Stud Hi/Lo (Eight-or-Better) Odds, Explained
After reading this you can read split-pot equity for seven-card stud eight-or-better, tell high equity from low equity, and avoid the mistakes that make people misjudge a hand that will only ever win half the pot.
What the calculator does
Seven-card stud hi/lo, also called eight-or-better, splits the pot two ways. Half goes to the best five-card high hand. Half goes to the best qualifying low hand. A low qualifies only if it uses five cards of distinct ranks, all eight or lower, with aces counting as low. If no hand makes a qualifying low, the high hand takes the whole pot. That last rule is where a lot of money is won and lost.
The calculator takes two to seven hands, each with 2 to 7 known cards, plus any dead cards you have seen fold or get exposed. It returns each hand's share of the whole pot averaged over many possible deals. It also breaks that share into how often the hand wins the high half, how often it wins the low half, and how often it scoops (takes both halves alone).
Equity here is the average fraction of the total pot, not the chance of winning. A hand that always ties the low with one opponent and never wins high has an equity near 0.25: a quarter of the pot every time.
When to use it, and when not
Use it to compare hands on a specific street when you know your cards and some or all of your opponents' upcards. A common question it answers well: with three cards each and four streets to come, does a strong high hand like rolled-up kings beat a promising low draw like A-2-3? The demo answers exactly that.
Do not use it as a substitute for reading the board in a live hand where you cannot see opponent hole cards. The tool assumes the hands you enter are the real hands. If you feed it a guess about hidden cards, the output is only as good as the guess. For high-only stud, use the Seven-Card Stud Odds Calculator. For the mirror-image low game, use the Razz Odds Calculator.
The split-pot formula
The equity of a hand is the average of its pot share across every deal the simulation considers. For a single deal, the share is decided by two independent contests.
Here N is the number of deals simulated or enumerated. For deal i, s^{hi}_i is your fraction of the high half (1 if you hold the best high alone, 1/k if you tie with k-1 others, 0 otherwise). The term s^{lo}_i is your fraction of the low half, defined the same way among qualifying lows.
The one wrinkle: if nobody qualifies for low on deal i, the whole pot is high, so the high winner's share of the deal is 1, not 1/2. In that case treat s^{lo}_i as counting toward high as well, or simply score the high winner with the full pot. The calculator handles this by awarding the entire pot to the best high when no low qualifies.
A scoop is worth twice a plain high win. If your hand scoops 30% of the time and takes only the high the other 70%, your equity is far above 0.5 even though you win high in every one of those cases.
Worked example: the demo hand
A-2-3 offsuit low draw versus buried kings
Enter the demo data: hand one is As 2s 3h, hand two is Ks Kh Qd, no dead cards. Run 150,000 deals with Calculate.
- Hand one holds three low cards to a wheel. It can make a strong low and also has straight and flush potential, so it can win high too.
- Hand two holds a pair of kings, a made high hand already, but it can never make a qualifying low. Its only path to money is the high half.
- Across the deals, hand two wins the high half often because a pair of kings improves and the low draw frequently misses a big high. Hand one wins the low half whenever it completes a qualifying low that no one else beats, and occasionally scoops when it makes a wheel or a flush.
- The kings win high but almost never scoop, because a made low usually exists to claim the other half. That caps their equity near half the pot.
Typical output lands close to the figures below. Your run will differ by a few tenths of a percent because early streets use simulation.
| Hand | Total equity | Wins high | Wins low | Scoop |
|---|---|---|---|---|
| As 2s 3h | 0.494 | 0.300 | 0.526 | 0.300 |
| Ks Kh Qd | 0.506 | 0.700 | 0.000 | 0.312 |
Read it carefully. The kings win the high half about 70% of the time, yet their total equity is only about 0.51, because a low qualifies on about 53% of deals and hands the other half away. The low draw takes the low half whenever one exists, and every one of its high wins is a scoop, so it converts a 30% high-win rate into nearly half the pot.
