Win rate is the proportion of bets or contest entries classified as wins. It counts successful outcomes without measuring how much each outcome earns or costs. Expected value (EV) is the probability-weighted average net gain or loss from a wager or contest entry.

Expected value and payout size

A gross payout is the total amount returned after an outcome, including any returned stake. Net profit is the gross payout minus the entry cost and additional costs. A losing wager with no refund has a gross payout of zero.

Expected value weights each possible gross payout by its probability, adds those amounts, and subtracts the total cost. For a wager with two outcomes, a fixed winning payout and nothing returned on a loss:

Expected net return = win probability × gross winning payout − stake − additional fixed costs.

Take a $10 wager that returns $12 when it wins and $0 when it loses. A win earns $2 in net profit; a loss costs $10. At an 80% win probability and with no additional costs, expected net return is 0.80 × $12 − $10 = −$0.40 per wager. One loss consumes the profit from five wins.

Take a second $10 wager that returns $22 when it wins and $0 when it loses. At a 50% win probability and with no additional costs, expected net return is 0.50 × $22 − $10 = $1 per wager. The second wager has a lower chance of winning and a higher expected net return.

These probabilities are inputs to the calculation. An observed win rate describes completed bets; it does not by itself establish the probability of winning the next bet.

Break-even probability

Break-even probability is the win probability at which expected net return equals zero. For a wager with a fixed winning payout, zero payout on a loss and no additional costs:

Break-even probability = stake ÷ gross winning payout.

The $10 wager returning $12 requires a win probability of 10/12, or 5/6: approximately 83.33%. An 80% win probability falls below that threshold. The $10 wager returning $22 requires 10/22, or approximately 45.45%.

Returned stake must be counted once. A $12 gross payout on a $10 wager contains $10 of returned stake and $2 of profit. Adding another $10 to that payout overstates the return.

Entry fees and additional costs

A payout that exceeds the entry price still has to cover additional costs. Take an entry with an expected gross award of $12, a $10 entry price and $3 of additional expenses. Expected net return is $12 − $10 − $3 = −$1.

Prize-pool accounting makes the same distinction. Take a contest with 100 entries costing $10 each and a total of $900 distributed as prizes. If every entry has the same expected award, expected gross payout is $900/100 = $9 per entry. Expected net return is $9 − $10 = −$1 before additional expenses.

The $100 difference between entry receipts and prizes is already reflected in that calculation. Subtracting the difference again as a separate fee would double-count it. Unequal entrant strength changes each entry’s expected share of the pool; $9 is not an individual forecast without the equal-expected-award assumption.

A winning ticket that only returns its cost

California Lottery’s $5,000,000 Extreme Cash, game 1744, listed a $20 ticket price and a $20 prize tier in its September 8, 2026 prize table. A ticket receiving that total prize returns its purchase cost. Net profit is zero before additional costs or separately valued benefits.

Counting that ticket as a prize winner increases the reported frequency of winning a prize without adding a profitable outcome. “Any prize” and “net profit” measure different events.

Scope of the expected-value calculation

Fixed-payout wagers, cash-prize contests and lottery tickets use the same accounting identity: probability-weighted gross payouts minus costs. What changes is the distribution of payouts and the costs attached to participation. Refunds, partial returns and multiple prize tiers require separate outcome terms; they do not fit a two-outcome calculation that assigns every loss a zero payout.

For a fixed payout distribution, expected net return is positive only when expected gross payout exceeds total cost. Equality defines the break-even cost. A win percentage becomes useful for evaluating that boundary only when the payout amounts and costs are specified.