Implied probability
Implied probability is the price of a bet written as a percentage. It is how often the bet has to win for you to break even. The sums are short, and they are the difference between betting a price and betting a team.
The one idea
Divide what you risk by the total you get back, stake included. That is the whole method, whatever format the odds are in.
At -150 you risk $150 and get back $250. 150 divided by 250 is 0.60, so the price implies 60 percent.
The sum for each format
The formats only change where the numbers sit, so each one gets its own version of the same division.
- American, minus price. Drop the minus sign, then divide the number by the number plus 100. For -150 that is 150 / (150 + 100) = 60 percent, and for -110 it is 110 / (110 + 100) = 52.38 percent.
- American, plus price. Divide 100 by the number plus 100. For +130 that is 100 / (130 + 100) = 43.48 percent, and for +300 it is 100 / (300 + 100) = 25 percent.
- Decimal. Divide 1 by the price. For 2.50 that is 1 / 2.50 = 40 percent, and for 1.91 it is 1 / 1.91 = 52.36 percent.
- Fractional. Divide the bottom number by the top and bottom added together. For 5/2 that is 2 / (5 + 2) = 28.57 percent.
If you'd sooner not do it by hand, the odds calculator does all three. I'd still learn a few by heart, because after a week of doing it they take seconds: -110 is 52.4, -150 is 60, -200 is 66.7, +100 is 50, +200 is 33.3.
What a bet pays
The same prices, worked the other way. On a minus price, divide your stake by the number and multiply by 100. On a plus price, divide the number by 100 and multiply by your stake.
| Price | Implied probability | A $100 bet wins | A $1,000 bet wins |
|---|---|---|---|
| -300 | 75.00% | $33.33 | $333.33 |
| -200 | 66.67% | $50.00 | $500.00 |
| -150 | 60.00% | $66.67 | $666.67 |
| -110 | 52.38% | $90.91 | $909.09 |
| +100 | 50.00% | $100.00 | $1,000.00 |
| +130 | 43.48% | $130.00 | $1,300.00 |
| +150 | 40.00% | $150.00 | $1,500.00 |
| +300 | 25.00% | $300.00 | $3,000.00 |
Those are the winnings. Your stake comes back on top, so $100 at +150 returns $250.
Read the table across and you can see the trade. The more likely the bet, the less it pays. That is all odds are.
Why the two sides add up to more than 100
Take both sides of one game, the favorite at -150 and the underdog at +130. The favorite comes to 60 percent and the underdog to 43.48 percent, which together make 103.48 percent. A game has 100 percent to give. The 3.48 over the top is the book's cut, and it is why the implied probability is not the book's honest opinion of the game; it is the opinion with the fee added.
To get the fee out, divide each side by the total. The favorite becomes 60 / 103.48 = 57.98 percent and the underdog 43.48 / 103.48 = 42.02 percent, and now they add up to 100. That is the no-vig price, and it is as close as you will get to what the book really thinks. The no-vig calculator does it for any pair of prices.
Your number against theirs
A price is only good or bad next to your own estimate.
Say you make the underdog a 46 percent chance. The book is offering +130, which needs 43.48 percent to break even, so you think it wins more often than the price requires, and that is a bet. At +110 the same team needs 47.62 percent, and it is no longer a bet. Nothing about the team changed. The price did.
Most players never do this. They decide who will win, then bet it at whatever number is on the screen, and a favorite at -300 has to win three times in four just to stay level (plenty of teams that "should win" don't win that often). When the two numbers are close, I pass. Close is not an edge.
I'd also be honest about my own number. The book's price is built from far more information than most bettors have, and "I think it's 46 percent" is a guess until a long record says otherwise. Even a real edge loses often, so size your bets so that being wrong about your percentages costs you a bad week and nothing worse.
The price is the book's side of the argument. The percentage is how you answer it.