The Hidden Math · pure math · no signup
What −110 really costs over 100 bets
A −110 line looks like a coin flip with a small tax. It isn’t quite. It needs a 52.38% win rate just to break even — and over a run of bets, that gap is the house edge, in real dollars. Below is the exact cost, worked out. This is market math, not a pick.
Break-even win rate at −110
52.38%
110 ÷ (110 + 100) = 52.38%
The break-even win rate is just the price’s implied probability — the share of bets you must win to come out even. Not 50%. That extra 2.38% is the vig.
The ledger — 100 bets of $100 at −110
Each win pays $90.91 (risk $100 to win $90.91); each loss costs $100. Total staked across the run: $10,000.
| If you win… | Wins | Losses | Net over 100 bets |
|---|---|---|---|
| 52.38% (break-even) | 52.38 | 47.62 | $0.00 |
| 50.00% (a true coin flip) | 50.00 | 50.00 | −$454.55 |
Win exactly 52.38% and you’re flat — you paid the vig by needing more than half. Win a true half, and you’re down $454.55. That is the hold — 4.55% of the $10,000 you put through — the book’s cut, cumulative, whether or not you notice it.
The same, at other prices
Break-even win rate, the two-sided hold, and the hold’s cumulative cost over 100 bets of $100 ($10,000 of action).
| Price | Break-even | Hold | Cost / 100 bets |
|---|---|---|---|
| -105 | 51.22% | 2.38% | $238.10 |
| -110 | 52.38% | 4.55% | $454.55 |
| -115 | 53.49% | 6.52% | $652.17 |
| -120 | 54.55% | 8.33% | $833.33 |
A dime of extra juice (−110 → −120) nearly doubles the toll. Shopping the price is the cheapest way to cut that cost — it lowers the number you have to beat.
Methodology
- • No live data. This is arithmetic, not a market snapshot — nothing to date-stamp. The prices shown are the standard round numbers.
- • Break-even = implied probability. For −110: 110 ÷ (110 + 100) = 52.38%. The win rate the price is built around.
- • Hold = the two-sided overround ÷ (1 + overround) — the book’s take on balanced action at that price. The ledger applies it to $10,000 of −110 bets.
- • Net = wins × payout − losses × stake, over 100 bets. At the break-even win rate it lands at zero; at 50% it lands at exactly the hold.
Related tools: break-even calculator · no-vig calculator · NFL futures cost · parlay vig calculator. This page shows the cost of a bet, not a prediction of the result.
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