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Seven-Card Stud Odds, Explained

After reading this you can turn a set of partial seven-card stud hands into win, tie and equity percentages, read those numbers correctly, and avoid the mistakes that quietly wreck stud calculations.

What this calculator does

Seven-card stud gives each player their own seven cards: no shared board. You get some cards face up, some face down, and the best five-card poker hand wins at showdown. The calculator takes two to seven hands with any number of known cards from third street (three cards) to the river (seven cards), then completes every hand to seven cards using the deck that remains. It reports each hand's chance to win outright, to tie, and its total equity.

Here is the hook. Give it aces up against queens with a jack showing, exactly the demo data: As Ah Ks versus Qd Qc Jd. Aces are ahead, but each hand still needs four more cards, so the queens win far more often than a beginner expects. The exact number appears in the worked example below.

When to use it, and when not

Use it to settle "how far ahead was I" questions after a hand, to build intuition about how quickly a lead in stud erodes, and to check whether a call on fifth street was justified by your equity. It answers a card-counting question, not a betting question. It does not know your opponents' hidden cards, their tendencies, or the money in the pot.

The result assumes every hand reaches showdown and no one folds. Real stud hands end early all the time. Treat the equity as the value of your cards if the hand is dealt to the end, not as your expected profit.

For shared-board games use the Texas Hold'em Odds Calculator or the Omaha Odds Calculator. For the low variants use the Razz Odds Calculator or the Stud Hi/Lo Odds Calculator.

The counting behind the odds

Start with the deck. A standard deck has 52 cards. Subtract every card you can see: the cards in all the entered hands plus any dead cards you supply. What remains is the pool of unseen cards, and each ordering of that pool is equally likely.

U = 52 - C_{\text{known}} - C_{\text{dead}}

Here U is the number of unseen cards, C_{\text{known}} is the total cards across all hands, and C_{\text{dead}} is the count of dead cards. With two hands of three cards and no dead cards, U = 52 - 6 = 46.

Each hand still needs 7 - n cards, where n is how many it already has. The calculator deals those missing cards from the unseen pool without replacement, ranks the completed seven-card hands, and awards the pot. Equity for one hand is its share of pots across all deals:

E_i = \frac{W_i + \sum_j \frac{T_{ij}}{j}}{N}

W_i is the number of deals hand i wins outright, T_{ij} is the number of deals it ties with j players total sharing the pot, and N is the number of deals evaluated. A tie among three hands pays each one third, which is why the tie term is divided by the number sharing.

When only a few cards are unknown, the calculator lists every possible completion and computes the answer exactly. When many cards are unknown, the number of completions is enormous, so it draws a large random sample instead. Two hands on third street leave 40 cards to distribute into eight future slots: the exact count runs into the trillions, well past the point where enumeration is practical.

Worked example: aces up versus queens

Reproducing the demo

Enter As Ah Ks and Qd Qc Jd, leave dead cards empty, and run the standard 150,000 deals.

  1. Known cards: 6. Dead cards: 0. Unseen pool U = 52 - 6 = 46.
  2. Each hand needs four more cards, drawn without replacement from those 46.
  3. The aces-up hand starts with a pair of aces plus a king. The queens hand starts with a pair of queens plus a jack.
  4. Across the deals, the aces hand wins about 63.8%, the queens hand wins about 36.2%, and exact ties are vanishingly rare.

Equity for the leader is therefore also roughly 63.8%. The pair of queens is a big underdog, yet it wins better than one hand in three. That is the shape of stud: a made pair on third street is a modest favorite, not a lock, because two of your four unseen cards can pair, trip up, or make two pair for either side.

The pair of aces wins about 64% and the pair of queens about 36%; ties are almost impossible here. The lead is real but small.

How the lead grows street by street

A favorite in stud gets safer with every card that misses the underdog. The interactive below lets you watch the same aces-versus-queens matchup as cards remain to come. On third street the aces hold about 64%. By the river, with all cards dealt, the equity is either 100% or 0%: someone has won.

With four cards to come the pair of aces has about 64% equity against the pair of queens. On a blank runout it grows to about 67% with three to come, 71% with two, and 77% with one. The fewer cards left, the harder it is for the trailing hand to improve past the leader.

Reading the results

Three numbers appear per hand. Keep them straight.

Win %
Share of deals this hand beats every other hand outright, taking the whole pot.
Tie %
Share of deals this hand ties for best. A 50% tie split still shows in this column, so a high tie percentage can mean chopped pots, not clean wins.
Equity %
Win plus the fair fraction of every tie. This is the number to compare against pot odds. All equities across the table sum to 100%.

Compare equity to the price of a call. If the pot lays you 3 to 1, you need 25% equity to break even. Feed the equity into the Poker Pot Odds & Outs tool to turn it into a call-or-fold answer.

Simulation noise shrinks as deals rise. At 150,000 deals a percentage is accurate to roughly \pm 0.25 points; at 1,000,000 deals to roughly \pm 0.1 points. If two hands report 49.9% and 50.1%, treat the race as even and rerun with more deals to confirm.

Common mistakes

The single biggest error in stud calculations is ignoring folded upcards. Every card an opponent showed and then folded is gone from the deck, and stud exposes many upcards. Suppose you hold three hearts and are chasing a flush. Nine hearts remain in a full 46-card unseen pool, so a fourth heart on the next card comes about 9/46 \approx 19.6\% of the time. If two hearts folded elsewhere as upcards, only seven help you out of 44 unseen, 7/44 \approx 15.9\%. That is a real drop. Enter those folded cards in the dead-cards field.

Two more traps:

  • Do not enter the same card twice. A card can live in exactly one place: one hand, or the dead pile, never both. Duplicates make the result meaningless.
  • Do not read equity as profit. It is your cards' fair share of the pot at showdown. Betting, folding and position are separate questions.
Each dead heart removes an out and shrinks the unseen pool. Two dead hearts cut your immediate flush chance from about 19.6% to 15.9%.

Related tools

For the split-pot version of stud, where a qualifying low takes half, use the Stud Hi/Lo Odds Calculator. Its Omaha cousin is the Omaha Hi/Lo Odds Calculator. If you enjoy the counting side of the game, the Lottery Odds tool uses the same draw-without-replacement math on a larger scale.

Frequently asked questions

Why can hands have different numbers of cards?

In real stud, players receive cards street by street and some fold early. A hand with five cards is on fifth street; a hand with three is on third street. The calculator completes each hand to seven using unseen cards, so mixed-length hands are normal and correct.

How many dead cards should I add?

Add every upcard you saw from folded opponents, plus any exposed cards from the dealer. Each one removes a card from the pool and shifts the odds. Missing dead cards is the most common source of wrong stud numbers.

Are the results exact or simulated?

Late streets with only a few unknown cards are enumerated exactly. Earlier streets, where completions run into the billions or more, use a seeded Monte Carlo simulation. More deals mean tighter estimates: 1,000,000 deals hold a percentage to about a tenth of a point.

Does this handle the low half of the pot?

No. This tool scores high hands only. For eight-or-better splits use the Stud Hi/Lo calculator, and for the pure low game use the Razz calculator.

Why does my clear favorite still lose sometimes?

Because unseen cards decide the hand. A pair of aces up on third street wins about 64% of the time against a pair of queens, which means it loses about 36% of the time. Favorites in stud are favorites, not certainties, until the last card is dealt.

Try it yourself in the tool

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