- Maths reviewed by Josh Miller
- Tested by Diana Westfield
A slot RTP calculator shows where a slot’s return comes from, symbol by symbol. Take three reels of 32 stops each. One seven on each reel lines up once every 32,768 spins, so paying it at 1,500 times the bet adds 4.6% to the RTP. Six lemons per reel line up once in 152 spins, and paying them 40× adds 26%. The free CasinoCalcs calculator above adds every symbol together; the sample pay table returns 90.45%.
Slot machine maths, step by step
Every slot pay table rests on the same sum: the chance of each win multiplied by what it pays. On a three-reel game the chance of three matching symbols is the stops for that symbol on each reel multiplied together, divided by all the possible stops multiplied together. Here’s the sample game:
| Symbol | Stops per reel | Pays | Lands | Adds to RTP |
|---|---|---|---|---|
| Seven | 1 | 1,500× | 1 in 32,768 | 4.58% |
| Triple bar | 2 | 400× | 1 in 4,096 | 9.77% |
| Double bar | 3 | 150× | 1 in 1,214 | 12.36% |
| Single bar | 4 | 60× | 1 in 512 | 11.72% |
| Cherry | 3 | 80× | 1 in 1,214 | 6.59% |
| Bell | 5 | 50× | 1 in 262 | 19.07% |
| Lemon | 6 | 40× | 1 in 152 | 26.37% |
| Blank | 8 | 0 |
Change one number and you can feel how slot design works. Swap one blank on reel 3 for a seven and the top prize lands twice as often, which pushes RTP up by another 4.6%. Designers do exactly this in reverse: they put the big symbols on reel 3 less often, so near misses on the first two reels are common and full lines rare.
Hit frequency and volatility
Our sample pays on only 1.4% of spins, because it counts three-of-a-kind wins only. Real games add mixed bars, single cherries and scatter pays, which is how they reach a 20% to 30% hit rate. Two slots can share a 96% RTP with a completely different feel: one paying small wins every few spins, the other holding most of its return in a feature that turns up once in 200. The volatility line measures that spread. The bigger the number, the faster a bankroll can disappear before the long run arrives.
Online slots use virtual reels with far more stops, many paylines and bonus features, and their reel strips aren’t public, so you can’t rebuild a real game here. The RTP on the game’s info screen is the figure that counts. To see what that RTP means for your money, try the slot bankroll and variance calculator, play a game out in the slot simulator, or check how often a feature should land with the slot hit frequency calculator.
Every spin is independent: a slot is never due. BeGambleAware.org can help if you’re spending more than you planned.