PLO variance calculator: interpreting pot-limit swings
A PLO variance calculator needs assumptions about your edge, standard deviation and hand count. These worked examples show how those inputs translate into uncertainty around your win rate, possible finishing results and a model bankroll, without treating an assumed edge as an established fact.
Start with a model that describes your Omaha game
For pot-limit Omaha cash games, you need to distinguish your average result from the spread around it. Your win rate describes the average in bb/100, while standard deviation describes variability on the same scale. Variance is the square of that standard deviation, although poker tools usually ask for standard deviation because its units are easier to interpret. A calculator cannot infer either input simply from the game name. Stack depth, opponents, rake and your decisions affect the results you are trying to describe. Choosing an optimistic edge makes every later estimate look more comfortable without adding any evidence that the edge exists.
For the main worked example, suppose your underlying win rate is 5 bb/100 and your standard deviation is 140 bb/100. These are stated assumptions, not typical values established for every PLO game. The model treats successive results as independent enough for a normal approximation over a large sample, with the same underlying edge and variability throughout. That excludes changes in stakes, game conditions and playing quality. You can still use the arithmetic to understand sensitivity, but a table built from stable assumptions cannot describe every changing poker environment. Keep the distinction between assumed inputs and measured evidence visible whenever you interpret an output.
Turn a hand count into a spread of finishing results
Suppose you play 10,000 hands under the main assumptions. Dividing the hand count by the block size of one hundred gives 100 blocks. Expected result equals win rate multiplied by that block count, giving 500 big blinds. The standard deviation of the total result equals your standard deviation in bb/100 multiplied by the square root of the block count, giving 1,400 big blinds. Notice the different growth rates: the expected total grows with volume, while the spread grows with its square root. The spread is a property of possible finishing results, not the amount you should expect to lose during a session.
An approximate central 95% result range is the expected total plus or minus 1.96 times that spread. Here its endpoints are -2,244 and 3,244 big blinds. The normal approximation also puts the chance of finishing below break-even at 36.0%. This describes the endpoint after the stated hand count, assuming the edge is real and stable. It does not describe the deepest fall along the way, the chance of touching a loss limit, or the sequence of winning and losing sessions. A path can finish above its starting point after passing through a substantial loss, so endpoint ranges cannot substitute for drawdown analysis.
Read a confidence band around your measured win rate
Now change the question: suppose 5 bb/100 is your measured win rate rather than a known underlying edge. With standard deviation assumed to be 140 bb/100, the approximate 95% confidence band has half-width equal to 1.96 times standard deviation divided by the square root of hands divided by one hundred. Add and subtract that half-width from the measured rate. Both endpoints remain in bb/100, because the band concerns an average rate rather than a total result. The table holds the observed rate and standard deviation fixed so you can isolate the effect of sample size.
A band crossing zero means the data remain compatible with a negative underlying rate under these assumptions. It does not establish that you are a losing player, and a positive observed rate does not settle the opposite conclusion. The confidence level describes the long-run coverage of this interval procedure across repeated samples; it is not a probability assigned to a fixed underlying rate after observing your particular results. These are approximate normal bands with standard deviation treated as known. Estimating that spread from limited or unrepresentative records adds uncertainty that the displayed arithmetic does not capture.
Understand what more hands can and cannot establish
The square-root relationship explains why a modest increase in volume often changes your confidence less than you expect. Halving the band half-width requires four times as many hands when standard deviation stays fixed. To find the sample size where the lower endpoint reaches zero, divide 1.96 times standard deviation by the positive observed win rate, square the result, then multiply by one hundred. With a rate of 5 bb/100 and standard deviation of 140 bb/100, the boundary is approximately 301,181 hands. Strictly clearing zero requires moving beyond the unrounded boundary while retaining the assumed observed rate and spread.
If the rate is instead 2 bb/100 at the same standard deviation, that boundary becomes approximately 1,882,384 hands. This is a sensitivity exercise, not a target you should pursue by playing longer than you intended. Your future observed rate can fall, and your standard deviation can change as your game changes. Nor does repeatedly checking the band and stopping at the first positive lower endpoint preserve the usual fixed-sample interpretation. Choose review points in advance when practical, and examine whether the sample still represents your present game. More historical hands can reduce sampling noise while becoming less relevant to the decisions you face today.
Use bankroll maths as a conditional risk estimate
A separate question concerns the chance of exhausting a starting bankroll over continued play. In the normal diffusion approximation, bankroll in big blinds equals minus standard deviation squared times the natural logarithm of the target risk, divided by twice the positive win rate. Use win rate and standard deviation in bb/100 throughout this formula. At the assumed rate of 5 bb/100, standard deviation of 140 bb/100 and target risk of 5%, the model gives approximately 5,872 big blinds, or 58.7 buy-ins of 100 big blinds. The buy-in conversion is a reporting convention, not an assumption about the stack depth of every hand.
