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Parlay Calculator

Combine each leg's odds into one price and payout, and fair odds showing how the margin compounds.

This prices a slip and shows the shape of betting it repeatedly. It does not assess whether any individual leg is priced correctly, which is the input you have to bring.

Combined odds (3 legs)

6.77

Stake$10Combined odds6.77Payout$67.66

Profit

$57.66

Fractional

444/77

American

+577

1. Build the slip

Every price field reads a decimal price (2.50). Switch the format above to enter prices the way your book quotes them, or open the odds converter to see one price in all of them.

2. Climb the ladder

0/0 wonSlips settled here, and how many came in.

  1. Stake100% of slips, staking $10.00
  2. Leg 1at 2.1047.6% of slips still alive, returning $21.00
  3. Leg 2at 1.8026.5% of slips still alive, returning $37.80
  4. Leg 3at 1.7914.8% of slips still alive, returning $67.66

Running

$0.00

Settle your slip leg by leg, one miss and the whole thing is dead. Each leg hits at the probability its own price implies, which is the optimistic case: a real price carries the bookmaker’s margin. This one is a single random draw per leg, not the seeded run below, so the same slip will not answer the same way twice.

A parlay only pays if every leg wins, and each leg carries its own bookmaker margin. Turning on fair-odds shows how that margin compounds: the EV of a parlay is usually worse than betting the legs singly.

Betting this slip 100 times

Simulating…

Each leg is simulated at the probability its own price implies, which makes every slip break even on average. That is the optimistic case, not a neutral one: a real price carries a margin, so a real season is worse than the spread above. Enter fair odds to see by how much.

Share this scenario

A link to this page opens the calculator on the same legs, prices and stake, with the same notes and limits shown here. It carries those inputs and nothing else: nothing is stored, and nothing in it identifies you.

Written and reviewed by Alexander Korsager · last reviewed October 7, 2026 · corrections

The idea

What this tool shows

A parlay (or accumulator) rolls several bets into one: every leg has to win, and the odds multiply together. Three legs at 2.10, 1.80 and 1.79 combine to 6.77, turning a $10 stake into a $67.66 return.

  1. The catch is that the bookmaker's margin compounds with the odds.Each leg carries a slice of overround, so a parlay's true expected value is usually worse than betting the legs one at a time. This calculator shows the price and payout so you can judge it.

FAQ

Questions players ask

How are parlay odds calculated?

Multiply the decimal odds of every leg together. 2.00 × 1.50 × 1.80 = 5.40. The payout is that figure times your stake.

Why are parlays considered bad value?

Because the bookmaker's edge is applied to each leg and then multiplied. A small margin per leg becomes a large combined drag over four or five legs.

When can a parlay make sense?

When the individual legs are genuinely +EV, or when correlated outcomes are priced as if independent. Mark the related legs in the calculator to see what that second case is actually worth at a correlation you are willing to defend, and note that it cuts the other way just as often: a leg pulling against the others makes the slip rarer than multiplying the prices suggests. Otherwise singles are usually better.

Methodology

How this is calculated

The combined price is the product of the legs' decimal odds, and the payout is that price multiplied by the stake. Marking legs as related switches how often the slip lands to a one-factor Gaussian copula, evaluated by numerical integration, which gives a fair price for the slip that the multiplication cannot.

Turning on fair odds separately adds three more figures, all of them arithmetic rather than simulation. Fair combined is the product of the fair prices you enter.

Parlay EV is the offered combined price divided by that fair one (or, with legs marked, by the joint probability the copula gives them), minus 1, read as a percentage of the stake on one slip.

Margin per leg is the geometric average of how far each offered price falls short of the fair price you gave it, which is the nth root of fair combined over offered combined, minus 1, and is unaffected by any relationship marked since it is a statement about price rather than about how the legs land together.

Those three are one relationship on an unrelated slip, and writing it out turns this page's central claim into something you can check rather than take on trust: at a margin of m per leg across n legs, the slip's EV is 1 / (1 + m) to the power n, minus 1.

The panel renders that curve at this slip's own margin per leg, across leg counts from one to twelve, right below the margin figure, so the identity is something to read off the page rather than something to retype.

The distribution above comes from a third method: a Monte Carlo simulation of 3,000 seasons, each one placing this same slip 100 times, recording what share of seasons finished ahead, how many slips landed, and where the season's profit or loss ended up.

A fourth block sits right after the slip you build, above that season run, and is none of those methods: it settles one slip leg by leg, as a single random draw per leg. That one is a demonstration, not a measurement.

It is unseeded on purpose, so it answers differently every time, and nothing else on the page reads anything it produces.

