What are these odds really saying?
Turn any betting line into a chance, find the bookmaker's cut, and see what a careful bettor would stake.
Try it with your own numbers
60% is what the odds say. At your 64%, a $100 bet is worth +$6.67 on average.
A championship game moneyline: pick who wins. The favorite is −150, the underdog +130. Made-up lines, not live prices.
Like −110 or +150. Add the other side to see the bookmaker's margin.
- Odds say
- 60%
- the chance you need just to break even
- Win on $100
- $67
- back as $167 with your stake
- Your EV per $100
- +$6.67
- what the bet is worth on average
- Careful stake
- 10%
- $100 of $1,000 · half Kelly $50
- Both sides add to
- 103.48%
- a fair line adds to 100%
- Bookmaker's margin
- 3.48%
- it keeps about 3.36% of all money bet, if both sides get the same
- Fair chances
- 58% · 42%
- with the margin taken out
That line means a $100 bet wins $67. The odds say 60%. At your 64%, a $100 bet is worth +$6.67 on average. A careful stake: 10% of your money, or 5% at half Kelly.
How this works, step by step
Odds are a price, written three ways.
American odds center on $100. A minus number is what you risk to win $100: −110 means risk $110 to win $100. A plus number is what $100 wins: +150 means a $100 bet wins $150. Decimal odds are what $1 brings back, stake included: 2.50 turns $1 into $2.50. Fractional odds are profit over stake: 3/2 wins $3 for every $2.
decimal = 1 + 100 ÷ |minus odds| · decimal = 1 + plus odds ÷ 100 · decimal = 1 + a/b
Turn the price into a chance.
Ask: how often would this bet have to win to break even? That is the implied probability. A coin flip at even money (+100) needs 50%. At −110 you risk more than you win, so you need to be right 52.38% of the time.
implied chance = 1 ÷ decimal odds · −110 → 1 ÷ 1.909 = 52.38%
Add both sides to find the house edge.
Real chances for the two sides add to exactly 100%. A bookmaker’s odds add to more. At −110 on both sides they add to 104.76%. The extra 4.76% is the margin, the price of playing. If money comes in evenly on both sides, the book keeps about 4.5 cents of every dollar bet no matter who wins.
margin = implied A + implied B − 100% · fair chance = implied ÷ (implied A + implied B)
Compare with your own chance.
Expected value, or EV, is what a bet is worth on average if you could make it many times. You win the profit with your chance, and lose your stake the rest of the time. A bet is only worth making when your chance is above the implied one. At −110 with a true 50%, every $100 bet loses $4.55 on average.
EV per $100 = your chance × profit − (1 − your chance) × $100
Decide how much, not just whether.
The Kelly fraction is how much of your money a careful bettor would stake: enough to grow fastest over many bets, never so much that a bad run wipes you out. Bigger edge, bigger stake. No edge, no bet. Your own chance is only a guess, and a wrong guess makes full Kelly far too big, so most pros stake half of it, called half Kelly.
Kelly = (b × p − (1 − p)) ÷ b, where b = decimal odds − 1 · p = 0.55 at +100 gives (0.55 − 0.45) ÷ 1 = 10%
Long shots are where the margin hides best. Across many sports, very long odds tend to pay less than their real chance deserves, which researchers call the favorite-longshot bias. A +2000 line implies 4.76%. If the real chance is 3%, every $100 bet is worth −$37 on average.
For learning, not financial, medical or betting advice.