House Edge vs RTP — What They Really Mean (With the Math)

Two names for one number

RTP (Return to Player) is the fraction of everything wagered that a game pays back over the long run. House edge is whatever is left over for the casino. They always add up to 100%:

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

So a game advertised at 96% RTP has a 4% house edge. There is no third quantity hiding anywhere — if you know one, you know the other.

A worked example

Suppose you wager $1 per spin for 10,000 spins — $10,000 of total action — on a 96% RTP game. On average:

            expected return = $10,000 × 0.96 = $9,600
expected cost = $10,000 × 0.04 = $400
          

Note the cost is 4% of the amount wagered, not of your deposit. This is why session length and bet size matter more than most players think: the edge is charged on every dollar that passes through the game, not once.

Expected value per bet

The same idea per single bet is the expected value (EV) — what one bet is worth on average:

EV = stake × (RTP − 1) = − stake × house edge

For a $1 bet at 96% RTP, EV = −$0.04. It is negative for every real casino game — that negative number is the house edge. Provably fair does not change this; it only proves the result was honest. (See Provably Fair, explained .)

Where RTP comes from in a simple game

For a bet that either wins a fixed multiple or loses, RTP is just payout times the chance of winning:

RTP = payout multiplier × win probability

Rearranged, that tells you the fair payout for a given house edge. On Dice, if you want a win chance w and the house takes edge e, the payout is:

payout = (1 − e) / w

Example: a 50% win chance at a 4% edge pays 0.96 / 0.5 = 1.92×, not 2×. The missing 0.08× is the edge. On Lumenbet, Dice runs a 2% edge and Crash a 3% edge, baked directly into the payout formulas — the same × (1 − edge) you can see in the fairness formulas .

Edge is not volatility

One last trap: house edge and volatility are different things. The edge is your average cost. Volatility is how wildly results swing around that average. A low-edge game can still be wild (rare, huge wins), and a high-edge game can feel smooth (frequent small wins). Two games at the same 96% RTP can play nothing alike. We’ll cover volatility on its own — for now, just don’t confuse “fair” or “low edge” with “low risk.”