An expected loss calculator multiplies the total you stake by the house edge to give the average amount those bets cost you. In the tool above, 100 bets of 10 units on a game with a 2.70% edge add up to 1,000 units staked and an expected loss of 27 units.
That 27 is an average, not a forecast. A single session can finish far above or far below it, and this page shows how far, with the working. It also explains why the edge is charged on everything you stake, not only on the money you start with.
What does an expected loss calculator tell you?
Expected loss is the average amount a series of bets costs you if the same bets could be repeated many times. It equals the total staked multiplied by the house edge. Researchers call the same quantity theoretical loss, defined as total bet size multiplied by house advantage.
The house edge is the share of each stake a game keeps on average. At 2.70%, the game keeps 2.70 units of every 100 units staked. It does not say you lose 2.70 units on every bet. Most bets lose all of the stake or win some of it, and the edge is the average of those outcomes over a very large number of bets.
The UK Gambling Commission makes the same point about slot machines: the return to player is an average achieved over a significant number of game plays, and not what happens each time a machine is played. The same paper found that, over shorter periods, theoretical loss is a steadier measure of gambling intensity than counting wins and losses, which makes it a fair way to compare the cost of different games.
How do you use the expected loss calculator?
Enter the stake for one bet, the number of bets and the house edge as a percentage. The result updates as you type. It shows the expected loss in units, the total staked and the edge on a bar. Start with the default numbers, then change one input at a time to see what drives the cost.
- Enter the stake per bet. Use the amount you put down each time, not your total budget. The default is 10 units.
- Enter the number of bets. For a session, multiply bets per hour by hours played. If you do not know your pace, count the bets in ten minutes and multiply by six.
- Enter the house edge. Pick the figure for your game and rules from the table below. The tool accepts 0% to 30%.
- Read the expected loss. Check the line that shows the total staked, then open the Formula line to see the multiplication.
- Change one input and compare. Switch the edge from 2.70 to 5.26 and the expected loss roughly doubles. Double the bets and it doubles again.
What is the house edge for common games and bets?
The house edge is the share of each stake a game keeps on average, and it depends on the exact rules. European roulette is 2.70%, American double-zero roulette is 5.26%, and blackjack played by basic strategy is about 0.43% under the rules named in the table. Change a rule and the number changes with it.
| Game and bet | Rules the figure assumes | House edge | Expected loss per 1,000 units staked |
|---|---|---|---|
| Roulette, any single bet | European wheel, one zero, no half-back rule | 2.70% (1/37) | 27.03 |
| Roulette, even-money bet | European wheel with la partage: half the stake returns when the ball lands on zero | 1.35% (1/74) | 13.51 |
| Roulette, most bets | American wheel, 0 and 00 | 5.26% (2/38) | 52.63 |
| Roulette, five-number bet | American wheel only (0, 00, 1, 2, 3) | 7.89% (3/38) | 78.95 |
| Blackjack, basic strategy | Six decks, dealer stands on all 17s, double after split allowed, blackjack pays 3 to 2, no surrender. Our own simulation of 1.5 billion hands | About 0.43% | 4.3 |
| Blackjack, basic strategy | Same rules, but blackjack pays 6 to 5. Our own simulation of 600 million hands | About 1.79% | 17.9 |
| Craps, pass line | Standard rules, no odds bet taken | 1.41% (7/495) | 14.14 |
| Craps, any seven | One-roll bet paying 4 to 1 | 16.67% (1/6) | 166.67 |
| Sports bet at -110 on both sides | Decimal price 1.909, and the true chance is exactly 50% | 4.55% | 45.45 |
| All slot machines in Nevada, 2025 | Measured statewide casino win as a share of the amount gambled, not the rule of any one machine | 7.13% | 71.30 |
The roulette numbers match our roulette odds and payouts guide, which also covers the half-back rules. Blackjack figures are per initial bet. Doubles and splits put more money out, so enter the stake you actually place if you want a closer match.
Slot machines publish a return, not an edge
For a slot, the edge is 100% minus the return to player (RTP). The limits depend on where you are. Tasmania’s Know Your Odds calculations page gives 13% as the maximum house edge, which is an 87% minimum return. The Western Australian policy for Crown Perth sets a minimum return of 90%. The UK Commission states that there is no minimum RTP on a gaming machine. The UNLV Center for Gaming Research reports a statewide win percentage of 7.13% for all Nevada slot machines in its Nevada Gaming Win 2025 report. Check the machine’s own displayed RTP where it is shown.
Why does the house edge apply to total staked and not to your bankroll?
