Three Odds Formats, One Price

Question

A sportsbook lists three different events: one at American +150, one at decimal 2.50, one at fractional 6/4. Convert each quote to an implied probability. (Hint: one number answers all three.)

Accepted Answer

All three are the same price in different clothes: implied probability is stake divided by total amount returned: - American +150: risk 100, returned 250 if it wins → frac100250 = 40%. - Decimal 2.50: total return per 1 staked → frac12.50 = 40%. - Fractional 6/4: risk 4, win 6, returned 10 → frac410 = 40%. Answer: 40% each. The conversion kit worth memorizing: decimal = fractional + 1; American +A Rightarrow d = 1 + A/100; American -B (risk B to win 100) Rightarrow implied = fracBB+100, e.g. -200 to frac200300 = 66.7%. Even money is the anchor: +100 = 2.00 = 1/1 = 50%. Two refinements that separate candidates: 1. Implied includes the vig. Book probabilities across all outcomes of one event sum to more than 100% (the overround); each quoted implied probability overstates the true chance. To de-vig as a first cut, normalize by the sum. 2. Direction of attractiveness: for the bettor, higher decimal = better price = lower implied probability. Comparing books is comparing implied probabilities, exactly like comparing offers across venues. Trap: dividing stake by winnings instead of by total returned, for +150 that gives 100/150 = 66.7%, which is the breakeven of the wrong side. Desk int

Three Odds Formats, One Price

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