How to calculate the true EV and effective RTP of casino bonuses
This article explains how to convert bonus terms into numbers a player can use to compare offers. The reader will learn which contract terms matter, how to turn wagering requirements into a cash amount, how to combine game contribution percentages with game RTPs, and a quick formula for the expected loss while clearing a bonus. Part 1 sets variables, core conversions and practical approximations; worked numerical examples and a compact EV formula follow in the next section.
Gather the exact bonus terms and translate them into variables
Before any calculation, extract these items from the bonus T&Cs and convert them to currency or percentages:
- Bonus amount (B): amount of bonus funds or number/value of free spins.
- Deposit required (D): the player’s deposit needed to trigger the bonus.
- Wagering requirement (W): multiplier and base (is W × bonus, or W × (bonus+deposit)?).
- Game contribution (c): percentage each game contributes toward W (slots often 100%, table games lower).
- Maximum cashout (M): cap on withdrawable winnings from the bonus.
- Expiration (T) and maximum bet (L): time limits and any per-bet cap while clearing.
Converting W into a single cash number gives the total wagering required, R (in currency):
- If W is applied to bonus only: R = W × B.
- If W applies to bonus+deposit: R = W × (B + D).
- Always confirm wording in the official T&Cs; some operators use different bases for different promotions.
Estimate the effective game RTP you will use while clearing
Players typically choose games with the highest contribution and RTP allowed. When mixing games, compute a contribution-weighted RTP that reflects both game RTP and contribution rates. Define for each game i: RTP_i (as a decimal), contribution c_i (0–1), and the share of wagering put on that game s_i (0–1, sum to 1).
Quick formula for contribution-weighted RTP:
RTP_eff = (sum over i of RTP_i × c_i × s_i) / (sum over i of c_i × s_i)
Example: if a player bets 100% on a slot with RTP 96% and c=100%, RTP_eff = 0.96. If splitting 50/50 between a 96% slot (c=100%) and blackjack 99.5% (c=10%), compute using the formula above to get the practical RTP while clearing.
Use a practical approximation for expected loss while meeting wagering
Under the standard approximation that the total required wagering R is placed on games with RTP_eff, the expected loss incurred while clearing is:
Expected loss ≈ R × (1 − RTP_eff)
This gives an immediate sense of how costly the wagering is. It ignores bankroll dynamics, volatility, and the interaction of bonus vs. deposit funds; those effects are covered in worked examples later. Also remember that a maximum cashout M reduces upside: if the expected cash remaining after clearing exceeds M, substitute M for that value when calculating final EV.
With variables R, RTP_eff, B, D and M defined and the expected loss estimate in hand, a player is ready to compute the net expected outcome. The next part applies these steps to concrete examples — matched deposits and free spins — and derives compact EV and effective-RTP formulas plus a decision checklist for players.
Worked examples — a matched deposit and a free-spins offer
Below are two concrete applications of the variables and approximation from Part 1. They use the same logical flow: convert W to R, pick RTP_eff, compute expected loss while clearing, apply the max-cashout M, and then calculate EV and effective RTP.
Example A — 100% matched deposit
– Terms: deposit D = $100, bonus B = $100, wagering W = 30× bonus (applies to bonus only), max cashout M = $500.
– Convert: R = 30 × B = 30 × 100 = $3,000.
– Choose games: player bets exclusively on a slot with RTP = 96% and contribution c = 100%, so RTP_eff = 0.96.
– Expected loss while clearing: L = R × (1 − RTP_eff) = 3,000 × 0.04 = $120.
– Expected cash after clearing (uncapped): C_uncapped = D + B − L = 200 − 120 = $80. Apply cap: C = min(M, C_uncapped) = $80.
– Net EV (relative to not taking the offer): EV = C − D = 80 − 100 = −$20.
– Effective RTP (normalized to total funds in play D + B): EffRTP = C / (D + B) = 80 / 200 = 40%.
Interpretation: under these assumptions the bonus reduces your expected balance by $20; the high playthrough wipes out much of the bonus’ nominal value even with a decent slot RTP.
Example B — no-deposit free spins
– Terms: free spins worth B = $6 (30 spins × $0.20), no deposit required D = $0, wagering W = 20× bonus, M = $100.
– Convert: R = 20 × B = 120.
– Choose games: spins are on a 96% RTP slot, so RTP_eff = 0.96.
– Expected loss: L = 120 × 0.04 = $4.80.
– Expected cash after clearing: C = max(0, min(M, D + B − L)) = max(0, 6 − 4.8) = $1.20.
– EV = C − D = $1.20. Effective RTP = C / (D + B) = 1.20 / 6 = 20%.
Interpretation: low-value free spins can have small positive EV, but wagering multipliers, game choice, and spin denomination strongly affect the result.
Compact formulas and a quick decision checklist
Compact formulas (use these as a checklist calculation):
– R = W × base, where base is either B or (B + D) depending on the T&C.
– L = R × (1 − RTP_eff).
– C = max(0, min(M, D + B − L)).
– EV = C − D.
– Effective RTP = C / (D + B) (defined when D + B > 0).
Quick decision checklist before accepting any bonus
– Confirm exactly which amount W applies to (bonus only or bonus+deposit).
– Compute R and check its absolute size — large R quickly kills value.
– Choose allowed games with the highest combination of RTP and contribution; compute RTP_eff.
– Calculate expected loss L and the post-clear cash C; compare C to the stated maximum cashout M.
– Check maximum-bet limits L_bet versus bankroll strategy — bet caps can force suboptimal play or invalidate clearing plans.
– Verify the expiration period T is realistic for the required playthrough.
– If C is near zero or negative, reject the offer; if near break-even, consider volatility and bankroll: small bankroll/high volatility increases risk of bust before clearing.
– When M is binding or rules are complex (mixed contribution rates, tiered caps), run a small simulation or use a dedicated bonus EV calculator rather than relying on the linear approximation.
Practical pitfalls and adjustments to watch for
- Volatility and bankroll: high-variance games increase the chance you’ll bust before completing R; adjust expectations and bet sizing accordingly.
- Bet-size ceilings: per-bet limits can force many tiny wagers that are inefficient for some clearing strategies—recalculate RTP_eff and time needed if L_bet is restrictive.
- Mixed contribution schedules: when contribution rates vary by game or change after milestones, break the clearing into phases and recompute R and RTP_eff for each phase.
- Max-cashout cliffs: if M is close to the uncapped expected value, small changes in RTP_eff or wagered amount can flip an offer from positive to negative—treat near-cliff cases cautiously.
- Expiration and session limits: short T windows increase the operational risk of failing to clear; ensure you can satisfy R within T without violating bet rules or behavioral restrictions.
- Use simulation for edge cases: where contribution mixes, variable bet sizing, or caps create nonlinear outcomes, a Monte Carlo simulation or a specialist calculator will give more reliable EV estimates than a linear approximation.
Final notes for deciding whether to take a bonus
Converting bonus terms into numbers gives you control: it turns marketing into a testable expectation you can accept or decline. Use the compact formulas for quick screening, but treat marginal offers with caution—small errors in RTP_eff, bank size, or timing often determine real value. If the math shows a clear edge and the practical constraints (bet limits, expiry, personal volatility tolerance) line up, the bonus can be worth pursuing; otherwise pass and wait for a cleaner opportunity.