#### Definition

First, what do those numbers mean? A -175 means 'you win $100 for each $175 that you bet' and a +140 means 'you win $140 for each $100 that you bet'.#### Example

Now, consider a matchup that's 60% chance for A and 40% chance for B. What does that convert to?Assuming no cost to bet, if there were 10 matches and you bet $100 on A each time, you'd put in $1000 and expect to get out $1000. Since A wins 60% of the time, you'd get 6 payouts and they would sum to $1000 (since you lose the bet on the 40% where A loses). Each bet would pay out $167, and subtracting off the initial $100 means a profit of $67. Thus, a $100 bet on A yields a profit of $67 when A wins which means that to get a profit of $100 you'd bet 100/.67, or $150. From the definition above, that means that a 60% chance of winning is a line of -150.

Doing the same with the 40% one, you'd get 4 payouts that sum to $1000, so $250 per payout and a profit of $150. You bet $100, and profit $150 on a win, so the line is +150.

Thus, a 60/40 matchup corresponds to a line of -150/+150. The general equation for the logic above is:

**favorite:**American line = - 100/[( 1/percent - 1)]**underdog:**American line = 100*[( 1/percent - 1)]

**favorite:**percent = 1/[(100/-American) + 1]**underdog:**percent = 1/[(American/100) + 1]

#### Real Life

- -200 => 66.67%
- +125 => 44.44%
- sum = 111.11%

- favorite: 66.67% / 1.1111 = 60%
- underdog: 44.44% / 1.1111 = 40%

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