Convert betting odds to implied probabilities

Question

A sportsbook posts American odds of +150 on Team A and, in a different game, -200 on Team B. What win probability does each price imply? Give the general conversion, including for decimal odds.

Accepted Answer

Plus odds (+150): risk \100 to win \150 profit. If p is the implied probability, fair pricing means p \cdot 150 - (1-p) \cdot 100 = 0 \implies p = \frac{100}{150 + 100} = 40\%. Minus odds (-200): risk \200 to win \100 profit: p \cdot 100 - (1-p) \cdot 200 = 0 \implies p = \frac{200}{200 + 100} = 66.7\%. General American-odds formulas: for +x, p = \frac{100}{x+100}; for -x, p = \frac{x}{x+100}. Decimal odds d (total return per 1 staked, e.g. 2.50): fair value requires p \cdot d = 1, so p = \frac{1}{d}. Decimal 2.50 \Rightarrow 40\%. Fractional odds a/b (win a for staking b): p = \frac{b}{a+b},…

Convert betting odds to implied probabilities

Your answer

More Market Making questions