The Parlay Leak
Everyone knows parlays are hard to hit. The more interesting question is what happens to the price.
Real parlays can contain correlated legs. Sportsbooks may adjust prices for that correlation. We use independent coin-flip legs here so you can see the multiplication clearly.
Each dot is one possible sequence of ten independent coin flips. Every added leg removes exactly half of the remaining worlds.
Now change what the sportsbook pays.
Odds format
The true probability stays at 50% per leg in every mode. The dot grid does not move and the hit probability does not change. Only the payout does.
The chance of winning never changed.
The payout did.
Each leg contains a pricing disadvantage. Multiplying the leg prices multiplies those disadvantages too.
The disadvantage does not sit still at -4.55%.
Rare does not mean bad.
High EV does not mean bet big.
Same +3% edge on every leg.
Bankroll $10,000The parlay has the bigger EV percentage. Kelly gives it the smaller stake.
Because 1,023 of the 1,024 possible ten-leg worlds lose.
What if you bet $100 anyway?
Want to feel 1 in 1,024?
Why normal parlays leak
When each individual leg is priced worse than fair, multiplying those prices multiplies the disadvantage.
What if every leg really has value?
Then the opposite happens. Positive edge compounds too.
So why not parlay everything?
Because EV percentage is not the same thing as bankroll allocation.
A bet that wins roughly once in a thousand attempts can have enormous positive EV and still deserve only a tiny fraction of bankroll.
If you enjoy a small parlay for entertainment, that is a different objective from bankroll growth.
Price the legs. Then size the bet.
Finished models for the sports you already follow.
See the modelsTen-leg reference: 1376.17 decimal at +106 per leg.