Break-Even Probability

This formula finds the minimum chance of winning needed so that a gamble has zero expected profit. It comes from setting the expected value of one bet to break even: the chance of losing times the loss equals the chance of winning times the gain, so the risk and reward balance out. If your actual win probability is higher than this threshold, the bet is favorable on average; if it is lower, you expect to lose money over many repeats.

Use this when comparing wagers, investments, or decisions with a clear amount you can lose and a clear amount you can gain. It is especially useful in gambling, business decisions, and game-theory style choices where you want to know the minimum success rate needed to justify the risk.

• Using the payout instead of the net win amount for W
• Forgetting that L is the amount risked if you lose, not the total amount staked plus winnings
• Treating the result as a guaranteed win threshold instead of a long-run break-even probability