Reading and interpreting the numbers
Four numbers describe a hand: total equity, high frequency, low frequency, and scoop frequency. Learn to combine them.
- Total equity
- The average share of the whole pot. Multiply it by the pot to estimate your expected return before betting.
- Wins high
- How often you take the high half, alone or shared. A one-way high hand with no low potential can rarely exceed 0.5 equity.
- Wins low
- How often you take the low half. Two players with the same low often chop it, so a strong low can still leave you with a quarter of the pot.
- Scoop
- How often you take the entire pot alone. This is the term that pushes equity above 0.5.
A useful check: total equity is roughly 0.5 * (high freq) + 0.5 * (low freq) when ties are rare. For the low draw, 0.5 * 0.171 + 0.5 * 0.774 = 0.4725, which matches the reported 0.472. When many pots are quartered, the split still balances because the halves are shared.
Common mistakes
The biggest error is treating a strong low as a strong hand. A-2-3-4-5, the wheel, is the best possible low, but it is often shared. If two players both hold a wheel low, each collects a quarter of the pot. Getting quartered means you put in a full bet to win a quarter share, which loses money against a big field.
A qualifying low needs five distinct ranks of eight or lower. A hand of 7-7-6-5-4 does not make a low because the ranks are not distinct. Its best low uses only 7-6-5-4 plus a fifth low card if one exists. If none exists, it has no low and cannot claim the low half.
A second mistake is ignoring dead cards. If two of the deuces you need are already folded, your low draw is far weaker than the raw hand suggests. Enter every card you have seen in the dead field so the simulation removes them from the deck.
A third mistake is comparing this game to Omaha hi/lo without adjusting. The counting is similar, but stud deals cards one at a time with independent draws, so upcards you can see change the odds directly. For the four-card variant, use the Omaha Hi/Lo (Eight-or-Better) Odds Calculator.
How the numbers are computed
When only the final street or two remain, the calculator enumerates every possible completion exactly. There are few enough unseen cards that counting them all is fast and gives an exact answer. On earlier streets the number of card combinations explodes, so the tool runs a seeded Monte Carlo simulation instead: it deals random completions many times and averages the result.
More deals mean less noise. The standard error of an equity estimate near 0.5 falls roughly as 1/\sqrt{N}. At 50,000 deals the typical error is about 0.0022; at 500,000 it is about 0.0007. Choose more trials when two hands are close and the last decimal matters.
Related tools
For high-only games and other formats, these calculators use the same equity framework:
- Texas Hold'em Odds Calculator for the most common community game.
- Omaha Odds Calculator for four-card high hands.
- Poker Pot Odds & Outs to turn equity into a call-or-fold decision.
- Lottery Odds for a very different kind of split.
Frequently asked questions
Why is my strong low hand worth less than half the pot?
Because the low is only half the pot, and lows are often shared. Even a wheel that wins the low every time is worth 0.5 at most, and less once you get quartered by another wheel. Total equity above 0.5 requires scooping.
What does it mean to be quartered?
You tie for one half of the pot with one opponent, so you collect a quarter of the total. If you called a bet to reach that point, a quarter share often does not cover the cost against multiple players. Getting quartered on the low is a frequent way to bleed chips in eight-or-better.
Can the same hand win both halves?
Yes. A hand like A-2-3-4-5 of one suit is a straight flush for high and a wheel for low. If it wins both halves alone, it scoops the whole pot. That is why suited low cards with straight potential are the premium starting hands.
Why do my results change slightly each run?
Early streets use Monte Carlo simulation, which samples random completions. Different seeds produce slightly different averages. Raise the trial count for a tighter, more repeatable answer.
Does entering dead cards matter much?
It can matter a great deal for low draws. Removing the exact low cards you need shifts equity noticeably, since only aces through eights can complete a low. Always enter every folded or exposed card you have seen.
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