How the margin grows in a parlay
A walk-through of the sportsbook margin at -110 and how it multiplies across parlay legs, assuming every leg is a true 50% chance.
At -110, you risk $110 to win $100.
American odds with a minus sign tell you what you must risk to win $100. At -110, a winning bet returns your $110 stake plus $100 in profit. A losing bet costs the whole $110. The price looks even-handed because the two amounts are close, but they are not equal, and that small gap is where the whole story starts.
At -110 you must win 52.4% of the time just to break even.
Every price implies a chance. At -110 the break-even rate is 110 divided by 210, which is 52.4%. A coin flip wins only 50.0% of the time, so someone who backs -110 on a pure coin flip is already behind. The bar shows the distance between the break-even rate and the coin flip.
Both sides at -110 imply 104.8% in total, and the extra is the margin.
A fair two-way market has implied chances that add up to 100%. When a sportsbook prices both sides at -110, each side implies 52.4% and the total is 104.8%. The extra 4.8 points is the margin, often called the vig or juice. It is the sportsbook's built-in fee, and you pay it whichever side wins.
On a true 50% chance, each $100 bet at -110 loses $4.55 on average.
Suppose a bet really is a 50% chance. Win and you collect $90.91 on a $100 stake, lose and you give up $100. Averaged over many bets, that works out to a loss of $4.55 per $100. The 50% here is an assumption chosen to isolate the margin. Real chances are never known.
Two legs at -110 pay +264 and break even at 27.4%.
A parlay multiplies the decimal prices of its legs, and every leg must win. Two legs at -110 pay about +264. The break-even rate is 27.4%, but two true 50% chances both win only 25.0% of the time. The gap between 27.4% and 25.0% is wider than the gap on a single bet.
Three legs pay +596 and need a 14.4% win rate to break even.
A third leg multiplies the price again, to about +596. Break-even falls to 14.4%, while three true 50% chances all win 12.5% of the time. The prize grows with each leg, but the share of it you have to win to break even is always further from the true chance than before.
Four legs pay +1228 and need 7.5% to break even, against a true 6.3%.
Four legs at -110 pay about +1228. Break-even is 7.5%, and four true 50% chances all win 6.3% of the time, which is 6.25% before rounding. The margin from each leg compounds, so a long parlay is the same fee charged over and over, with a bigger payout on the side that hides it.
Average loss per $100 grows with every leg, from $4.55 to $16.98.
Put the expected results side by side. One leg at -110 loses $4.55 per $100 staked, two legs lose $8.88, three lose $13.03 and four lose $16.98. All of them assume each leg is a true 50% chance. A single result can still win, because averages describe many bets, not one.
Remove the margin: four legs at +100 pay +1500 and the expected loss is $0.00.
At true even money, +100 on every leg, four legs pay +1500 and the expected loss is exactly $0.00. Break-even and the true chance both land at 6.3%, so the bars are equal. This is the check on the arithmetic: the whole expected loss in the earlier steps comes from the margin and nothing else.