245.

These are probabilities of completing quads, not your overall chance of winning with pocket aces.

Can quad aces lose—or split?

Yes. Suppose you hold A♣ A♦ and the board is A♠ A♥ J♥ Q♥ K♥. You have quad aces, but an opponent holding 10♥ 9♥ has a royal flush. Quad aces are therefore not automatically the best possible hand on every hold’em board.

If all four aces are on the board, everyone still needs a fifth card. On A♠ A♥ A♦ A♣ 7♠, a player holding a king beats one whose best kicker is a queen. On A♠ A♥ A♦ A♣ K♠, everyone remaining at showdown has the same best five-card hand: four aces with a king kicker. The pot is shared under the equal-hand rule.

Only the best five cards count—not a sixth card to break the tie. Our split-pot guide explains how those ties differ from side pots.