Bonus conversion math

Required turnover, and the basis that decides it

A wagering requirement is a multiple of some starting balance. Which balance it multiplies is the single biggest lever in the entire calculation, and it is the part most bonus terms leave to a footnote. Two conventions exist, and the difference between them is not cosmetic:

• Bonus-only basis: required turnover T = WR × B — the multiple applies to the bonus alone.
• Deposit+bonus basis: required turnover T = WR × (D + B) — the same multiple applies to the deposit and the bonus combined.

A single worked example makes the gap concrete. Take a €100 deposit with a 100% match (bonus = €100, so the starting balance is €200), a 35× wagering requirement, and a 96% RTP game (house edge e = 0.04):

Arithmetic from the stated assumptions above (WR = 35, D = €100, B = €100, RTP = 96%). Grind ratio and naive EV are defined precisely in the next two sections.

Just moving from a bonus-only basis to a deposit+bonus basis doubled the required turnover here, at a 100% match. That effect does not stay this mild — it gets sharper the lower the match percentage goes, which is exactly the range most real offers sit in.

The basis multiplier: what a low match percentage really costs

The gap between the two bases has a name and a closed form:

T_(D+B) / T_B = (D + B) / B = 1 + D/B = 1 + 1/m, where m is the match rate expressed as a fraction (e.g. 0.5 for a 50% match).

Because the multiplier is 1 + 1/m, it grows as the match percentage shrinks — the smaller the match, the larger the gap between the two bases:

The headline finding of this article: the lower the match percentage, the more punishing a deposit+bonus basis becomes. A “50% match, 35× (D+B)” offer is a 105× bonus-only offer wearing a friendly number. Operators routinely ship this without knowing it, because the term sheet only ever states the 35, never the 105.

Grind ratio: the one number the rest of this article keeps using

Required turnover and basis are inputs to a single question: given the house edge, does the expected cost of clearing the wagering fit inside the balance the player is playing with? That question has a name here — the grind ratio:

G = (T × e) / (D + B) — the expected cost of the required turnover, divided by the starting balance.

• G < 1 — the average path completes the wagering.
• G > 1 — the average path busts before completing; only a run above expectation finishes.

In the worked example above, the bonus-only basis carries G = 0.70 and the deposit+bonus basis carries G = 1.40. That single number — not the raw “35×” — is what tells an operator whether an offer is, on average, completable at all. Every lever covered from here on (weighting, RTP, the cashout cap, free spins) is a way of moving G, and this article names each one explicitly as it goes so the effects stay comparable.

Why the naive EV number is wrong

The −€40 and −€180 figures above come from the simplest possible model:

EV_naive = B − T × e

That formula treats the wagering requirement as a single deterministic loss, applied once, to every player. Real play is not like that, for two reasons that both matter and both depend on the exact path a player's balance takes, not just its endpoint:

• Ruin. A player cannot lose more than their balance. Once it hits zero, the grind stops — the naive formula has no floor and can imply a loss deeper than the player ever had to lose.
• Cap truncation. A player cannot cash out more than the maximum cashout cap, however far above it their balance runs. The naive formula has no ceiling either.

Both truncations depend on the sequence of wins and losses along the way, not just the starting terms — which means there is no clean closed form for the realistic payout distribution once volatility, ruin and a cap are all in play at once. That is the stated justification for the Monte Carlo tool below: the article earns the simulator here, it does not decorate itself with one. Try the bonus conversion simulator to see the real distribution behind any set of terms, not the naive point estimate.

Volatility, the cap, and what actually drives bonus hunting

Running the engine across volatility classes and both bases produces the completion rate below. This is measured simulator output, not a formula:

Both rows: 12 batches × 2,500 paths = 30,000 requested per cell, seed_b = 20260820 + b, every batch verified complete — 30,000 requested / 30,000 completed, no truncation. D=€100, 100% match, WR=35, RTP=96%, weighting 1, bet €1, max bet €5.

Finding 1 — volatility always lowers the chance of completing, at every grind ratio. Higher variance means more ways to hit zero before the finish line. There is no regime in which it helps completion.

Volatility does something else entirely to what a completion is worth. Holding the bonus-only basis fixed (G = 0.70) and varying only the maximum cashout cap:

Figures are player EV in euros against a €100 deposit, with the bracketed range the 95% confidence interval on the estimate. Bold marks the highest point estimate in each row — not a colour, and not a claim of significance: the €500/medium cell's interval straddles zero and cannot be called positive, even though it is the row's highest point estimate. Measured across 12 batches × 2,500 paths = 30,000 requested per cell (seed_b = 20260820 + b); every batch verified complete — 30,000 requested / 30,000 completed, no truncation. Mean and completion are direct simulateBonus output; the 95% CIs come from an independently written replay verified bit-identical to the engine.