Keeping the same spread and target risk but reducing the assumed edge to 2 bb/100 raises the estimate to 146.8 buy-ins. That sensitivity matters because the edge is usually less certain than the bankroll balance. This approximation assumes continued play at constant stakes, a stable positive edge, no withdrawals and no move-down policy. Real poker has discrete losses and changing conditions, so its ruin probability need not match the diffusion model exactly. If your evidence leaves a non-positive edge plausible, quoting a precise bankroll from the optimistic rate conceals that problem. Set affordable limits and a move-down rule separately from this conditional mathematical estimate.
Build inputs from records with consistent units
To estimate your rate, express each cash result in big blinds at the stake played, total those results, divide by the number of hands and multiply by one hundred. Include losing sessions and account for rake consistently; exclude deposits and withdrawals because they are transfers rather than poker results. Keep different game formats separate when their conditions differ materially. Combining deep Omaha games with short-stack games may describe your historical mixture, but it need not represent the game you plan to play next. A reliable total also depends on a reliable denominator, so a guessed live hand count should be labelled as an estimate.
Standard deviation needs more detailed information than a net result and total hours. If you have comparable blocks containing the same number of hands, their result spread can be rescaled under the independence assumption: divide the block standard deviation in big blinds by the square root of the block hand count divided by one hundred. Unequal session lengths require a method that accounts for exposure, rather than treating every session as an equivalent observation. An all-in equity-adjusted graph also measures something different from realised results and removes only a particular source of variation. Use realised outcomes for the examples here, and keep any decision-quality review distinct from the statistical summary.
Keep the evidence useful and the stakes affordable
A practical review starts with whether your records are complete and whether their context still matches your current play. Note changes in stakes, playing conditions and session length so you can recognise when an old average no longer describes the same activity. Overshove's free core logs every cash session, including stakes, hours and result, so the numbers above can come from a full history. Session records still need credible hand counts and suitable result detail before you can estimate the hand-based standard deviation used here. Treat a statistical review as one part of deciding whether to continue, alongside your spending limits, available time and willingness to accept losses.
Poker is an adult pastime with real financial risk. Play only with money set aside as a bankroll, never with money meant for bills. An unfavourable result does not create an obligation to recover it, and a positive model estimate is not a reason to increase your stakes. Stop if you find yourself chasing losses, borrowing to play or hiding expenditure from people affected by it. The responsible play page lists free, confidential support. You can use that support before a situation becomes severe, including when you are unsure whether your habits are changing. Mathematical uncertainty should help you recognise limits to your knowledge, while personal limits determine what you can afford to risk.
Sources
Sources checked on 2026-10-03. The figures on this page come from the stated model and formulas.
- →Treat 5 bb/100 and 140 bb/100 as example assumptions, not established PLO benchmarks.
- →At 10,000 hands, the assumed model gives a 36.0% chance of finishing below break-even.
- →Confidence bands describe uncertainty in a win rate; endpoint ranges describe total results in big blinds.
- →Bankroll estimates depend heavily on a positive edge and do not measure the deepest drawdown within a sample.
Questions
Can I use these examples as a PLO variance calculator?
Yes, as a static worked reference. Follow the formulas for expected result, result spread and confidence-band width using consistent hand counts and bb/100 inputs. For other assumptions, the linked poker variance calculator provides a separate tool; the figures on this page remain the stated examples.
Is there a standard deviation I should always use for Omaha?
No single value describes every Omaha game. The assumed 140 bb/100 illustrates the method without claiming to represent your stakes, stack depths or playing style. If you lack enough detailed records to estimate your spread, compare several plausible assumptions and treat the resulting uncertainty explicitly.
Does running below expectation prove that I am unlucky?
No. A gap from an assumed expectation can reflect random variation, an overstated edge, changed conditions or errors in the records. Reviewing individual decisions can identify issues that an aggregate result cannot, while a complete history helps you assess whether the statistical inputs remain credible.
Can I substitute sessions or hours for hands?
Not in these formulas. Their standard deviation and win-rate inputs use bb/100, so the exposure must be a hand count. Replacing hands with hours while retaining those inputs produces incompatible units. An hourly model requires separately estimated hourly inputs and an appropriate treatment of session duration.
Does the result range tell me how much I could lose?
It describes a central range of finishing outcomes under the model, leaving outcomes outside that range possible. It is neither a loss cap nor an estimate of the largest decline from an earlier peak. Your actual financial exposure also depends on stakes, deposits and when you stop playing.