The ten-leg parlay: the jackpot price and the real chance of hitting it
Parlays
Ten legs that are each a coin flip all win 0.098% of the time, one parlay in 1,024. At -110 per leg it pays 643.08 for 1 against a fair 1,024: an edge of 37.20%.
- 0.098%chance to win
- 643.08payout
- 37.20%bookmaker's edge
The Probability of Success
Each leg acts like a coin flip. The chance of winning one leg is half. Ten independent legs multiply these chances. The result is a very low probability of success. As the key figures show, the win rate is minimal. Most attempts fail. The table below lists the specific chance for ten legs. It shows how the probability drops as legs are added. Each new leg multiplies the previous chance by one-half. This multiplication explains why long parlays are difficult to win. Short runs may vary, but the average holds true over time.
| Legs | Chance to win | Pays at -110 |
|---|---|---|
| 4 | 6.2% | 13.28 |
| 6 | 1.6% | 48.41 |
| 8 | 0.39% | 176.45 |
| 10 | 0.098% | 643.08 |
| 12 | 0.024% | 2,343.79 |
Payout Structure and Fair Odds
A standard price applies to each leg. This price sets the payout ratio. For ten legs, the total payout compounds these ratios. The table above shows the final number. It is significantly lower than the reciprocal of the win probability. The fair payout would match the inverse chance exactly. The actual payout falls short of this fair value. This gap represents the cost of the bet. The difference is not random noise. It is a fixed feature of the pricing model used by operators.
Understanding the House Edge
The difference between the actual payout and the fair payout creates the edge. As the key figures show, this edge is substantial. It exceeds the win probability itself. The comparison confirms the edge is larger than the chance of winning. This means the expected return is less than the stake. Over many bets, this shortfall accumulates. It does not depend on skill or luck. It is a mathematical certainty derived from the price structure. The edge ensures the operator retains a portion of every stake. This calculation applies specifically to the ten-leg structure described here. If gambling stops being fun, free help is available via support resources.
Questions
Why does adding legs lower the win chance?
Each leg must win independently. Multiplying halves reduces the total probability quickly. Ten halves result in a very small fraction. The chance decreases rapidly with each added leg.
Is the payout fair for a ten-leg bet?
No. The actual payout is lower than the fair odds derived from the win probability. This difference creates the house edge. The table above shows this gap clearly.
Does a higher payout mean better value?
Not necessarily. The payout is adjusted to account for the low win chance. The house edge remains constant per unit staked. Higher payouts do not offset the mathematical disadvantage.
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.