Razz Odds, Explained

This guide shows you how razz hands are ranked, how the calculator turns partial seven-card-stud lows into win, tie and equity percentages, and how to read those numbers without fooling yourself.

What razz is and one quick example

Razz is seven-card stud played for the lowest hand. There is no board and no shared cards. Each player builds the best five-card low from their own seven cards. Straights and flushes do not count against you, and aces are always low. That means the best possible hand is A-2-3-4-5, known as the wheel, and it cannot be beaten.

To compare two lows, line up each player's five lowest distinct ranks from highest card down and read them like a number. A hand of 8-6-4-2-A beats 8-7-3-2-A because at the second card the 6 is lower than the 7. Pairs hurt you: if you cannot make five distinct ranks, the paired ranks push your hand higher. So 7-7-5-3-2 loses to any genuine five-card low.

The calculator takes this ranking and answers a harder question. Given the cards you know now, and the cards already dead, what fraction of the remaining possible deals does each hand win?

When to use it, and when not

Use the calculator when you have partial information: two to seven cards per player, plus any cards you have seen fold or expose. That matches real razz, where you see opponents' upcards on third through seventh street and must estimate equity before the hand completes.

The most useful moment is early. On third street each player has three cards, one hidden and two showing to you in a live game. You know your own three and your opponents' upcards, and you want to know whether your draw is ahead. That is exactly what the tool estimates.

If every hand already has seven cards, there is nothing to deal and no uncertainty. The winner is fixed and the calculator simply reports it as 100 percent. Equity math only matters while cards are still unknown.

Do not use it to price a call by itself. Equity is only half of a call decision. The other half is the pot and the bet you face, which the Poker Pot Odds & Outs tool handles.

The math behind the percentages

Equity is the average share of the pot a hand takes if the deal runs to the end many times. For a single completed deal, a hand's share is 1 if it holds the unique best low, 1/t if it ties with t hands, and 0 otherwise. Averaging that share over every possible completion gives equity.

E_i = \frac{1}{N} \sum_{d=1}^{N} s_i(d)

Here E_i is the equity of hand i, N is the number of deals considered, and s_i(d) is that hand's pot share in deal d. When the number of unknown cards is small, N is the exact count of all completions and the answer is exact. When it is large, the tool draws N random completions instead, a Monte Carlo estimate.

The size of an exact enumeration grows fast. Suppose two players each hold three cards and no cards are dead. That accounts for 6 known cards, leaving 46 unknown. Each player needs 4 more cards, so the count of completions is

\binom{46}{4} \times \binom{42}{4} = 163185 \times 111930 \approx 1.83 \times 10^{10}

Over 18 billion deals is too many to enumerate quickly, so this case uses simulation. By seventh street, with only a handful of unknown cards left, the count drops into the thousands and the tool enumerates every one.

How accurate the simulation is

A simulated equity is a sample proportion. Its standard error is roughly \sqrt{p(1-p)/N}, where p is the true equity and N is the deal count. This shrinks slowly: to halve the error you must quadruple the deals.

At the standard 150,000 deals and a near-coinflip p = 0.5, the standard error is \sqrt{0.25/150000} \approx 0.00129, about 0.13 percentage points. So an equity printed as 50.0 percent is really 50.0 plus or minus roughly 0.25 points at two standard errors. At 1,000,000 deals the same error falls to about 0.05 points.

Approximate two-sigma margin near 50 percent equity, by deal count
Deals	Standard error	Two-sigma margin
50,000	0.224%	±0.45%
150,000	0.129%	±0.26%
500,000	0.071%	±0.14%
1,000,000	0.050%	±0.10%

For most decisions the standard setting is plenty. Raise the deal count only when two hands are close enough that a fraction of a percent changes your read.

The margin falls with the square root of the deal count, so gains slow down as you add more deals.

A worked example with the demo hands

As 2h 3s versus 4d 5c 6d on third street

Load the demo: hand one is As 2h 3s, hand two is 4d 5c 6d, and no cards are dead. Both hands are strong three-card draws. Hand one already has A-2-3, the three lowest ranks. Hand two has 4-5-6, still excellent but starting one full rank higher.

