Why parlays cost more: the bookmaker's margin compounds with every leg
Parlays
One bet at -110 costs 4.55% of the stake on average; a four-leg parlay of such bets costs 16.98%. It pays 13.28 for 1 where the fair price is 16.
- 4.55%one leg
- 16.98%four legs
- 24.36%six legs
How margins accumulate
A single bet at -110 pays 1.91 for 1 on an outcome that wins half the time, so the bookmaker keeps 4.55% of every stake on average. A parlay multiplies the prices of its legs, and every price already holds back part of the fair payout, so each leg cuts the payout again: two legs cost 8.88% of the stake, four legs 16.98%, six legs 24.36%. Each extra leg adds a little less than one more margin, because it takes its cut from a payout the earlier legs have already reduced, but the share of the fair price you are paid keeps shrinking.
| Legs | Bookmaker's edge |
|---|---|
| 2 | 8.9% |
| 3 | 13.0% |
| 4 | 17.0% |
| 5 | 20.8% |
| 6 | 24.4% |
| 8 | 31.1% |
| 10 | 37.2% |
The role of independence
The figures assume every leg is a genuine 50/50 outcome, independent of the others. Four such legs all win one time in sixteen, so a fair four-leg parlay would pay 16 for 1; at -110 per leg it pays 13.28. Per unit staked, that parlay costs almost four times as much as a single bet. In money, one four-leg parlay costs a little less than four single bets of the same stake on the same games, but it risks one stake instead of four and loses it fifteen times in sixteen. Adding legs never improves the chance of winning; it only raises the price of each unit staked. If betting stops being fun, free help is available.
Comparing payout structures
The table compares, for each number of legs, what the parlay pays, what it would pay without a margin, and the bookmaker's edge. The gap between the two payouts is the price of the bet, and it widens with every leg. The same arithmetic holds for any fixed-odds parlay: the bigger the margin on each leg, the faster the gap grows.
Questions
Why does the house edge increase with more legs?
Because a parlay multiplies the prices of its legs, and every price is shaded by the bookmaker's margin. Each leg cuts the payout again: at -110 one leg costs 4.55% of the stake, four legs 16.98%.
Is a single bet better than a parlay?
Per unit staked, a single bet costs less: 4.55% at -110 against 16.98% for a four-leg parlay. Neither wins money on average.
How is the fair price calculated?
For legs that each win half the time, the fair price doubles with every leg: 16 for 1 with four legs. The real payout, 13.28, is lower by the margin of every leg.
Every figure on this page is computed by code from exact fractions for odds, margins and parlays, and closed-form Kelly growth, each checked by a seeded simulation. See the methodology.