What is the break-even rate?

The break-even rate is the minimum win rate a player must achieve at a given odd to avoid losing money in the long term. It is the win rate at which the expected value is exactly zero: the player neither gains nor loses. Any win rate above the break-even rate produces positive expected value; any win rate below it produces negative expected value.

The break-even rate is simply the implied probability of the odd:

d: decimal odd
b: break-even rate

b = 1 / d

This follows directly from the expected value formula. Setting the expected value to zero:

e = w · (d − 1) − (1 − w) = 0
w · d − w − 1 + w = 0
w · d = 1
w = 1 / d

Examples

At a decimal odd of 2.00:

b = 1 / 2.00 = .50 = 50%

The player must win at least 50% of his bets to break even. Every percentage point above 50% generates profit; every percentage point below generates loss.

At a decimal odd of 1.50:

b = 1 / 1.50 ≈ .6667 ≈ 66.67%

The player must win approximately two out of every three bets.

At a decimal odd of 3.00:

b = 1 / 3.00 ≈ .3333 ≈ 33.33%

The player must win approximately one out of every three bets.

At a decimal odd of 10.00:

b = 1 / 10.00 = .10 = 10%

The player must win at least one out of every ten bets.

Practical use

The break-even rate provides a quick reference for evaluating whether a bet is potentially profitable. If a player estimates that an option has a 40% actual probability of winning, and the odd offered is 2.80, the break-even rate is:

b = 1 / 2.80 ≈ .3571 ≈ 35.71%

Since the estimated actual probability (40%) exceeds the break-even rate (35.71%), the bet has positive expected value. The expected value is:

e = .40 · (2.80 − 1) − .60 = .40 · 1.80 − .60 = .72 − .60 = .12 = 12%

Conversely, if the estimated actual probability were 33%, which is below the break-even rate:

e = .33 · 1.80 − .67 = .594 − .67 = −.076 = −7.6%

The bet has negative expected value and should not be placed.

Break-even rate and margin

The break-even rate also reveals the bookmaker's margin. In a fair market with two equally probable options, the fair odd for each would be 2.00, and the break-even rate would be 50% for each, summing to 100%. When the bookmaker adds a margin, the odds are lowered (for example, to 1.91 each), and the break-even rates become:

b₁ = 1 / 1.91 ≈ 52.36%
b₂ = 1 / 1.91 ≈ 52.36%

The sum is approximately 104.72%, which exceeds 100% by 4.72 percentage points — the margin. The player must win more often than the true probability to overcome this built-in disadvantage. The break-even rate at each odd is therefore higher than the actual probability of the event, and this difference is the margin's practical effect on the player.