RTP and volatility: what a slot’s numbers mean

RTP, return to player, is the share of all bets a machine pays back over a very long run. Our three return 95.14% to 95.36%, so they keep about 5 debens of every 100 bet. Volatility describes how unevenly that money comes back — a few big wins or many small ones — and it decides how long your purse lasts.

Take every outcome a machine can produce, multiply each win by its probability, add it all up and divide by the bet. That is the RTP. On Sevens of Ra you can do it with a pencil and a lot of patience: there are 64,000 equally likely reel positions. Play each one exactly once at 5 debens a spin and you bet 320,000 and get back 305,150 — 95.359375%.

For the two bigger machines we let a computer do the same thing: 55,566,000 positions for Book of Thoth and 87,852,960 for Treasures of Horus, with the bonus rounds worked out by formula. Then we checked every figure with 100 million simulated spins using the code the server runs. The difference between the RTP and 100% is the house edge:

The gap between the best and the worst machine is 0.22%: 216 debens per 1,000 spins at 100. As you will see below, no session you could ever play is long enough to notice it.

• It is not what you get back tonight. After 1,000 spins on Sevens of Ra, 95% of players end up somewhere between about 62% and 129% of what they bet. RTP is the centre of that spread, not a promise.
• It is not a cycle. A machine does not “owe” anything after a losing run. Each spin is drawn fresh; past losses are never paid back, they are just diluted by the millions of spins that follow.
• It is not personal. Every player, every bet size and every hour of the day get the same strips and the same paytable. There is no setting that makes a machine tighter for you.
• It does not say how many players win. Most sessions end below the start even on a 95% machine; the average is held up by fewer, larger wins.

Two machines with the same RTP can feel nothing alike. The usual measure is the standard deviation of one spin, in bets: the larger it is, the more of the return arrives in rare lumps instead of steady drips.

Read the rows, not just the first column. Sevens of Ra pays something almost every other spin, but half of those wins are smaller than the bet. Treasures of Horus has a bonus every 102 spins that pays 15 to 50 bets nearly nine times in ten, so its mid-size wins are frequent, while anything over 150 bets is essentially the GRAND. Book of Thoth is silent seven spins in ten and keeps the fattest tail: its free spins sometimes pay hundreds of bets.

One number cannot hold all that, which is why we show the session results below as well.

Here is the most useful fact about slots. The house edge grows in step with the number of spins: twice the spins, twice the expected loss. Luck, the spread around that expectation, grows only with the square root: four times the spins, twice the spread. Over a short session luck wins easily; over a very long one the edge always does.

The edge overtakes one standard deviation of luck after about 13,000 spins on Sevens of Ra, 19,500 on Treasures of Horus and 31,000 on Book of Thoth. That is many hours of non-stop play, even in turbo. In any evening at the reels you are mostly watching luck, and a good night proves nothing about the machine, just as a bad one does not.

For Book of Thoth these ranges are only a rough guide: its results are lopsided. Most players finish below the average, and a few big free-spins rounds pull the average up.

We played 20,000 sessions on each machine with the game’s own spin code: 10,000 debens, 100 a spin, until the purse could not cover another bet.

On average a session lasts 2,050–2,150 spins on all three — that is simply the purse divided by the edge — but the average is dragged up by rare marathons of several thousand spins. The median is the honest number. Notice the trade: Treasures of Horus keeps you playing longest yet doubles the purse least often, because its frequent bonuses top the purse up without ever lifting it very far. Book of Thoth ends sessions soonest and doubles them almost as often as the classic.

The simulator below plays a session on a model of each machine. It draws every spin from a simplified table of the machine’s real payouts, so the return and the swings are the machine’s own, even though it is not the game itself. Play a few single sessions on Book of Thoth and on Sevens of Ra and watch how differently the line moves; then run a thousand.

• Pick a machine by temper, not by RTP. A 0.22% difference is invisible; the difference between steady drips and rare lumps is not.
• Count your purse in bets. 10,000 debens is 100 bets at 100 and only 10 bets at 1,000. Fewer than a hundred bets, and even the gentlest machine can be over in minutes.
• Decide when to stop before you start. Autoplay can stop at a loss limit you set; a good run is also a fine moment to walk away.
• Enjoy a big win as luck. It does not mean the machine is hot, and it does not mean the next one is far away.