Learn · Odds
Dice house edge explained
The dice house edge is the share of every bet the casino keeps on average. It is built into the payout: a 49.5% chance pays 2x at a 1% edge, where a fair game would pay 2.0202x. This page shows how the edge sets the payout, why your expected loss is the amount wagered times the edge, and why no betting pattern changes that.
What the house edge is
A dice roll in DiceSim is a number from 0.00 to 100.00. You pick a win chance, and the game pays a multiplier of your stake when the roll lands in the winning range. In a fair game the multiplier would be exactly 100 / chance, so the average return would equal the stake.
A casino pays a little less than that. The house edge is the gap, written as a percentage. The return to player (RTP) is the other side of the same number: a 1% edge means a 99% RTP, and a 2% edge means 98%. The edge differs from site to site, so use the figure your site publishes. DiceSim uses 1% by default and lets you set the edge in the simulation settings.
How the edge sets the payout
payout = (100 − edge) / chanceMultiply the payout by the win chance and you get the RTP back, at every chance. Low chances pay more because they win less often, and the edge takes the same share at each of them.
| Win chance | Payout at 1% | Payout at 2% | Chance × payout (1%) |
|---|---|---|---|
| 49.5% | 2x | 1.9798x | 99% |
| 24.75% | 4x | 3.9596x | 99% |
| 9.9% | 10x | 9.899x | 99% |
| 3.35% | 29.5522x | 29.2537x | 99% |
| 1% | 99x | 98x | 99% |
The last column is the same for every row. That is the definition of the edge at work, and it is why a 1% chance and a 98% chance have the same expected loss per unit staked. The odds by win chance pages list these figures for each common chance.
Expected loss = wagered × edge
For one bet of size s at chance p (as a fraction) and payout m, the expected result is s · (p · m − 1). Substituting the payout formula gives −s · edge / 100. Summed over a session, the stake sizes add up to the total wagered:
expected loss = total wagered × edge / 100Worked numbers: 1% vs 2% edge
Say you place 10,000 bets of 0.0001 BTC each, for 1 BTC wagered in total.
| House edge | RTP | Payout at 49.5% | Wagered | Expected loss |
|---|---|---|---|---|
| 1% | 99% | 2x | 1 BTC | 0.01 BTC |
| 2% | 98% | 1.9798x | 1 BTC | 0.02 BTC |
At a 1% edge the expected loss is 0.01 BTC. At 2% it is 0.02 BTC, twice as much for the same play. The bet size, the win chance and the order of the bets do not appear in the formula. Only the volume and the edge do.
Expected loss is an average over many sessions. A single session of 10,000 bets can end well above or below it, and the expected value and variance guide shows how wide that spread is.
Why bet systems change volume and variance but not the edge
Each roll is independent of the ones before it, so the expected result of a bet depends only on its size, chance and payout. A betting system decides the size of the next bet from past results. It cannot change the expectation of that bet, so the expected result of the whole session is still the sum of −size × edge over all bets.
What a system does change is how much you wager and how the results are spread. Compare flat betting with a martingale that uses the same base bet of 0.000001 at 49.5% and a balance of 0.01:
| Strategy | Average bet per roll | Wagered in 10,000 rolls | Expected loss |
|---|---|---|---|
| Flat betting | 0.000001 | 0.01 | 0.0001 |
| Martingale (×2 on loss) | 0.0000068366 | 0.06836567 | 0.00068366 |
The martingale bets about 6.8 times as much per roll on average, because every losing streak raises the stake. Its expected loss is higher by the same factor, and it is still exactly 1% of what it wagered. The average bet comes from the calculator's stationary estimate, which assumes the run does not go bankrupt first. The extra risk shows up as risk of ruin, the chance that one long streak takes the bankroll.
Rakeback
Some sites return part of the house edge to players as rakeback. The exact rules differ between sites: some base it on wagered volume and the edge, others on net losses, and many add tiers or conditions. For the volume-based kind, the expected result is easy to adjust:
expected net loss = wagered × edge / 100 × (1 − share)Using the example above with 1 BTC wagered at a 1% edge and 10% of the edge returned, the expected net loss falls from 0.01 to 0.009 BTC. Rakeback lowers the effective edge. Unless the share reaches 100%, the expected result stays negative, and a system that wagers more also collects more rakeback only because it pays more edge first.
For bankroll planning with a given edge, see dice bankroll management.
Finding a site's edge from its payout
Sites usually state their edge, but you can also work it out from any chance and the payout shown next to it. Rearranging the payout formula:
edge = 100 − payout × chanceA game that pays 1.98x at 49.5% has an edge of 1.99%. Check two or three chances. If the result differs between them, the site rounds its payouts, and the chance with the lowest implied edge is the cheapest one to play.
Seeing the edge in a simulation
Every DiceSim run reports the total wagered next to the net profit. Multiply the wagered amount by the edge to get the expected result for that run, then compare it with the actual profit. Over a few thousand rolls the two can be far apart. Over millions of rolls of flat betting at 49.5%, the net profit settles close to −wagered × edge / 100. The guide on reading simulation results covers the other numbers on the panel.
Try it
- House edge calculatorExpected loss for any wagered amount and edge, with a rakeback offset.
- Payout calculatorConvert between win chance, payout multiplier and the over/under target.
- Dice odds by win chancePayout, streak odds and risk figures for common chances from 1% to 98%.
- Dice bot simulatorChange the house edge in the run settings and compare the same script at 1% and 2%.
FAQ
What does a 1% house edge mean in dice?
The payout is set so that the average return on each bet is 99% of the stake. Over many bets the expected loss is 1% of the total amount wagered, at any win chance.
How is the dice payout calculated from the house edge?
Payout multiplier = (100 − house edge) / win chance. At a 1% edge, a 49.5% chance pays 2x and a 9.9% chance pays 10x.
Can a betting system beat the house edge?
No. Each roll is independent and every bet carries the same negative expectation, so a sequence of bets has an expected result equal to the sum of their expected results. A system changes how much is wagered and how the results are spread out.
Does rakeback make dice profitable?
Rakeback returns part of the house edge, so it lowers the expected loss. As long as the share returned is below 100% of the edge, the expected result stays negative.