The edge is charged on every bet, and money that comes back to you is staked again. A 100-unit bankroll that is bet, returned and bet again can produce thousands of units of turnover. Expected loss grows with turnover, which is the total staked, and not with the balance you started with.
This is the most common misreading of the house edge. A 2.70% edge does not mean you lose 2.70 units of a 100-unit bankroll. It means you lose 2.70 units for each 100 units you stake. The table shows how quickly the stakes pile up when a bankroll is recycled.
| Hours played | Bets | Total staked | Times the 100-unit bankroll | Expected loss at 2.70% | Expected loss at 5.26% |
|---|---|---|---|---|---|
| 1 | 40 | 400 | 4 | 10.80 | 21.04 |
| 2 | 80 | 800 | 8 | 21.60 | 42.08 |
| 3 | 120 | 1,200 | 12 | 32.40 | 63.12 |
| 5 | 200 | 2,000 | 20 | 54.00 | 105.20 |
| 10 | 400 | 4,000 | 40 | 108.00 | 210.40 |
At 0.27 units of expected loss per 10-unit bet (2.70%), the average cost passes 100 units after about 370 bets. At the assumed 40 bets an hour, that is a little over nine hours of play. At 5.26% it takes about 190 bets.
There is a limit to this arithmetic. Play stops when the money is gone, so a small bankroll has no way to lose the 108 units shown for ten hours. The expected loss is best read as the cost of the play you choose, not as a promise of what you will end up down.
How far can a real session drift from the expected loss?
Much further than most people expect. Over 100 even-money roulette bets of 10 units on a single-zero wheel, the expected loss is about 27 units, but the standard deviation, a measure of typical spread, is about 100 units. Roughly 19 sessions in 20 end between a loss of 223 and a gain of 169 units.
Here is the working for one bet of 1 unit on red or black. It wins with probability 18/37 and loses with probability 19/37.
- Average result per bet: 18/37 x (+1) + 19/37 x (-1) = -1/37 = -0.0270 units. That is the 2.70% edge.
- Variance per bet: the average of the squared results minus the square of the average. Each result is +1 or -1, so the squares are always 1. Variance = 1 – 0.0270 x 0.0270 = 0.99927.
- Standard deviation per bet: the square root of 0.99927, which is 0.9996.
- For n bets of s units: bets are independent, and for independent bets the variances add, as set out in these university lecture notes on variance and standard deviation. So the standard deviation is s x the square root of n x 0.9996.
- For 100 bets of 10 units: 10 x 10 x 0.9996 = 99.96. The expected result is -27.03. About 95% of outcomes fall within 1.96 standard deviations: -27.03 minus 195.9 = -223, and -27.03 plus 195.9 = +169.
The table repeats this for longer runs. The range uses the normal curve as an approximation. The chance of finishing ahead is worked out exactly from the binomial distribution.
| Bets of 10 units | Total staked | Expected loss | Standard deviation | About 95% of sessions end between | Chance of finishing ahead |
|---|---|---|---|---|---|
| 100 | 1,000 | 27 | 100 | -223 and +169 | 35.5% |
| 500 | 5,000 | 135 | 224 | -573 and +303 | 25.8% |
| 1,000 | 10,000 | 270 | 316 | -890 and +349 | 18.8% |
| 5,000 | 50,000 | 1,350 | 707 | -2,737 and +34 | 2.7% |
| 10,000 | 100,000 | 2,700 | 1,000 | -4,662 and -743 | 0.3% |
Expected loss grows in step with the number of bets. The spread grows only with the square root of the number of bets. After 100 bets the expected loss is about a quarter of one standard deviation, so luck dominates and about one session in three finishes ahead. After 10,000 bets it is 2.7 standard deviations, and the chance of finishing ahead is about 3 in 1,000. This is the law of large numbers at work. It does not mean a loss is “due” after a win, because each spin is independent of the last.
Does a riskier bet change the expected loss?
Not the average, but it changes the spread. A straight-up bet on one number pays 35 to 1 on the same wheel, so the edge is still 2.70% and 100 bets of 10 units still have an expected loss of 27 units. The standard deviation per unit staked is 5.84, so for 100 bets of 10 units it is 584 units, almost six times larger. About 51% of those sessions finish ahead, because three or more wins are enough. About 6.5% lose all 100 bets, which is the full 1,000 units staked.
What do 100 roulette bets cost on each type of wheel?
One hundred roulette bets of 10 units cost 27 units on average on a single-zero wheel, 52.60 units on a double-zero wheel and 13.50 units on a single-zero wheel with la partage. Only the house edge differs between the three.
