Parlays, accumulators and bet builders: how the maths works

A parlay (the UK calls it an accumulator or acca) is one bet made of several selections. Every selection, or leg, must win. The odds of each leg multiply together, which is why small stakes can show large potential returns. The bookmaker's margin multiplies in exactly the same way, which is the part the bet slip does not show you.

How the odds multiply

Take three illustrative legs in decimal odds: 1.80, 2.00 and 1.50. The parlay price is 1.80 × 2.00 × 1.50 = 5.40. A £10 stake returns £54 if all three win and nothing if any one loses.

If a leg is void (a postponed match, a non-runner), it is usually removed and the rest of the bet is settled at the lower combined odds. Check the sportsbook's rules for the market.

To switch between American, fractional and decimal prices before you multiply, use the converter:

Why the margin compounds

Every price a bookmaker offers is shorter than the fair price. As an illustration, suppose each leg is a two-way market where both outcomes are truly 50/50. The fair price is 2.00. A book with a 4.5% margin (the two implied probabilities add up to 104.5%) prices each side at 2.00 ÷ 1.045 = 1.914.

On a single, you get back on average 1 ÷ 1.045 = 95.7% of your stake. On a parlay, that fraction is multiplied once per leg:

The arithmetic: 0.957 × 0.957 = 0.916 for two legs; raise 0.957 to the fourth power for 0.839; to the eighth for 0.703. An eight-leg parlay at these prices costs you nearly 30% of your stake on average, against about 4% on a single. Real margins vary by sport and market, but the pattern holds for any margin: the more legs, the bigger the share the bookmaker keeps.

This is also why long parlays win so rarely. Eight true coin-flips all landing has a probability of 1 in 256, about 0.4%.

Same-game parlays and bet builders

A same-game parlay (US) or bet builder (UK) combines several selections from one match: a team to win, over 2.5 goals, a player to score. The difference from a normal parlay is correlation. Events in the same game are linked.

As an illustration, say a team has a 50% chance to win and the match has a 50% chance of three or more goals. If the two were unrelated, both happening would be 25% likely, a fair price of 4.00. But a team that wins is more likely to have been in a high-scoring game. If the true chance of both is 32%, the fair price is only 3.13.

Bookmakers model this and price the combination below the simple product. In the example, an offer of 2.90 would return 0.32 × 2.90 = 92.8p per £1 on average, a margin of over 7%. Bet builders usually show one combined price and do not let you see each leg's adjustment, which makes the margin harder to judge than on a normal parlay.

Teasers

A teaser is a US parlay where you move the point spread or total in your favour on every leg by a set number of points, in exchange for a much lower payout. Every leg must still win. Moving the line makes each leg more likely to win, but the payout table is set by the sportsbook, so whether a teaser is fair or poor value depends entirely on how much the shifted points are actually worth in that sport. Points that move a line across a common final margin are worth more than points that do not, so the same teaser can be fair on one game and poor on another.

Cash-out on parlays

Many sportsbooks offer cash-out on a parlay that is still running: an amount now, in place of waiting for the remaining legs. The UK Gambling Commission notes that bookmakers reserve the right to withdraw cash-out at any time, that markets are suspended during match incidents such as goals, and that this makes it difficult to cash out a bet that contains multiple selections. Its in-play guidance says operators offering cash-out must set out clear terms on availability, acceptance and settlement.

The cash-out figure is priced from the current odds of the remaining legs, and those odds include a margin. On a parlay, that margin applies to every open leg, so cashing out is a cost, not a neutral exit. Our live in-play betting guide works through a cash-out example.

Acca insurance: the terms to read

Acca insurance refunds your stake, or part of it, if one leg of an accumulator loses. It is a promotion, so the terms set its value. Before you count on it, check:

• Refund form. Is the refund cash or a bet credit? A bet credit usually does not return its stake when used, so it is worth less than its face value. See our odds boosts and promotions guide for the arithmetic.
• Minimum legs and minimum odds. Offers often need a set number of legs, each at or above minimum odds, which pushes you towards longer parlays with a larger total margin.
• Maximum refund. A cap on the refund limits its value on larger stakes.
• Exactly one leg. Check whether the offer applies only when a single leg loses.
• Cash-out. Cashing out may void the insurance.
• Market restrictions. Some markets or bet types may not qualify.

UK advertising guidance from CAP says that if a promotion needs a qualifying bet, the advert must say so clearly, and that significant conditions such as minimum odds and time limits must be stated.

Mistakes to avoid

• Adding legs for a bigger number. Each extra leg raises the margin you pay.
• Treating a bet builder like independent selections. Correlation pricing means the combined odds are shorter than they look.
• Picking insured accas for the insurance. The terms often shape the bet in the bookmaker's favour.
• Cashing out by habit. It is a sale back to the bookmaker at its price.

Where to bet

See our UK betting site listings, New Jersey sportsbook listings and the sports betting markets hub. For the basics, read how to read betting odds and sports bet types explained.