Six cards are known, so 46 remain in the deck.
Each hand draws four more cards to reach seven, then keeps its five lowest distinct ranks.
Hand one wins whenever its final five-low reads lower than hand two's. Its head start on the three smallest ranks makes that common.
Ties happen when both settle on the same five ranks, for example if both end holding 6-5-4-3-2.

Running the standard 150,000 deals gives roughly these results. Hand one wins about 52.9 percent, hand two about 47.1 percent, and exact ties are rare (under 0.1 percent), because hand one almost always keeps its ace in the final five. Equity therefore sits close to 53 percent against 47.

The gap is much smaller than most players guess. A three-low starting at 4-5-6 is only a mild underdog against A-2-3, winning nearly every other deal because either hand can brick with high pairs, and hand two can still catch a wheel card while hand one pairs.

The A-2-3 draw leads, but the 4-5-6 draw keeps nearly half of the equity.

Reading and interpreting the output

Three numbers describe each hand. Win percent counts deals where it is the sole best low. Tie percent counts deals where it shares the pot. Equity folds ties in at their pot share, so for two hands equity equals win plus half of tie.

Win: Fraction of deals this hand alone holds the lowest hand.
Tie: Fraction of deals this hand shares the best low with one or more others.
Equity: Average pot share, which is what you use for expected value.

In razz, ties matter more than in high poker because good lows converge on the same few small ranks. Two players both drawing to wheels can easily both make 6-4-3-2-A. Watch the tie column; a hand with 45 percent wins and 8 percent ties has more equity than one with 47 percent wins and 2 percent ties.

Common mistakes

Do not enter cards twice. If a rank and suit appears in a hand it cannot also be a dead card, and no two hands can hold the same card. The calculator treats every card as unique, so a duplicate breaks the deal.

The most frequent error is forgetting dead cards. In a live razz game you see many upcards fold. Every low card that is already dead cannot help your opponents, which raises your equity. Leaving those cards out of the dead list makes the estimate too pessimistic for a hand chasing low cards and too optimistic for the field.

The second mistake is reading razz like high stud. Pairs are the enemy, not friends. A pair of aces is close to worthless here. And a straight or flush is irrelevant, so 5-4-3-2-A is the nuts even though it is a straight.

The third is treating a simulated 51 percent as a lock. With the standard margin near 0.26 points, 51.0 and 49.0 are clearly different, but 50.4 and 49.6 are not. When the split is that tight, raise the deal count or accept that the hands are effectively even.

Related calculators

Razz shares its seven-card structure with several other tools here. For the high version of the same game, use the Seven-Card Stud Odds Calculator. For the split-pot variant where a qualifying low takes half the pot, use the Stud Hi/Lo Odds Calculator.

Community-card games work differently but the equity idea is identical. See the Texas Hold'em Odds Calculator, the Omaha Odds Calculator, and the Omaha Hi/Lo Odds Calculator for those. To turn equity into a call-or-fold decision, pair any of them with Poker Pot Odds & Outs, and for unrelated draw-number problems there is the Lottery Odds tool.

Frequently asked questions

Do straights and flushes count in razz?

No. Razz uses ace-to-five low, where suits and runs are ignored for ranking. The best hand is the wheel 5-4-3-2-A, which is a straight but still unbeatable.

Why does the tie percentage seem so high?

Strong razz lows draw to the same small ranks, so two players often finish with identical five-card lows. Ties of several percent are normal when both hands are premium draws.

How many cards should I enter per hand?

Enter what you actually know: three on third street, up to seven by the end. The fewer cards you enter, the more uncertainty remains and the more the equities move toward even.

When is the answer exact rather than simulated?

When only a few cards are unknown, usually on sixth or seventh street, the tool enumerates every completion and the result is exact. Earlier streets have too many completions, so it simulates.

Does adding dead cards change the odds much?

It can. Removing low cards from the deck helps a made low and hurts a drawing hand. On third street, three or four dead low cards can shift equity by several points, so always include the upcards you have seen.

Try it yourself in the tool