Parlay Probability Calculator

The Parlay Probability Calculator multiplies independent win probabilities for two or three legs. Inputs: Leg 1 Win % (default 55), Leg 2 Win % (default 60), Leg 3 Win % optional (default 0, meaning unused). If p3 > 0 the combined probability is (p1/100)×(p2/100)×(p3/100)×100; otherwise it is (p1/100)×(p2/100)×100. Defaults with p3 = 0: 0.55 × 0.60 = 0.33 → 33.00%. That is the chance both legs win if they are independent. It is not the chance the book pays; the book’s price is a different object (see the parlay payout tool).

Add a third leg at 50%: combined = 0.55 × 0.60 × 0.50 = 0.165 → 16.50%. Drop Leg 1 to 50% with Leg 2 at 50% and no third: 25.00%. Four 50% legs would be 6.25% if you had a fourth field; you do not — this form stops at three. Zero on Leg 3 is the off switch, not a 0% chance of winning a live third leg. If you actually have a third selection at 0% you have a 0% parlay; type 0.01 if you meant “almost impossible but present.”

Independence is the landmine. Same-game parlays (a team to win and that team to cover, a striker to score and his team to win) are positively correlated; the product understates the joint if both legs load on the same match-state, or overstates it if the legs are negatively related. The calculator always multiplies. A 33.00% default is 55% of 60% under independence, a teaching number, not a correlated-soccer number.

Compare 33.00% to a book’s combined decimal. If two 1.91 prices multiply to 3.65, implied joint is 1/3.65 ≈ 27.4% if you trust the book’s singles. Your 33% model says the parlay is +EV versus that book if the singles were already +EV and independence holds — a stack of ifs. This page does not take odds, only probabilities.

Work the default out loud: coin-like 55% and 60% are not coins. They are estimates. Garbage in, 33% out. The product is the only math.

A parlay (accumulator, multi, patta in some markets) pays only if every leg wins. The probability of that event, under independence, is the product of the leg probabilities. Bookmakers love parlays because correlation, rounding, and the multiplication of already-padded singles inflate the margin. Players love them because a 3.65 combined price looks like a shortcut to a good story. SorteCalc’s probability tool isolates the product so you can see 33% before you look at a payout.

The independence assumption is the scientific scandal of same-game parlays, which US books productized in the 2020s. A wide receiver’s anytime TD and his team’s win are not independent Bernoulli trials. Sports statisticians build joint models; this page does not. For distinct sports, distinct times, distinct leagues, independence is a less ugly approximation. For 55% and 60% on two Premier League matches kicking off simultaneously, maybe. For two legs in the same match, no.

History: parlays are as old as bookmaking. The mathematics is undergraduate probability, P(A∩B) = P(A)P(B) under independence, a definition in Feller and every measure-theoretic text. What is new is the UX of clicking three player props. The optional third leg with 0 as “off” is an engineering choice shared with SorteCalc’s parlay payout calculator (odds 0 means unused).

Limits: three legs max, no odds, no correlation parameter, no push rules (a push typically reduces a parlay to the remaining legs; that is not modelled), no dead-heat. A 33.00% is not “almost one in three so it hits often.” A 33% event in independent trials still fails twice as often as it succeeds. Variance of a 1-unit parlay is large because the payout, if you took fair 1/0.33 ≈ 3.03 decimal, is a rare lump.

Use the page to deflate intuition. Two “likely” 70% legs are 49% together, a coin flip, not a lock. Three 70% legs are 34.3%. The product is how parlays eat players who add a “safe” extra team. Educational, not a tip.

Independence is the extra hypothesis that turns a joint chance into a product, and that is how an accumulator probability is calculated. Convert each typed win percent into a proportion of one, multiply those proportions, and scale the product back to a percent. When the third field is unused, conventionally by entering zero, the product stops at two factors. The teaching defaults are fifty-five percent, sixty percent, and an unused third leg: 0.55 times 0.60 equals 0.33, reported as 33.00 percent. That figure is the chance both legs win if they are independent trials. It is not the chance a bookmaker pays a posted combined price.

Huygens already multiplied chances of successive independent games in the seventeenth century. Fermat and Pascal treated a run of throws as a product of factors. Kolmogorov's axioms make an intersection factor only after independence is assumed, and Feller is blunt that the assumption is structure you add, not a free gift from the sample space. Same-game parlays violate it routinely: a striker to score and his team to win share a match state. Fréchet bounds then constrain how far the true joint can sit from the product. This lecture still multiplies; a conditional chance of the second leg given the first is never requested.

A third live leg at fifty percent yields 0.55 times 0.60 times 0.50 equals 0.165, printed as 16.50 percent. Forty, fifty, and sixty percent with the third field live give 12.00 percent. Returning that third field to unused leaves the same forty and fifty as 20.00 percent. Two even coins, fifty and fifty with no third, are 25.00 percent. Three even coins would be 12.50 percent, a useful classroom check that is not the page default. Two seventy-percent legs are 49.00 percent together, a coin flip dressed as a lock. Three seventy-percent legs are 34.30 percent. Adding a supposedly safe extra selection is how parlays devour intuition.

Fair combined decimal odds, if the product were a true probability, equal one hundred divided by the combined percent. At 33.00 percent that is about 3.0303. Two singles at 1.91 multiply to about 3.65, whose implied joint is roughly 27.4 percent if you trust those singles. Comparing 33.00 percent with 27.4 percent is a conversion exercise, not a proof of value: the singles may already contain overround, and independence may fail. This calculation never takes odds; it only multiplies probabilities.

Variance of an all-win indicator is p times one minus p. At 33.00 percent that is 0.33 times 0.67, namely 0.2211, so the standard deviation on a zero-one scale is near 0.47. A unit stake at a fair 3.03 therefore has a fat right tail and a frequent total loss. Pushes, voids, and dead-heats break the product because a push typically reduces a parlay to the remaining legs. Four legs sit outside the form; multiply the two-leg 33.00 percent by a fourth chance yourself if you must. Assumptions: independence, an unused third means two legs rather than a live zero, and the typed percents are true chances rather than implied prices.