What a stated return of 96.5 per cent gives back over 500 spins

A slot information screen states a return of 96.5 per cent. The figure is true, checkable and almost useless for the evening in front of you, because it describes an average over a run far longer than any player will ever complete. What we can do is work out what it says about five hundred spins, which is a realistic session, and what it very deliberately does not say.

The straightforward part

Five hundred spins at fifty pence is a stake of £250. At a declared return of 96.5 per cent the expected amount returned is £241.25, so the expected loss is £8.75 — three and a half per cent of everything staked, exactly as the subtraction in house edge and return as one figure written twice says it should be. Per spin that is 1.75 pence. It is a small number, and it is the only part of the session the stated return actually fixes.

The noise is several times the loss

Everything else about those five hundred spins is spread, and spread has its own arithmetic. Suppose the game’s per-spin standard deviation is five times the stake, which is the sort of figure a medium-volatility game carries. Over 500 independent spins the spread grows with the square root of the number of spins, not with the number itself: five times fifty pence is £2.50 per spin, and £2.50 multiplied by the square root of 500 — about 22.4 — is £55.90.

So the arithmetic says: expected loss £8.75, typical deviation from that expectation about £56. The thing the stated return pins down is roughly a sixth of the size of the thing it does not. Finishing £40 up and finishing £70 down are both entirely ordinary results for the same five hundred spins, and neither of them is evidence about the game.

Why the typical session is worse than the average session

This is the part the headline figure hides, and it is not a trick: it follows from where the return is stored. Big-win games keep a slice of their return in very rare events, and an average that includes a rare event is not the result most people get.

Work it through with a stated assumption. Say the top feature of a game pays 2,000 times the spin, and say it accounts for ten percentage points of the game’s return. Ten per cent of stake returned through an event paying 2,000 times stake means the event has to land once in 20,000 spins. In 500 spins the expected number of such events is 0.025 — about one session in forty contains one. The other thirty-nine sessions are running on the remaining 86.5 per cent, which on £250 staked returns £216.25 and loses £33.75.

That is the whole mechanism. The average of the forty sessions really is £8.75 of loss; the ordinary session loses nearly four times that, and one session in forty pays for all of them. A game that keeps more of its return in the tail has a lower typical result at exactly the same stated percentage, and nothing on the information screen tells you how the return is distributed — that is what the volatility band is for, and why hit frequency sits next to return rather than underneath it.

What it means for a bankroll

The expected cost of putting money through the game is 1.75 pence a spin, so £100 covers an expected 5,714 spins before the arithmetic alone exhausts it. Nobody gets 5,714 spins out of £100, because the spread arrives first: with a typical deviation of £56 per 500 spins, a £100 balance is inside one ordinary swing of zero. If the point of the session is to last, the lever is the stake, not the game — halve the stake and both numbers halve with it, while the ratio between them stays where it was.

Reading the figure honestly

A stated return of 96.5 per cent licenses exactly one sentence: over an enormous number of spins, this game gives back 96.5 per cent of what is staked on it. It does not say the next hundred spins will return £96.50 of £100. It does not make a 96.5 game better than a 96.0 game over an evening — the half point between them is £1.25 on £250, which is a fiftieth of the ordinary swing. And it is not a promise about any particular session, because the figure averages across sessions that look nothing like each other. Over an evening, the stake you choose and the way the game stores its return matter more than the headline. Which game to take that to is a question of what kind of ride you want, and our newsroom piece on matching a game to a risk profile is the place that argument gets made.