How Do Parlays Work? The Math Behind Those Big Payouts
The gateway ritual of Taiwan sports betting - and the truth about its expected value
The Rules
A parlay ties the predictions from several games onto a single ticket. The total odds are the product of every leg's odds, and the ticket only pays out if every pick hits - one miss and the whole ticket is dead. Under Taiwan Sports Lottery rules, a parlay requires at least 2 legs (some events are flagged "no single bet" and require 3 or more legs).
But if each of the three legs has about a 52% hit rate, the odds of hitting all three are only 0.52³ ≈ 14%.
Why More Legs Means Worse EV
The book takes its cut on every single leg. If a single leg returns 95% in expectation (5% vig), an n-leg parlay returns 0.95 to the nth power: 2 legs 90.3%, 4 legs 81.5%, 6 legs 73.5% - legs compound the vig. To check whether a given parlay is worth it, plug each leg's odds into the parlay calculator, then use the expected value calculator to vet each leg one by one.
A Sensible Way to Use Parlays
Treating a parlay as a "small stake, big upside" bit of entertainment is fine; treating it as your main profit engine is not. In practice: put your core bankroll on the single leg (or 2-leg) you're most confident in, keep parlays under 10% of your total stake, and make sure every leg is itself a pick you consider +EV - not a weak recommendation stuffed onto the ticket just to add a leg.
Frequently Asked Questions
Can I place a single-game bet on Taiwan Sports Lottery?
For most events the law requires at least 2 legs (a parlay). Some popular events allow single-game bets, but they're usually flagged as such. Always defer to the official Taiwan Sports Lottery rules for each bet type.
How are parlay odds calculated?
You simply multiply each leg's decimal (European) odds together. Example: 1.85 × 1.90 × 2.00 = 7.03x.
Why are parlays hard to profit from?
The vig is charged once on every leg, so expected value decays with each added leg through compounding; on top of that, the probability of hitting everything is the product of each leg's probability, which drops faster than intuition suggests.