Blackjack Expected-Loss Calculator

By Originally published Last updated

Estimate the long-run mathematical cost of a blackjack session from your average initial bet, pace of play, session length and estimated house edge. The result is an average over extensive play—not a prediction of what will happen today.

Transparent session math

Estimate expected loss

Amounts are shown in currency units. The mathematics is currency-neutral.


Use the average initial wager, before doubles and splits.


Live tables are usually slower than automated games.


Decimals are accepted—for example, 1.5 hours.


Enter 0.5 for 0.50%, not 0.005.


These are teaching estimates, not universal game values. The 6:5 preset adds the sourced approximate 1.39-percentage-point payout effect to a 0.50% baseline.

Estimated long-run average

Session results

Estimated hands160
Total initial wagers4,000.00 units
Expected loss per hour10.00 units
Expected loss for session20.00 units
Expected loss per 100 hands12.50 units

This estimate uses initial wagers as the action base. Actual money placed can be higher when you double or split.

If the house edge changes

The comparison below changes the edge by 0.25 percentage points while holding bet size, speed and duration constant.

Lower edge10.00 units0.25% edge · 10.00 fewer units
Entered edge20.00 units0.50% edge
Higher edge30.00 units0.75% edge · 10.00 more units

Session expected loss at several house-edge values
House edge Expected loss Relative size

Quick 3:2 versus 6:5 approximation

With the entered edge treated as the 3:2 baseline, 6:5 is modeled by adding approximately 1.39 percentage points. The exact difference varies slightly with the full rules.

Blackjack payout Modeled edge Session expected loss
3:2 baseline 0.50% 20.00 units
6:5 approximation 1.89% 75.60 units
Approximate added expected loss +1.39 points 55.60 units

JavaScript is unavailable. You can still use the formulas below. For the default example—25 units, 80 hands per hour, 2 hours and a 0.50% edge—the estimate is 160 hands, 4,000 units wagered, 10 units lost per hour on average and 20 units for the session.

Formula and methodology

Total initial hands = initial hands per hour × hours

Total initial wagers = average initial bet × total initial hands

Expected session loss = total initial wagers × house edge

Expected loss per hour = average bet × hands per hour × house edge

The calculator converts the percentage to a decimal before multiplying. A 0.50% house edge is 0.005. Results retain full precision internally and are rounded only for display.

Worked example

Suppose the average initial bet is 25 units, play averages 80 hands per hour, the session lasts 2 hours and the estimated house edge is 0.50%.

  • Total hands: 80 × 2 = 160
  • Total initial wagers: 25 × 160 = 4,000 units
  • Expected loss per hour: 25 × 80 × 0.005 = 10 units
  • Expected session loss: 4,000 × 0.005 = 20 units
  • Expected loss per 100 hands: 25 × 100 × 0.005 = 12.50 units

Compare sessions using the same wager basis

Two hours at 40 initial hands per hour and 25 units per hand means 2,000 units in initial wagers. At a 0.50% edge, expected loss is 10 units. At 80 hands per hour, the same stake, duration and edge produce 4,000 units in initial wagers and 20 units of expected loss. Faster play changes how much action you put through the game; it does not improve the odds on each hand.

Count each starting hand once, including pushes. A split creates additional betting exposure, not another original round for this input. If you play two positions for 40 rounds per hour, enter 80 initial hands per hour and the average initial wager per position. Do not also double the bet input for the same two positions.

When your stake changes, calculate a weighted average. For example, 60 starting hands at 10 units and 40 at 25 units give (60 × 10 + 40 × 25) ÷ 100 = 16 units per hand. Entering 17.50, the simple average of the two stake sizes, would overstate the initial wagering in this example.

The result does not tell you how much money is sufficient to survive a session. A 20-unit expected cost can accompany a much larger actual loss. Use the bankroll guide to separate a spending limit from an average mathematical cost.

Assumptions and limitations

  • Use the average initial wager per starting hand. The conventional main-game house edge includes the expected effects of doubles and splits under its stated strategy; do not add that extra action to the initial-wager base. Insurance and side bets need separate cost estimates unless explicitly included in the entered edge.
  • The entered house edge must match the game’s complete rules and the player’s strategy. A low published edge normally assumes accurate basic strategy.
  • Hands per hour is an estimate. Table occupancy, dealer speed, online automation and breaks change actual pace.
  • Expected loss is linear in bet size, hands and edge. Variance is not: short-session results can depart widely from expectation.
  • The 6:5 comparison isolates an approximate payout effect. It is not a full rules engine.

Why one session can look completely different

Expected loss is the center of a long-run distribution, not a promise that every session will lose that amount. Naturals, doubles, splits, pushes and ordinary streaks produce substantial variance. Winning in one session does not disprove a house edge; losing more than the estimate does not mean the formula failed.

Sources

Michael Shackleford’s definition of house edge distinguishes the initial wager from additional money committed during play.