Finding 2 — the cap decides whether volatility pays. The ordering across the table shifts with the cap: under a tight €200 cap the best point estimate belongs to the lowest-variance game; uncapped, it belongs to the highest. The crossover sits around €500–€1,000 — 5–10× the bonus, which is exactly the range operators actually write into terms. Only the €200 and uncapped extremes are unambiguous once the confidence intervals are read — the €500/medium cell in between is not distinguishable from zero at this sample size.

Read down any single column of the completion table again: 46.63% / 29.76% / 20.40% / 13.11%, regardless of which cap column you pull the EV numbers from. The cap never appears in that first table at all, because it cannot — it changes only what a completion pays, never whether one happens.

Finding 3 — the cap does not change P(complete). Operators hold two independent dials, and conflating them is the most common design error in this area:

Put the two findings together and the real bonus-hunting mechanism comes into focus — and it is an EV story, not a completion story. A hunter who selects high-volatility games is not maximising the chance of finishing the wagering; the first table shows that choice makes completion less likely, not more. What high volatility does is raise the value of the completions that do land, and that only pays out when the cap is loose enough to let the tail through.

Look at the top-right of the EV table: an uncapped 35× bonus-only offer on a very-high-volatility game carries a mean player EV of +€50.01 (95% CI [€42.7, €57.3] — revised down from an earlier, under-sampled +€53.3) — on its face a losing product for the operator. But that mean sits on top of a 13.11% completion rate and an 86.89% bust rate: eight or nine players in ten walk away with nothing, and the small fraction who both clear the wagering and land above where the (now-absent) cap would have sat carry the entire positive mean. Dispersion is wide — standard deviation on payout per bonus granted is ±€645, so the €50.01 mean is only about 0.08 of one SD. The operator's loss is concentrated in a thin tail, and a short campaign can land on either side of zero purely on variance before enough bonuses have run for the mean to assert itself.

The mechanism matters as much as the number, because it is the part most often misread: volatility changes the distribution of outcomes and the probability of completing the wagering requirement — it does not change the game's underlying RTP. At 96% RTP, this offer is positive EV specifically because ruin truncates most players' turnover before they ever reach the requirement. Ruin cuts average turnover from the €3,500 the terms demand to about €1,239, so the house edge collects €49.55 rather than the €140 it would take on a fully-wagered bonus. Add the small forfeiture effect — the stub of balance left stranded below one bet when a player busts, worth €0.45 — and the player's total cost is €49.99 against a €100 bonus, leaving the +€50.01 above. The offer loses money because the wagering requirement mostly goes uncollected, not because the game's mathematics changed. Run the same offer to full completion with no ruin and no cap and it is −€40, exactly the naive closed-form figure.

Ruin-truncation is not the only route to positive EV, and the two should not be conflated. Above a theoretical break-even RTP — where house edge equals 1/WR — a wagering offer is positive EV even under full completion, with no ruin involved at all: 97.142857% RTP for a bonus-only offer at WR=35, or 98.571429% for a 100%-match deposit+bonus offer at the same WR. Below that line, as here at 96% RTP, any positive EV comes from the ruin-truncation effect above, not from the game's mathematics crossing into the player's favour.

Completion probability and player EV move in opposite directions with volatility. They are controlled by different terms, and a bonus economy has to manage both deliberately rather than assume tightening one also tightens the other.

Game weighting: the strongest lever most operators set by copying

Not every stake counts fully toward the wagering requirement. A game's weighting w is the fraction of each stake credited as turnover, so the real stake required to clear the same target is T / w, and the effective grind ratio is:

G_effective = G / w

This is a sharper lever than it looks. Take the bonus-only example from earlier — a completable G = 0.70. Route the same play through a game weighted at 10% and G_effective becomes 0.70 / 0.10 = 7.0 — a 10× grind, arithmetically uncompletable, despite the headline 35× term never changing. Weighting tables are, in practice, the strongest single term in most bonus economies, and they are usually set by copying a competitor's published list rather than by calculating what a given weighting does to G for the segment the offer targets.

The RTP lever moves more than the WR lever

Because G is directly proportional to the house edge e, the biggest single lever on grind ratio is not the wagering multiple at all — it is which games the wagering can be cleared on. Moving from a 96% RTP game (e = 0.04) to a 99% RTP game (e = 0.01) quarters the grind cost, for the same wagering requirement, deposit and bonus. No realistic change to the WR number produces an effect that size.

This is the mathematical reason excluded-game lists and low-RTP-weighted contribution rules exist at all: they hold e — and therefore G — inside a target band regardless of what the headline WR says. It is a note on term design, not a recommendation to steer players toward or away from any particular game.

Free spins: cheaper than the notional value, and the right reactivation tool

A spins grant runs the same mathematics on a smaller balance, with the wagering requirement applied to winnings rather than to a deposit. Take 100 spins at €0.10 on a 96% RTP game, with a 35× requirement on the winnings and a €100 max-win cap:

• Notional value: 100 × €0.10 = €10.
• Expected raw winnings: 100 × €0.10 × 0.96 = €9.60.
• Required turnover on those winnings: 35 × €9.60 = €336.
• Grind ratio: G = 336 × 0.04 / 9.60 = 1.40.

