Expected Loss Per Hour: How to Estimate Gambling Cost

Expected loss per hour is the average amount a player gives up in an hour of play. The formula is simple: bets per hour × average bet × house edge. Thirty $20 even-money bets an hour on a European roulette wheel, where the house edge is 1/37 (about 2.70%), cost an average of $16.22 per hour. On a double-zero wheel, the same hour costs about $31.58.

This guide explains where the formula comes from, works through hypothetical examples with every step, compares wheel types, speeds and bet sizes in tables, and shows why a real hour of play can land far from the average. It states its assumptions throughout, because an hourly estimate is only as good as its inputs.

What Expected Loss Per Hour Means

Expected loss per hour converts a percentage into dollars. A house edge says what share of each dollar wagered the casino keeps on average. Multiply that share by the total amount wagered in an hour, and the result is the hourly cost of the game.

Two ideas matter here. The first is total amount wagered, sometimes called the action: every bet placed counts, including bets made with winnings. A player who bets $20 thirty times has wagered $600, even if the bankroll never drops below $200. The second is the average: an expected loss is a long-run mean over many similar hours, not a forecast for tonight’s session.

The house edge itself comes from comparing payouts with the true chance of winning, a derivation covered in the true odds and payout odds guide. Once the edge is known, the hourly estimate is only multiplication. Assumptions are stated up front: the edge must belong to the exact bet and rule set being played, and the bets-per-hour figure must be realistic for the game’s speed.

The Expected Loss Per Hour Formula

Start from the expected value of one bet, as in the expected value formula guide: average bet × house edge is the expected loss on each bet. Multiplying by the number of bets in an hour gives the hourly figure.

where:

bets per hour = number of bets resolved in one hour (spins, rolls or hands)

average bet = typical stake in dollars, per bet

house edge = expected loss as a fraction of the amount wagered (2.70% = 0.0270)

The same relationship can be written in two steps, which is useful for checking.

For a session of several hours, multiply by the hours played, provided the pace, bet size and game stay the same. The formula assumes independent bets with a fixed edge. If bet sizes change from bet to bet, use the average bet size, weighted by how often each size is used; a system that raises stakes after losses, such as the Martingale system, does not change the edge, only the amount wagered.

Worked Example: One Hour of Roulette

Example 1: a single-zero wheel. Suppose a player bets $20 on red (an even-money bet) on a European wheel, 30 spins per hour, with the same $20 stake every spin.

Step 1: House edge = 1 ÷ 37 ≈ 0.02703, or about 2.70%.

Step 2: Amount wagered per hour = 30 × $20 = $600.

Step 3: Expected loss per hour = $600 × (1/37) ≈ $16.22.

Step 4: Expected loss per bet = $20 × (1/37) ≈ $0.54. Check: 30 × $0.54 ≈ $16.22 (using the unrounded $0.5405).

Step 5: For a 3-hour session at the same pace = 3 × $16.22 ≈ $48.65.

Example 2: the same play on a double-zero wheel. Suppose the same $20 bets and 30 spins per hour, now on an American wheel (38 pockets).

Step 1: House edge = 2 ÷ 38 ≈ 0.05263, or about 5.26%.

Step 2: Amount wagered per hour = 30 × $20 = $600 (unchanged).

Step 3: Expected loss per hour = $600 × (2/38) ≈ $31.58.

The extra zero costs about $15.36 more per hour on identical play. Both numbers are averages: some hours will lose much more, and some will show a profit.

How Wheel Type, Speed and Bet Size Change the Cost

Each input scales the answer in a straight line. Doubling the bet size or the pace doubles the expected loss; halving the edge halves it. The first table fixes the play at 30 spins an hour of $20 each ($600 wagered) and changes only the wheel and rule. La partage returns half of an even-money stake when the ball lands on zero, which cuts the even-money edge in half.

The second table fixes a European wheel with no la partage and varies the pace and the bet size. Each cell equals spins × bet × (1/37).

Pace matters as much as the edge. A fast game with a small edge can cost more per hour than a slow game with a larger one. For roulette-specific derivations of each edge, see the roulette house edge guide. All speeds and bet sizes here are hypothetical; real pace varies by table and player.

Why Real Hours Swing Around the Average

The expected loss is an average, and single hours vary widely around it. For an even-money bet, the standard deviation is about 1 unit per bet, so the hourly standard deviation is roughly $20 × √30 ≈ $109.5 for 30 bets of $20. The expected result is −$16.22, which is small compared with that spread.

As a rough guide, using the normal approximation (which is less reliable for short sessions), about 68% of hours would land within one standard deviation of the average, between roughly −$126 and +$93. Counting exactly instead (30 bets, 15 wins is break-even), about 37% of hours finish ahead, 14% break even and 49% finish behind. Those winning hours are real, and they are fully consistent with a negative expected value.

Over longer play, the picture shifts. Expected loss grows in proportion to the number of hours, while the standard deviation grows with the square root of the hours. After 100 such hours, the expected loss is about $1,621.62 against a standard deviation of about $1,095 (109.5 × √100), so a loss becomes the likely outcome. The variance in gambling guide explains this scaling in detail.

Common Mistakes When Estimating Hourly Loss

Multiplying the edge by the bankroll instead of the amount wagered is the most common error. A $200 bankroll that is bet 30 times at $20 produces $600 of action, not $200. Using the starting bet instead of the average bet is the second: if stakes change during play, the average is what counts.

Applying the wrong edge is the third; a bet on a double-zero wheel does not carry the single-zero edge. Ignoring pace is the fourth, since slower tables produce fewer bets per hour. The fifth is treating the average as a promise: a $16.22 expected loss does not mean every hour costs $16.22. The sixth is assuming a staking plan changes the cost; it changes the amount wagered and the shape of results, never the edge. Gambling should be treated as paid entertainment, and the hourly cost is the price of that entertainment on average.

Quick Reference and Check Your Answer

Follow four steps for any game: find the edge for the exact bet and rules, estimate bets per hour, find the average bet, and multiply the three numbers.

To check the result, compute the amount wagered ($600) and confirm that loss ÷ wagered returns the edge: $16.22 ÷ $600 ≈ 2.70%. If it does not, recheck the units, since the edge must be entered as a decimal.

Related Concepts and Next Steps

To see where the edge comes from, read true odds and payout odds, which turns the gap between payout and probability into a percentage. For the full average-result framework, work through the expected value formula guide. For the swings around that average, read variance in gambling, and for the derivation behind each roulette edge used here, see the roulette house edge calculation.