Inside Our Math Model: How We Design Pay Tables and Simulate Billions of Spins

Players see symbols, animations and sound. What they never see is the spreadsheet-and-simulation engine that decides how a game behaves. At SlotOnline Studio, every title starts and ends with its maths model. Art can be redone in a week; a weak maths model sinks a game no matter how beautiful it looks. This post walks through how our math team designs a model, from the first brief to the final sign-off.

Step 1: the brief

Before anyone opens a spreadsheet, our lead designer and math team agree on a short brief. It usually covers:

• Target RTP, often with two or three alternative configurations for operators in different markets.
• Volatility band, such as medium-high.
• Grid and win system: 5x3 lines, 5x4 ways, 6x5 cascades and so on.
• Feature concept: free spins, hold-and-win, cascades, a pick bonus.
• Experience targets: roughly how often the feature should trigger, the typical feature win, and the maximum win.

Those experience targets matter as much as the headline numbers. A game where the bonus triggers every 400 spins will feel very different from one where it lands every 120, even at the same RTP. If you want the background on these concepts, see our guides to RTP and volatility.

Step 2: the RTP budget

We think of RTP as a budget to be spent across the different parts of the game. A typical split for a medium-volatility game might look like this:

For a high-volatility title like Outback Gold, the balance shifts heavily towards the hold-and-win feature, which carries a far larger share of the return. That's what makes the base game feel leaner and the feature feel so important.

Step 3: reel strips and the pay table

With the budget agreed, the math team builds the reel strips: the ordered lists of symbols each reel can land on. Every decision has knock-on effects. Adding one more premium symbol to reel three raises the RTP, the hit frequency and the frequency of five-of-a-kind wins all at once.

The pay table is designed alongside the strips. We aim for a pay table that reads sensibly to players (premium symbols clearly worth more, five-of-a-kind clearly special) while hitting the mathematical targets. A common trap is a pay table that looks generous but only because the top symbols are almost impossible to land. We avoid that: if a symbol pays big, it should appear often enough that players actually see it.

Exact calculation where possible

For the base game, we can usually calculate the RTP exactly by enumerating every possible stop combination. On a 5-reel game with strips of around 60 positions each, that's roughly 777 million combinations, well within reach of a modern computer. Exact calculation gives us a precise theoretical RTP, hit frequency and win distribution.

Step 4: simulating billions of spins

Features complicate things. Cascades, sticky wilds, respins and hold-and-win mechanics create chains of dependent events that are hard or impossible to enumerate. For those, we use Monte Carlo simulation: we play the game, in software, billions of times and measure what happens.

Our simulation tooling runs the same game logic that powers the real server, not a separate approximation. That's deliberate. If the simulator and the game ever disagreed, our numbers would be worthless. A typical sign-off run is several billion spins per RTP configuration, distributed across many processor cores.

From each run we extract:

1. Total RTP and its confidence interval.
2. RTP contribution from each feature.
3. Hit frequency and feature trigger frequency.
4. The full win distribution, from tiny wins up to the maximum.
5. Session-level metrics, such as how a 200-spin session at a fixed budget tends to unfold.

Why billions?

Rare events need big samples. If the maximum win in a game happens once in 50 million spins, a simulation of 100 million spins would only see it a couple of times, and the RTP estimate would be noticeably wobbly. With several billion spins, the statistical uncertainty on RTP shrinks to a few hundredths of a percent, which is the level of precision we want before a game leaves the studio.

Step 5: tuning for feel

Numbers that pass don't automatically make a good game. Once the model is on target, our designers play it, and we look at simulated sessions rather than just averages. Questions we ask include:

• How long is the typical gap between meaningful wins?
• Does the feature usually pay enough to feel worth the wait?
• Are there "dead" outcomes where a feature triggers but pays almost nothing too often?
• Does the max win cap feel reachable or purely theoretical?

We then nudge strips, weights and feature rules, re-run the simulations and repeat. A model might go through dozens of iterations. For Dragon Lantern, for example, the multiplier ladder in free spins was reworked several times so that mid-sized wins appeared more often without inflating the maximum.

Step 6: documentation for testing

The final model is written up in a detailed maths document: every strip, weight, pay value, feature rule and the calculations behind the RTP. That document travels with the game to independent testing, where the lab checks both the paper maths and the game's real behaviour. We explain that stage in RNG testing and certification.

What players should take from this

All of this work produces a game whose long-run behaviour is precisely known and whose individual spins are completely unpredictable. Both are true at once. No amount of maths makes any slot online session a reliable way to win money; it simply makes the game honest and consistent with what it says on the tin.

You can explore the results of our maths work for free in demo mode on the games page, read about our server and client stack on the technology page, or head back to the online slot studio home page. Our games are intended for players aged 18 and over.

18+ only. Our games are entertainment products. If gambling stops being fun, contact Gambling Help Online on 1800 858 858 (24/7, free and confidential).