Running that scenario through the engine — model output, not a formula; €0.10 bet, €1 max bet, €100 cap, 40,000 paths, seed 20260820 — gives an expected cashout that depends heavily on the volatility of the game the spins are granted on:

• Low volatility: €3.30 — about a third of the €10 notional.
• Medium: €5.44. High: €5.74. Very high: €4.24.

So the real expected cost sits somewhere around a third to a little over half of face value — a 1.7× to 3× overstatement if you book spins at notional, not the order of magnitude the structure's severity might suggest. Note the shape: cost rises with volatility up to a point and then falls again at the extreme, because a very high-volatility game busts the small spins balance before it can convert (completion drops to roughly 6%). Both of the levers from the volatility-and-cap section are visible here at once, which is why the number has to be modelled per offer rather than assumed.

That is the operator conclusion this whole article has been building toward, applied to the instrument CRM teams hand out most often: the true expected cost of a “100 free spins” grant is a fraction of its €10 notional value, because the WR-on-winnings structure plus the cap strips out most of it before it ever reaches a player's withdrawable balance. That is exactly why spins are the highest perceived-value-per-cost instrument available and the right tool for reactivation campaigns — and also why booking them at face value in a campaign P&L overstates their real cost, sometimes substantially.

Seven patterns the math predicts, and how they show up in your data

Everything above describes rational responses to a set of terms — a player pursuing the strategy the math actually rewards, not a defect in the player. This section is a detection-and-design brief for the operator: the economic incentive behind each pattern, the data signature it leaves behind, and the lever that prices or blocks it. It is not a guide to exploiting a bonus, and it deliberately names no specific game and no player-tuned parameter.

1. 01Variance selection

   Incentive

   An EV play, not a completion play. As the volatility-and-cap section above shows, high volatility reduces the chance of completing the wagering and raises the value of the completions that do happen — and only pays when the cap is loose enough to let the tail through.

   Data signature

   Game mix concentrated in high-volatility titles, bet size pinned at the maximum permitted, very short time between bonus credit and first bet.

   Operator lever

   The cashout cap is the direct counter — it removes the tail the strategy depends on. Max bet and volatility-aware weighting are secondary levers.

2. 02House-edge arbitrage

   Incentive

   Because G is proportional to the house edge, choosing the lowest-edge game that still carries full weighting minimises the grind cost directly.

   Data signature

   Game-mix concentration in low-house-edge titles that carry 100% weighting.

   Operator lever

   Weight by RTP band rather than by game category.

3. 03Low-risk / opposing-outcome play

   Incentive

   Covering complementary outcomes manufactures turnover at near-zero variance.

   Data signature

   Paired stakes, near-zero net position, turnover velocity far above the segment norm.

   Operator lever

   Explicit low-risk-play terms, and detection rather than retrospective voiding.

4. 04Max-bet breach

   Incentive

   A single stake placed above the term threshold during an active wagering cycle.

   Data signature

   A stake above the max-bet limit landing mid-cycle, usually a void trigger under standard terms.

   Operator lever

   Block the bet at the point of placement, rather than voiding after the fact. Retrospective voiding is a CX and complaints problem, and where most regulatory friction on bonuses actually originates.

5. 05Multi-accounting / bonus farmingFraud problem, not a CRM-terms problem

   Incentive

   Claiming the same offer repeatedly across multiple identities.

   Data signature

   Device, payment instrument, address, and behavioural clustering across accounts.

   Operator lever

   Risk/fraud integration — this is a fraud problem wearing a CRM costume, and CRM should hand it over rather than try to solve it with bonus terms.

6. 06Playing the capRational, not abuse

   Incentive

   Stopping the moment the max cashout cap is reached, rather than continuing to play with no further upside.

   Data signature

   Withdrawal or session-end timed closely to a balance at or just above the cap.

   Operator lever

   None needed — this is rational, not abuse. It does change cost modelling, though: an operator’s E[cashout] figure has to assume cap-aware stopping, not a player who keeps playing past it.

7. 07Non-converting churners

   Incentive

   Taking every offer on the calendar with no intent, or no ability, to convert it into sustained play.

   Data signature

   High offer-uptake, low turnover per grant, low deposit recency.

   Operator lever

   Eligibility segmentation — the practical recommendation this consultancy makes most often here.

Design to a target, not to a competitor's headline

A wagering requirement is a blunt, single-dimension lever, and operators lean on it heavily mainly because it is the only one they can price on sight. Basis, weighting, the cashout cap, max bet, and eligibility are collectively far stronger levers than the WR number alone — and they are usually set by imitating a competitor's published terms rather than by calculating what they do to grind ratio and bonus cost for a given segment.

The better process runs the other way: pick a target grind ratio and a target bonus cost percentage per segment, then set the basis, WR, weighting, cap, and eligibility rules that land there — rather than copying a headline number and finding out what it actually costs after the fact. That per-segment design work is what a lifecycle and retention strategy engagement is for.