Common misreadings8
  • A relationship strength turned up until the slip looks good is a number about you rather than about the game. The setting exists to show the size of the effect at a strength you are willing to defend, and the price it produces is only ever as good as that guess.
  • A large positive figure against the offered price is usually not something left on the table. It more often means the book has already priced the correlation into a same-game market, or will not accept those legs on one slip at all, both of which happen before any of this arithmetic applies.
  • A payout figure is what one winning slip returns. On a long slip it is also the rarest thing that happens, and the share of simulated seasons in which no slip landed at all is shown next to it for that reason.
  • More seasons finishing ahead than behind does not mean the bet is profitable. On a long slip the losing seasons lose the entire outlay, which is exactly why the average and the typical season disagree.
  • A simulated season finishing ahead is not a forecast of your season. It is the share of runs that did, at the prices you entered.
  • Parlay EV is a percentage of one slip's stake, not of a season's turnover, and a single-digit figure reads smaller than it spends. Betting a slip priced at 8% against you a hundred times is where that number actually lands, which is the spread above rather than the stat.
  • A margin per leg in the low single digits is not a small margin. It is the per-leg figure, and the point of the identity above is that the slip charges you the compounded version of it, not that one.
  • Climb the ladder keeps a running won/played tally and nothing else. It used to keep a dollar total too, first a best payout, then a lifetime staked-and-returned figure, and both were removed rather than reworded: a number that only ever accumulates reads as win-only the longer you play, which is exactly the misreading the spread above exists to correct. The hit rate is what is left, and it gets worse as readily as it gets better, which a dollar total that mostly rises could not.
Assumptions10
  • Legs are treated as independent unless you mark them as related. Marking puts the marked legs on one shared driver: legs marked the same way land together more often than the product of their prices implies, and a leg marked the other way pulls against them. Marking never changes what an individual leg is worth, only how often the legs land together.
  • Related legs are modeled with a one-factor Gaussian copula. Each leg lands when a hidden standard normal falls below the threshold its own price sets, and the marked legs share part of that draw. The joint probability is computed by numerical integration rather than simulated, so the fair price shown for a relationship is exact for the model.
  • The relationship strength is a setting you choose, not a measurement of any market. It is the tetrachoric correlation between the marked legs, which is a standard statistic, but nobody publishes values for arbitrary same-game legs and this tool does not invent any. The page shows how often the marked legs land together at each setting so the choice is made against something observable.
  • The offered price is always the product of the legs' odds, whatever relationship is marked, because that is what a bookmaker pays. Only how often the slip lands changes.
  • Each leg is simulated at the probability implied by the odds entered, which makes every slip break even on average. That is the optimistic case, not a neutral one: a real price carries a bookmaker margin, so a real season is worse than the simulated one.
  • Where fair odds are entered for every leg, those are used instead, so the margin you have implied is priced into the simulation. Both sides have to be complete for that: if a leg's own price is blank or half-typed, the fair figures are held back and the page says so, rather than setting a fair combined across every leg against a combined price built from fewer.
  • The fair odds are yours. Nothing on this page estimates them, so the EV and the margin figures carry your read of the market rather than a measured one, and they are exactly as good as the prices you supply. The no-vig calculator is the usual way to get a fair price out of a real market rather than out of a hunch.
  • 3,000 simulated seasons of 100 slips, run in your browser from a fixed seed, so the same inputs always produce the same picture.
  • The stake is the same on every slip and the bankroll is not modeled, so a season is not stopped early by running out of money.
  • Climb the ladder, right after the one you build, settles each leg at the same probability the season simulation is using, which is the fair odds where you supplied a complete set and the price entered otherwise. What a winning slip pays there is always the offered price, because that is what a book would actually hand you. Unlike the season run it is unseeded, by design: settling the same slip twice should not give the same answer.
Limits5
  • A relationship runs through one shared driver. A slip with two genuinely separate stories in it is more than this models, and what it returns for that case is the closest single-driver answer rather than the exact one.
  • 100 slips is a stated stretch of betting, not a career, and the spread scales with it. A longer run of the same slip has a narrower spread around the same average.
  • Simulating the same slip repeatedly is a model, not a description of how anyone bets. It isolates the effect of the slip's shape by holding everything else fixed.
  • Margin per leg is not the overround a market is normally quoted at. Overround is measured across every price in a market at once; this is measured on the one side you actually took, against a fair price you supplied. The two agree only where a two-way market is shaded evenly on both sides, and books rarely shade a favorite and a longshot the same way.
  • The EV figure inherits the independence assumption above, so on correlated legs it is wrong by however much the legs move together. It usually errs in the book's favor rather than yours: a book willing to combine those legs has normally priced the correlation already, which is the case where a parlay looks cheapest and is not.
Evidence

The season simulation is covered in simulate.test.ts, which checks that slips land at the combined implied probability, that a season nets zero on average at implied prices, that a margin taken out of the fair odds turns that negative, and that a long slip produces the pattern the page describes.

The correlation model is covered in correlation.test.ts, which pins the two-leg case against Sheppard's closed form for the bivariate normal orthant at every strength offered, checks that no setting ever changes what an individual leg is worth, checks the result stays inside the Frechet bounds, and cross-checks the integrated price against 200,000 simulated slips drawn by separate code.

The price, EV and margin figures are a different kind of claim: they are closed-form identities rather than a model, and math.test.ts pins the identity in the summary along with the rule that the fair figures are withheld unless both sides carry a readable price for every leg.

That rule is there because it once was not: until 2026-09-10 a leg left blank or caught mid-edit dropped out of the offered price and stayed in the fair one, so the panel could set three fair legs against two offered ones and print the result as an EV.

The identity is also a check you can run yourself, by taking the three numbers off the panel and putting them back through the relationship in the summary. A passing test means the code matches the model, not that the model fits every real market.

Climb the ladder is deliberately in none of those categories: it is one random draw per leg rather than a model, so there is no claim there for a test to pin, and its running total lives only in your own browser.

Gambling can cause serious harm. The National Problem Gambling Helpline is free, confidential and open 24/7, call or text 1-800-MY-RESET (1-800-697-3738), or chat at ncpgambling.org/chat.

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