Parlays and Props

A parlay chains several bets into one ticket, and every leg must win or the ticket dies. Payouts multiply, which is the appeal; the bookmaker's margin multiplies too, which is the catch. Use the parlay calculator to see both numbers for any combination of legs. Props are side markets on events inside a game, like a player's passing yards, and they carry their own pricing warning.

A three-leg parlay, fully worked

Build a parlay from three ordinary -110 legs, each converting to decimal 1.909. The combined price multiplies: 1.909 x 1.909 x 1.909 = 6.96, so a $10 ticket returns $69.60 if all three legs hit. So far, so shiny. Now check what that price implies.

• Implied probability of the ticket: 1/6.96 = 14.4%. The book is pricing your parlay as a 14.4% shot.
• True chance if each leg is a fair coin flip: 0.50 x 0.50 x 0.50 = 12.5%.
• Fair payout for a 12.5% event: decimal 8.00, so $10 should return $80.
• The gap: you're paid at 6.96 for an 8.00 risk, surrendering about 13% of fair value versus roughly 4.5% on one straight bet.

Where does 1.909 come from? It's the decimal form of -110: 100/110 + 1. And 6.96 rounds from 6.958, which books often display as +596, meaning $100 wins $596. Every number on the ticket traces back to arithmetic you can redo yourself.

The compounding is the whole story. Each leg quietly re-charges the vig, so the total cost snowballs: two legs give up about 9% of fair value, three about 13%, five over 20%. Meanwhile the win probability collapses toward lottery territory. Parlays are the rare product where the price gets worse precisely as the bet gets harder to win.

Props and same-game parlays

Props, markets like first touchdown scorer or a player's total rebounds, tend to carry wider margins than main lines. Fewer bettors study them, less sharp money disciplines the numbers, and books face little pressure to keep them tight. Fun market, expensive prices.

A quick self-test for any prop: convert both sides to implied probabilities and sum them, exactly as you did for spreads. Where a main line totals 104-105%, props often total 107-110%. Nothing about the market is hidden; it's just that almost nobody checks.

Same-game parlays deserve extra care. When legs are correlated, say a quarterback's passing yards and his team's total points, books reprice the combination rather than naively multiplying, and the repricing rarely favors you. The ticket looks like clever stacking; the math underneath has already accounted for the cleverness.

The mistakes parlays manufacture

The signature parlay mistake is emotional accounting. Hitting four legs of five feels agonizingly close, so people re-up, but a ticket missing one leg pays exactly what missing every leg pays: nothing. Near-misses are baked into the product. A five-leg parlay of coin flips misses by exactly one leg about 16% of the time, five times as often as it wins.

The second mistake is reading a big payout as a good price. Payout size and price quality are independent, and in parlays they usually point in opposite directions. The third is staking real money on longshots because the potential number looks life-changing. If a ticket only makes sense when you imagine it winning, it doesn't make sense.

There's no rule against parlays or props in an informed bettor's life. The rule is knowing what you bought: a lottery-shaped product where the house edge compounds per leg. Straight bets at good prices are boring, and boring is what the math rewards.