Slot machines

What “pays back 96%” means

Slots advertise their RTP (return to player), what they pay back on average. This one pays back 96.3%: of every €100 that goes in, about €96 comes out as prizes in the long run. But careful: that average belongs to the machine over millions of spins, not to you. What happens to one person varies enormously. Try “1,000 spins” a few times: you will almost always lose, and once in a while win big.

Technical How the exact RTP is computed

Each reel shows 14 positions, but the outcome is decided on a 64-stop “virtual reel” with different weights. The RTP comes from going through all 14³ = 2,744 combinations:

RTP = Σ P(i)·P(j)·P(k) · prize(i, j, k), P(i) = weight(i)/64

Result: 96.333%, with a prize on 35.5% of spins. The top prize (7 7 7) pays 5,000× and comes up once every 65,536 spins: much of the return is packed into that very rare prize, which makes the machine highly volatile. The tests check that sampling reproduces the exact RTP.

The “so close” is designed

You may have noticed that the 7 often shows up just above or below the line, especially on the third reel. That is no accident. On this machine, as on many real ones, the third reel has a single 7 that lands on the line 1.6% of the time but stops right next to it 23.4% of the time: 15 times more often. The feeling of “I nearly had it” is not bad luck: it is manufactured.

It matters because those near-misses make us want to keep playing. Brain-imaging studies have found they activate the same areas as a real win (Clark and colleagues, 2009).

Technical Virtual reels

The player sees a 14-position physical reel; the outcome is picked on a 64-stop virtual reel. On the third reel the 7 takes 1 virtual stop and each blank next to it takes 8. Since the symbols above and below the line are read off the physical reel, the 7 appears next to the line with probability 0.234 versus 0.0156 on it. On the first reel the ratio is only 2.5. This is the virtual reel mapping technique used by electronic machines.

Wins that are really losses

When a ♠ lands on the first reel, the machine celebrates a €1 prize. But you staked €1: you have won nothing, you just got your own money back. Modern multi-line machines go further and celebrate “wins” smaller than the stake. The brain experiences them as victories even while you lose money (Dixon and colleagues, 2010).

Same machine, different experience

Two slot machines can pay back exactly the same and feel completely different. Volatility decides how the money is handed back: lots of small wins, or almost nothing and now and then a huge one. Play a session and compare the peak you reach with what you have left at the end.

Technical How volatility is modelled

Each volatility is a distribution of multipliers with their probabilities. The table is rescaled so its expectation is exactly the chosen RTP, so volatility changes the shape (the variance) without touching the mean. Every session uses a seeded generator (mulberry32): the comparison runs 500 reproducible sessions per type.

Speed is the real price

Losing 3.7 cents per euro sounds small. But a spin lasts a few seconds. At one spin every 3 seconds that is 1,200 spins an hour: at €1 a spin, €44 an hour on average. And volatility means you often lose much faster than that. See it with thousands of players in the Ruin Lab.