Expected Loss Calculator

The Expected Loss Calculator turns a house edge, a betting rate, and a session length into an expected dollar drain. Four inputs: House Edge (default 2.7%, the European roulette straight-up / even-money edge of 1/37), Avg Bet (default $1000), Hours (default 2), Hands / Hour (default 60). Total Wagered = wager × hours × hands-per-hour. Expected Loss = total × (edge/100). On the defaults, total = 1000 × 2 × 60 = $120,000.00 and loss = 120000 × 0.027 = $3,240.00.

That $3,240 is not a bill you will pay on the nose. It is the mean of a high-variance sum. A European roulette session of 120 even-money bets at $1000 has standard deviation on the order of $1000 × √(120 × (18/37)×(19/37)) ≈ $11,000; the $3,240 mean sits inside a wide cloud. The calculator does not print the cloud. It prints the mean, which is what Allan Wilson’s casino mathematics and Edward Thorp’s expectation arguments isolate before variance is discussed.

Change the game via the edge field. Blackjack at 0.5% with the same $1000, 2 hours, 60 hands: total still $120,000, loss = $600. Slots at 4%: loss = $4,800. Baccarat banker at 1.06%: loss = $1,272. Hands / Hour is the lever people forget. A leisurely 30 decisions per hour halves the loss to $1,620 at 2.7%; a 100-spin-per-hour slot pace at $1000 and 4% edge for 2 hours is 200 × $1000 × 0.04 = $8,000 expected.

Hours can be a fraction. 0.5 hours at the defaults: total $30,000, loss $810. Avg Bet is the mean stake, not the table minimum; if you mix $100 and $1900 bets, type the turnover-weighted average. The engine does not know correlation between bet size and count, so a card-counting spread is the wrong use — use the blackjack count tool for edge, then this for a flat-bet sketch.

Read Total Wagered even when you only care about loss. $120,000 through a 2.7% edge is how a “$3240 expected” is generated; without the $120,000 the 2.7% is an orphan percentage. This is the same identity casinos use internally: win ≈ hold × drop, with hold standing in for edge on table games.

Expected loss is the first number a mathematically literate player should compute and the last number marketing wants on a banner. If you bet a unit with house edge e for N independent trials, expected net is −e × unit × N. Allan N. Wilson’s The Casino Gambler’s Guide and Edward O. Thorp’s writing on expectation made that identity public in the 1960s. It is older than that: Huygens’s expectation, applied to a negative-mean game, is the same object. Casinos know it as theoretical win.

SorteCalc’s version multiplies four scalars instead of hiding N. Edge is a percent, wager is dollars per decision, hours × hands-per-hour is the decision count. The product is total handle; handle times edge is expected casino win, which is expected player loss. European roulette’s 2.7% is the default because 1/37 is the single most-cited table-game edge in Europe. American double-zero would be 5.26% on even money; type 5.26 if that is your wheel.

What expected loss is not: a session cap, a martingale warning (that is a different calculator), or a promise you will lose $3,240. You might win. The mean of a random variable is compatible with a positive realization. After 120,000 units of handle the law of large numbers starts to pinch, which is why the house builds the building. After 120 bets it does not.

Limits: independent trials, constant edge, constant bet, no toke, no discount, no betting-system dependence. A progression that inflates the average bet when you lose will make the true expected loss larger than this linear map if you keep playing a fixed number of hours (you will put more money in motion). A player who leaves after a win has a stopping time; optional stopping does not change the per-bet expectation but it changes the distribution of session P&L. This form assumes you complete hours × hph bets.

Use it to compare games at the same handle, to see why 60 hands an hour at a $1000 average is a different hobby from 400 slot spins at $1, and to put a dollar unit on 2.7%. Thorp’s point stands: if the expectation is negative, time is not your friend. The $3,240 figure is that point with the defaults filled in.

A lecture on how to turn a house edge into an expected dollar drain uses linearity of expectation and four scalars. Edge 2.7 percent, average wager 1000, two hours, sixty hands per hour. Handle, or total wagered, is 1000 × 2 × 60 = 120000. Expected loss is 120000 × 0.027 = 3240. That 3240 is the mean of a high-variance sum, not a bill you will pay on the nose. Allan N. Wilson’s The Casino Gambler’s Guide and Edward O. Thorp’s writing on expectation isolated this identity before variance is discussed. Huygens’s expectation, applied to a negative-mean game, is the same object. Casinos know it as theoretical win.

European roulette even-money is the source of the 2.7. Eighteen winning pockets in 37 at even money, nineteen losing: expected profit per unit is 18/37 − 19/37 = −1/37 ≈ −0.027027, that is 2.7027 percent, rounded to one decimal as 2.7. Straight-up thirty-five to one has the same 1/37 leak. American double-zero even-money would be 5.26 percent; type that if that is your wheel. Blackjack at 0.5 percent with the same handle loses 600. Slots at 4 percent lose 4800. Banker baccarat at 1.06 percent loses 1272. Hands per hour is the lever people forget: thirty decisions per hour halves the 3240 to 1620. Half an hour at the defaults: handle 30000, loss 810.

Variance is not printed and must still be named. For even-money roulette the standard deviation per unit is about 1, so after N = 120 bets the session deviation is about 1000 × √120 ≈ 10954. The 3240 mean sits inside a cloud ten thousand dollars wide. You might win. The mean of a random variable is compatible with a positive realization. After 120000 of handle the law of large numbers starts to pinch, which is why the house builds the building. After 120 bets it does not.

A betting system cannot repair this mean. Each incremental dollar still has expectation minus the edge; dependence changes variance, not the sum of expectations. A progression that inflates the average bet when you lose will make true expected loss larger than this linear map if you keep playing a fixed number of hours. Optional stopping changes the distribution of session profit, not the per-bet expectation. This calculation assumes you complete hours times hands-per-hour bets at a constant stake.

Assumptions: constant proportional edge, constant bet, no toke, no discount. Independence is not even required for the mean. Wilson and Thorp’s pedagogical move was to write loss equals handle times edge in dollars, not to leave players with a 2.7 percent abstraction. Feller’s caution that the mean is not the mode of a session sits on top. If the expectation is negative, time is not your friend. The 3240 figure is that sentence with the defaults filled in. Read the 120000 even when you only care about loss; without the handle the 2.7 percent is an orphan.