Expected Loss, Explained

After reading this you can estimate the honest cost of any casino session from four numbers: house edge, bet size, speed and time, and compare that cost across games.

What expected loss actually measures

Expected loss is the average amount a game takes from you over a session, computed before you sit down. It is not what will happen tonight. It is the long-run cost per session that the math guarantees on average.

Here is the hook. European roulette has a house edge of 2.7%. If you bet $10 per spin at 60 spins per hour for 3 hours, you wager $1,800 in total. The expected loss is 2.7% of that, or about $48.60. You might walk out ahead or you might lose $200. But if a thousand people played that exact session, their average loss would sit very close to $48.60.

The number tells you the price of the entertainment, the same way a movie ticket has a price. Everything else is variance around that price.

When to use it, and when it misleads

Use expected loss to budget, to compare games on equal footing, and to see how bet size and speed drive cost. It answers "what does three hours of this game cost me on average?" cleanly.

It misleads in two situations. First, over a single short session, variance dominates. In three hours of roulette the standard deviation of your result is several hundred dollars, so the actual outcome bounces far from $48.60. Second, expected loss assumes flat betting at a fixed edge. If you use progressive betting, take side bets, or deviate from basic strategy, the real edge changes and the estimate drifts.

Expected loss is an average, not a prediction. A session with an expected loss of $48.60 can easily end at +$150 or -$300. The average only reveals itself over hundreds of similar sessions.

The formula and why it works

Expected loss is a straight product of four quantities.

E[L] = h \times b \times r \times t

Here h is the house edge as a decimal (2.7% becomes 0.027), b is the average bet per round in dollars, r is rounds per hour, and t is hours played. The product b \times r \times t is your total handle, the sum of every wager you make. Multiply the handle by the edge and you have the expected cost.

The intuition: house edge is the fraction of each dollar wagered that the game keeps on average. It applies to money wagered, not money you bring. If you bet $10 a hundred times, you have wagered $1,000 even if you only ever had $200 in your pocket, because winnings get bet again. That recycled money is why the handle grows so fast and why speed matters as much as bet size.

House edge by game

The edge is the one number that separates a cheap game from an expensive one. These are typical figures the calculator uses. Real values depend on rules and bet choice.

Typical house edge and cost per $1,000 wagered
Game	House edge	Cost per $1,000 handle
Blackjack (basic strategy)	0.50%	$5.00
Baccarat (banker)	1.06%	$10.60
Craps (pass line)	1.41%	$14.10
Roulette (European)	2.70%	$27.00
Slots (typical)	5.00%	$50.00
Roulette (American)	5.26%	$52.60

The gap is large. Blackjack at 0.50% costs ten times less per dollar wagered than European roulette, and about a hundred times less than a 5% slot. Keno is worse still, often 20% to 30%, which is why it does not sit near the others.

Same $10 bet, same 60 rounds per hour, same 3 hours. Only the edge changes. Slots and American roulette cost roughly ten times what blackjack does.

A worked example with the demo numbers

European roulette, $10 a spin, 3 hours

These are the demo button values: game European roulette, bet $10, 60 rounds per hour, 3 hours.

Look up the edge. European roulette is 2.7%, so h = 0.027.
Count rounds. 60 \times 3 = 180 spins.
Compute the handle. 180 spins at $10 each is $1,800 wagered in total.
Apply the edge. 2.7% of $1,800 is $48.60.

Your expected loss is $48.60. Notice that you never had to bring $1,800. You cycle a smaller bankroll through the game 180 times, and the edge nibbles each wager.

Reading and interpreting the result

Treat the output as a price tag on your time at the table. Divide by hours to get a cost per hour. The demo session costs $16.20 per hour ($48.60 over 3 hours). The same session on American roulette costs about $31.56 per hour ($94.68 over 3 hours).

Speed is the quiet driver. A dealer who runs 100 hands an hour instead of 60 raises your cost by two thirds without changing your bet. Slots that spin 600 to 800 times an hour are expensive mostly because of speed, not only the edge. On a 5% slot at $1 a spin and 600 spins per hour, the hourly cost is $30 (0.05 times $1 times 600), matching a $10 American roulette table.

To cut expected loss without changing games, slow down. Take breaks, bet on fewer rounds, or pick a fuller table. Fewer rounds per hour lowers the handle and the loss in direct proportion.

Common mistakes

The most frequent error is applying the edge to your bankroll instead of your handle. The edge does not take 2.7% of the $200 in your pocket. It takes 2.7% of every dollar wagered, and you wager far more than $200 across a session because winnings get replayed.

A second mistake is confusing expected loss with a guaranteed loss. Half of short blackjack sessions end in profit even though the average is negative. Expected loss is the center of a wide distribution, not a floor.

A third is ignoring how strategy shifts the edge. Blackjack is 0.50% only with correct basic strategy and good rules. Play by instinct and the edge can climb to 2% or more, quadrupling the cost. Baccarat banker is 1.06%, but the tie bet is around 14%, so mixing in side bets wrecks the estimate. Check your real edge before trusting the number.

Related calculators

To find the exact edge for the game you actually play, use the game-specific tools. Roulette Odds gives the win probability, payout and house edge for every roulette bet. Blackjack House Edge computes the edge from your exact table rules, which matters because dealer-hits-soft-17 and 6:5 payouts swing it noticeably. Craps Odds covers the main bets, and Slot Session Calculator adds the outcome spread so you see variance, not just the average.

Frequently asked questions

Does expected loss mean I will definitely lose that amount?

No. It is the average across many identical sessions. A single three-hour roulette session with an expected loss of $48.60 might end anywhere from +$200 to -$300. The average only emerges over hundreds of sessions.

Why does the number use bet size times rounds instead of my bankroll?

House edge applies to money wagered, not money brought. If you bet $10 a hundred times you have wagered $1,000 even with a $200 bankroll, because you keep rebetting the same chips. Total handle, not bankroll, drives the loss.

Which game gives the lowest expected loss?

Blackjack with correct basic strategy, at about 0.50%, is usually the cheapest common game. Baccarat banker at 1.06% and craps pass line at 1.41% follow. American roulette at 5.26% and typical slots at 5% cost about ten times as much per dollar wagered.

How much does playing faster cost me?

Rounds per hour scales the loss directly. Going from 60 to 120 rounds per hour doubles the expected loss with the same bet. This is why slots, which spin 600 or more times per hour, drain a bankroll quickly even at small bets.

What edge should I enter for a game not in the list?

Use the custom option and enter the game's published or computed edge. Keno commonly runs 20% to 30%, most video poker variants land between 0.5% and 5% depending on the paytable, and casino war sits near 2.9%. When in doubt, look up the specific bet rather than guessing.

Try it yourself in the tool