Hold and Win, Cascading Reels, Bonus Buy: Three Slot Mechanics from the Maths Side

Three mechanics dominate the release lists of the last five years: hold and win, cascading reels and bonus buy. Players know them by feel; operators know them by performance. What is rarely explained is how each one is built on the maths side — what it costs in RTP, what it does to volatility and where the traps are for a studio that adds it to a game. This is the designer’s view of the three, with the numbers that matter.

Hold and win

What the player sees: money symbols land with values on them; six of them trigger a respin feature where the paying symbols lock in place and every new one resets three respins. At the end the values are summed, and corner or jackpot symbols can multiply or award fixed prizes.

What the mathematician builds: two random processes stacked. The first is the trigger — the probability of landing six or more money symbols on a spin, tuned by how many money symbols sit on each reel strip. The second is the respin phase, where the reels are usually replaced by a separate “feature strip” with a much higher density of money symbols and a distribution of values on them. The value distribution is the lever: a table with many 1x and 2x values and rare 50x and 100x values produces a long tail.

RTP and volatility: hold and win is expensive in RTP because the feature is visible and frequent — 30–40% of the return often lives in it. It is medium in volatility unless the value table has a fat tail or the grand jackpot is large and rare. The most common design error is a feature strip so dense that the board fills every time; the “one more symbol” tension disappears and so does the appeal.

Trap: the number of distinct outcomes. Fifteen positions, each with a value from a table of eight, produces a combinatorial explosion. On a pre-computed RGS this has to be capped by design.

Cascading reels

What the player sees: winning symbols explode, symbols above fall into the gaps, and new wins can form — often with a multiplier that grows with each cascade.

What the mathematician builds: a sequence of dependent events. The first grid is drawn from the strips; each cascade draws replacement symbols from either the same strip (continuing where the reel “stopped”) or from a separate distribution. The maths has to compute the expected value of the whole chain, not of one grid, and the chain length depends on the win frequency of the grid itself — a game with a high hit frequency cascades longer.

RTP and volatility: cascades add small, frequent wins, which pushes hit frequency and lowers volatility — until a progressive multiplier is attached. A multiplier that grows +1 per cascade turns the chain into a compounding process and raises volatility sharply, cheaply in RTP terms, because long chains are rare. This is why nearly every cascade game since 2019 ships with a multiplier: it is the combination that gives both frequent action and a big ceiling.

Trap: unbounded chains. Without a cap on the multiplier or the number of cascades, the max win is theoretically unlimited, which regulators dislike and pre-computed platforms cannot represent. A cap is a maths decision and has to be in the design document.

Bonus buy

What the player sees: a button that buys the feature directly, typically at 50–100x bet for free spins, sometimes a menu of options at different prices.

What the mathematician builds: a separate bet mode. The purchased feature must return the buy price times its RTP — if the buy costs 100x and the mode is targeted at 96.5%, the feature’s expected payout must be 96.5x. This is usually not the same feature as the naturally triggered one: designers give the bought version a slightly higher RTP (a common pattern is 0.3–0.8 points above base) and a different volatility, because the buyer wants the feature to be worth its price.

RTP and volatility: bonus buy is the most volatile way to play a game. The player converts 100 spins’ worth of budget into a single event with a heavy tail. The “naturally triggered” feature has its rarity to smooth the experience; the bought one has nothing.

Trap: regulation. The UK banned bonus buy for its market in 2019; other jurisdictions restrict it. A game built around the buy — with a base game that is dry by design because everyone is expected to buy — collapses in markets where the button must be removed. The base game has to stand on its own.

Combining mechanics

Modern hits stack these: a cascade base game with a progressive multiplier, a hold-and-win feature, and buy buttons for both. Every combination multiplies the number of things to simulate and the number of edge cases to test. The design principle we use is simple — one mechanic carries the base game, one carries the feature, and every added layer has to justify itself with a specific target: hit frequency, feature share or max-win probability. Adding a mechanic because a competitor has it is how games end up with 92% base RTP and a confused player.

When a client asks for “a hold-and-win game”, the first deliverable is not art; it is a maths model that shows what the feature strip, value table and trigger rate do to the profile. That model — and the simulation that proves it — is what we quote under game logic and mathematics, on its own or as the first step of full production.

Background reading (German, Russian): the German-language explanation of Risikoleiter and gamble features, and Russian guides to hold-and-win and cascade mechanics on slotcatalog-ru.com.