Example: You place 100 bets of 10 units on red. Enter 10, 100 and 2.70 in the expected loss calculator. The total staked is 10 x 100 = 1,000 units, and the expected loss is 1,000 x 2.70 / 100 = 27.00 units.
Now change only the edge. On an American wheel, enter 5.26. The expected loss becomes 1,000 x 5.26 / 100 = 52.60 units, almost double, because the extra zero costs a further 2.56 points. On a European wheel with la partage on even-money bets, enter 1.35 and the result is 13.50 units. Same bets, same stake, three different costs.
For comparison, a blackjack session of the same 100 bets of 10 units at the 0.43% edge in the table gives 1,000 x 0.43 / 100 = 4.30 units. The same session at the 1.79% edge for 6 to 5 payouts gives 17.90 units. One payout rule changes the cost about fourfold.
What mistakes do people make with expected loss?
The most frequent errors are applying the edge to the wrong number, reading an average as a forecast and using an edge figure without checking the rules. Each one can make a game look cheaper or safer than it is.
- Applying the edge to the starting balance. The edge applies to the total staked. See the turnover table above.
- Reading expected loss as a prediction. It is the centre of a wide range. A result far from it does not mean the game is “hot” or “due”.
- Using one edge for a whole game. Roulette ranges from 1.35% to 7.89%, and blackjack from about 0.43% to 1.79% in our table, depending on rules.
- Ignoring speed. More bets an hour means more turnover, and turnover is what the edge is charged on.
- Thinking a betting system cuts the cost. Raising the stake after a loss raises the total staked, so it raises the expected loss. No staking pattern changes the edge on an individual bet.
- Treating a sports price as a fixed edge. The cost of a bet depends on the true chance, which nobody knows exactly. The 4.55% in the table holds only if the true chance is 50%.
How do you turn expected loss into a cost per hour?
Multiply the stake by the bets per hour to get hourly turnover, then multiply by the house edge. At 10 units a bet, 40 bets an hour and a 2.70% edge, hourly turnover is 400 units and the expected cost is 10.80 units an hour. At 5.26% it is 21.04 units an hour.
To do this here, enter your hourly number of bets in the second box and read the result as a cost per hour. A dedicated session cost calculator for gambling is planned for this site and will take hours and pace as separate inputs. The hourly figure helps you judge whether the cost of a session is one you are comfortable with.
What should you do next?
Try your own numbers, then decide a limit you can afford to lose before you start, not afterward. If the expected loss or the swing range is more than you are comfortable with, the Safer play toolkit has limit-setting tools, and the Get help page lists support services if gambling is causing worry.
To compare two games, run both through the calculator with the same stake and number of bets, and use the edge for the exact rules at your table.
How to read the result
Expected loss is the average amount the bets cost you, in units, if the same bets were repeated many times. It is not what will happen in one session, which can finish well above or below it. The line under it shows the total staked, which is stake per bet multiplied by the number of bets. The bar shows the house edge on a scale of 0 to 30%. Typical edges run from under 1% for blackjack played by basic strategy to 2.70% for single-zero roulette and 5.26% for double-zero roulette. Open the Formula line to see the multiplication with your numbers.
How it is calculated
Total staked = stake per bet x number of bets. Expected loss = total staked x house edge / 100. The house edge is entered as a percentage, so 2.70 means 2.70%. The result and the total staked are rounded to two decimal places for display. The calculator accepts a stake of 0.01 or more, at least 1 bet, and a house edge from 0 to 30. The unit label is taken from the stake field.
Worked example
Worked example
Stake per bet 10 units, 100 bets, house edge 2.70% (the default inputs). Total staked: 10 x 100 = 1,000.00 units. Expected loss: 1,000.00 x 2.70 / 100 = 27.00 units. The result card shows 27.00 units, the line Total staked: 1,000.00 units., and the edge bar at 2.7%. Change the edge to 5.26 and the expected loss becomes 52.60 units.
Limits
The calculator multiplies the total staked by the house edge you enter and nothing else. It gives an average over many bets, not a prediction for one session, and it does not show how far results can vary. It assumes the same stake and the same edge on every bet. It does not model a bankroll running out, so for a small bankroll over a long run it can show a loss larger than the money you have. The edge is your input, and the right figure depends on the exact rules of the game or bet. Fees, commissions, tax and any other charges are not included unless you build them into the edge. The edge must be between 0 and 30, the stake at least 0.01 and the number of bets at least 1. Amounts are shown in units, not a currency. Results are estimates.