Your edge at decimal odds of 1.65

Question

A market offers decimal odds of 1.65 on an outcome you believe wins 65\% of the time. Solve in your head. What is your expected profit per \1 staked? Aim: under 15 seconds.

Accepted Answer

Per \1 staked, you get back 1.65 with probability 0.65, else nothing: EV = 0.65 	imes 1.65 - 1. Fast product: 0.65 	imes 1.65 = 0.65 + 0.65 	imes 0.65. And 65^2 = 4225 (ending-in-5 trick), so 0.65 	imes 0.65 = 0.4225: EV = 0.65 + 0.4225 - 1 = 0.0725 \approx +7.25 	ext{ cents per dollar.} Quick cross-check: break-even probability is 1/1.65 \approx 0.606. You believe 0.65, about 4.4 points of probability edge, times the 1.65 payout \approx 7.3 cents. Consistent. Takeaway. Two equivalent lenses: EV = p \cdot d - 1, or (probability edge) × (decimal odds). The second, comparing your p against…

Your edge at decimal odds of 1.65

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