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House edge calculator: expected loss from wager volume

The house edge calculator turns the amount you wager into an expected loss. Enter a total, or a number of bets and an average bet, plus the house edge and any rakeback. The second table shows how a martingale wagers more than flat betting over the same number of rolls, which raises the expected loss.

Inputs

Total wagered10,000
Expected loss1001% of the amount wagered
Rakeback returned0
Expected loss after rakeback100Effective edge 1.0000%

The expected loss is an average over many sessions. A single session can end far above or below it.

Flat betting vs martingale at the same number of rolls

StrategyAverage betTotal wageredExpected loss
Flat betting110,000100
Martingale x1.5 on loss2.009620,096.39200.9639
Martingale x2 on loss4.647346,473.48464.7348
Martingale x3 on loss10.8404108,404.471,084.04
Average bet is the long-run average stake per roll for each progression, reset after a win, assuming the balance is never lost. The edge per coin is the same in every row.

Expected loss formula

expected loss = total wagered × house edge / 100
rakeback (share of edge) = expected loss × rakeback / 100
rakeback (share of wager) = total wagered × rakeback / 100
net expected loss = expected loss − rakeback

The edge comes from the payout: a dice game pays (100 − house edge) / win chance, slightly less than the fair (100 / win chance). The dice payout calculator shows that conversion, and dice house edge explained goes through why the edge applies to every bet.

Worked example

  • 10,000 bets of 1 wager 10,000. At 1% edge the expected loss is 100; at 2% it is 200.
  • With 10% rakeback on the edge, 10 comes back and the expected loss is 90, an effective edge of 0.90%.

How wager volume sets the expected loss

Over the same 10,000 rolls at 49.5% with a base bet of 1 and a balance of 1,000, these are the long-run averages for flat betting and for multiplying the bet after each loss:

  • Flat betting: average bet 1, wagered 10,000, expected loss 100.
  • Martingale x1.5 on loss: average bet 2.0096, wagered 20,096.39, expected loss 200.9639.
  • Martingale x2 on loss: average bet 4.6473, wagered 46,473.48, expected loss 464.7348.
  • Martingale x3 on loss: average bet 10.8404, wagered 108,404.47, expected loss 1,084.04.

The edge per coin is 1% in every row. The expected loss differs only because the progressions wager more coins. The average bet comes from the same model the main crypto dice calculator uses for its expected profit figure: the stake after k losses is weighted by how often a run of k losses happens, up to the longest run the balance can pay for. It ignores the chance of losing the whole balance, which the martingale calculator and the losing streak calculator cover.

FAQ

House edge questions

How do I calculate expected loss from the house edge?

Multiply the total amount wagered by the house edge. 10,000 bets of 1 at 1% edge is 10,000 wagered and an expected loss of 100.

Does my betting strategy change the house edge?

No. Every bet loses the house edge on average whatever its size or timing. A strategy changes how much you wager in total and how the results are spread out, and the expected loss follows the amount wagered.

Why does a martingale have a higher expected loss than flat betting?

It wagers more. After losses the bets get larger, so the average stake per roll goes up. At 49.5% with a 1 base bet and a 1,000 balance, doubling averages 4.6473 per roll, so 10,000 rolls wager 46,473.48 and the expected loss is 464.7348, against 100 for flat bets.

How does rakeback change the expected loss?

Rakeback returns part of what you lose to the edge. It can be quoted as a share of the house edge or as a share of the amount wagered, and the calculator supports both. With 10% of the edge returned, the 100 expected loss above becomes 90.

Can I end up ahead even with a house edge?

Yes, in a single session. The expected loss is an average; short sessions vary a lot around it. The more you wager, the closer the result tends to get to wager times edge.

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