Parlay math: the hold multiplies and the payout does not

Run the arithmetic once and the product stops being confusing

Minus 110 is decimal 1.9091. Three of those multiply to 6.9589, so a three-leg parlay pays about plus 596. If each leg is a genuine coin flip, you win one time in eight, and the fair payout would be decimal 8.0, or plus 700. You are being paid 6.96 for something worth 8. That is a 13.0% expected loss on every dollar, against 4.55% for a single bet.

The pattern is exact and worth memorising as a multiplier. Each leg keeps 95.45% of fair value, so n legs keep 0.9545 to the power n. Five legs: 79.3% retained, 20.7% given up. Ten legs: 62.8% retained, 37.2% given up. A ten-leg parlay is a slot machine with a spreadsheet attached, and the house edge is in slot-machine territory.

• Convert every leg to decimal odds.
• Multiply them together for the fair combined price.
• Compare that against the payout the book is actually offering.
• The shortfall, divided by the fair price, is the hold you are paying.

Correlation is priced, and it is priced against you

The old rule was that books refused correlated legs because a correlation you can see is free money. That rule is gone: same-game parlays are now a headline product. They were not made available because the correlation stopped mattering. They were made available because the books learned to price it, and a correlated parlay is repriced from the independent product down to something reflecting the real joint probability, plus margin on top.

Which means the intuitive correlation, the quarterback throwing for a lot in a game his team wins, is already in the number. The correlations still worth anything are the ones that are structural rather than narrative, and they are mostly gone within a season of anyone finding them. Treat a same-game parlay as a single bespoke bet on a joint outcome, priced by someone with more data than you, and judge it on that basis rather than by multiplying the legs yourself.

The one parlay with a real argument behind it

If every leg is genuinely independent and genuinely positive expected value, the edges multiply exactly the way the hold does. Three legs each returning 1.05 per dollar staked combine to 1.05 cubed, which is 15.8% expected return rather than 5%. This is real, it is the mirror image of the hold arithmetic, and it is the only version of the argument that survives contact with a calculator.

It comes with a condition almost nobody meets: you need a demonstrated edge on all three legs at once, and independence you can defend rather than assume. Variance also multiplies, so the same parlay that triples your edge also drives your win rate into the low single digits, which pushes the sample size you would need to prove any of it out past the point of being answerable. Every other justification for a parlay, the correlated hedge, the round robin, the low-stake lottery ticket, is a story about entertainment spending. That is a legitimate thing to buy. It is not an investment thesis.