House Edge vs RTP: The Only Two Numbers That Matter

House edge is the fraction of every wagered dollar a game keeps over the long run. RTP — return to player — is the fraction it gives back. They are the same number inverted:

RTP = 1 − house edge and house edge = 1 − RTP

A 1% house edge is a 99% RTP. A 4% edge is a 96% RTP. There is no third number, no hidden adjustment, and no game where the two figures disagree. Everything else on this page is about what that number does to you in practice.

The definitions, precisely

Both figures are ratios of money returned to money wagered, computed as an expectation over the game’s full outcome distribution.

For a single bet with win probability p and a total payout of m times the stake (the “×” figure that includes your stake back), the expected return per $1 staked is:

RTP = p × m

And the expected profit — the expected value — is:

EV = (p × m) − 1

Worked: a dice bet with a 49.5% win chance paying 2.00×.

RTP = 0.495 × 2.00 = 0.99 EV = 0.99 − 1 = −0.01

So 99% RTP, a 1% house edge, and an expected loss of one cent per dollar staked. That construction is not an accident — a 1% edge dice game sets its payout as m = 0.99 ÷ p, which produces the same 99% at every risk level:

Same edge across five wildly different bets. Whatever changes between those rows, it is not the cost.

What 99% RTP means over 1,000 bets

Bet $1 a thousand times at a 1% edge. Total wagered: $1,000. Expected loss: 1,000 × 0.01 = $10. Expected returned: $990.

That is the whole calculation, and its most important feature is what does not appear in it. Not bet size relative to bankroll, not the order of wins and losses, not whether you doubled after a loss. Expected loss is turnover multiplied by edge, and nothing you do at the staking level enters the formula. This is precisely why martingale cannot fix a negative edge — it changes the shape of the distribution, not its mean.

Why your session looks nothing like the RTP

RTP is an asymptote. Individual sessions scatter around it, and the scatter is usually larger than people expect.

Consider four bets that all carry the same 1% edge, played 1,000 times at $1 each. The expected result is −$10 in every case. The standard deviation of the total is not remotely the same:

The standard deviation of a 1,000-bet total is SD per bet × √1000 ≈ SD × 31.62. For the even-money bet that is 1.00 × 31.62 = $31.62; for the long shot, 9.85 × 31.62 = $311.50.

Read the last row carefully. A single 1% edge produces a one-standard-deviation band roughly 60 dollars wide on one bet type and roughly 620 dollars wide on another. Sessions in that bottom row will regularly finish hundreds up or hundreds down, and neither outcome says anything about whether the game is fair or the RTP is honest.

The probability of being ahead

For the even-money dice bet (49.5% win chance, 2.00× payout), the chance of finishing a session in profit falls steadily with volume. These are exact binomial figures, not estimates:

The remaining probability is split between finishing behind and finishing exactly level. At a hundred bets you are close to a coin flip on the session; at a hundred thousand, the edge has effectively removed the possibility of profit. Nothing about the game changes across those rows — only the sample size does.

The edge applies to turnover, not to your deposit

The most common and most expensive misreading of RTP is treating it as a percentage of what you put in.

Deposit $100 and place 100 bets of $10. You have wagered $1,000, not $100. At a 1% edge your expected loss is $10 — which is 1% of turnover but 10% of your deposit. Play 1,000 such bets and you have wagered $10,000, with an expected loss of $100, which is your entire deposit.

The same idea expressed as recycling: if you wager your bankroll, take the return, wager it again, and repeat n times, the expected fraction remaining is RTP ⁿ.

Starting from $100 in both columns. 0.99¹⁰ = 0.9044 and 0.96¹⁰ = 0.6648; at a hundred cycles, 0.99¹⁰⁰ = 0.3660 while 0.96¹⁰⁰ = 0.0169.

This is why speed and stake size dominate the outcome even though they never touch the edge. A 99% game played at a thousand bets an hour generates more turnover, and therefore more expected loss, than a 96% game played at fifty.

It is also the arithmetic behind wagering requirements. A $100 bonus with a 40× wagering requirement obliges $4,000 of turnover. At a 1% edge that carries an expected cost of 4,000 × 0.01 = $40; at 4%, 4,000 × 0.04 = $160. The requirement is priced in the game’s edge, and the same headline bonus is worth completely different amounts depending on which games clear it.

Typical published RTP ranges by category

Treat the figures below as commonly published ranges rather than measurements. Actual values are set per game by the operator or studio, vary between builds of the same title, and should be read from the specific game’s own information panel.

The originals row is the reason those games are worth understanding rather than dismissing: a published edge near 1% is genuinely low. It is still negative, and the variance in crash or a high-multiplier dice bet will move you far from the mean in either direction long before the edge shows up.

How caps and limits change the real number

A published RTP describes the payout table as designed. Two operator settings can pull the number you actually experience well below it.

Maximum win caps

If a game caps a single win at a fixed amount, any bet whose full payout would exceed the cap is not paid in full — and the RTP for that bet collapses.

Worked example. Suppose a limbo-style bet targets a 100,000× multiplier under a 1% edge, so the win probability is 0.99 ÷ 100,000 = 0.0000099. Intended RTP:

0.0000099 × 100,000 = 0.99

Now apply a $10,000 maximum win to a $1 stake. The payout is truncated to 10,000× and the RTP becomes:

0.0000099 × 10,000 = 0.099

A 99% RTP bet has become a 9.9% RTP bet — a 90.1% house edge — with no change to the game’s published figure and no failure of any hash. The bet is still provably fair in every technical sense, which is one of the sharper examples of what provably fair does not prove.

Bet caps and rounding

Maximum stake limits interact the other way: they bound how much turnover you can generate per bet, which bounds absolute loss rate but does nothing to the percentage.

Rounding matters more than it looks on small stakes. If payouts round down to two decimal places, a 1.0102× payout on a $0.01 stake pays $0.01, not $0.010102 — and the shaved fraction is house edge that never appears in the published number. On low-payout, high-frequency bets this is not negligible.

Which number to look up first

Before the seed panel, before the strategy, before anything: find the game’s published RTP or house edge, and confirm what turnover you intend to generate. Those two figures multiply into your expected cost and they are the only inputs that do.

Provability is a separate axis entirely. A verified sequence under a 25% edge is still a 25% edge, and checking a result yourself tells you the draw was honest without telling you the price. The reason to learn both is that they answer different questions, and the edge is the one that determines what the session costs.