Every figure is an expectation โ the average outcome if you ran the
promo many times. One session will land above or below it.
The qualifying stake
Wagering ยฃS on a game with RTP rs doesn't cost you ยฃS โ you get
ยฃS ร rs back on average. So the real cost is only the house edge:
stake cost = S ร (1 โ rs)
At 96% RTP, a ยฃ10 stake costs an expected 40p, not ยฃ10.
The reward
Cash is withdrawable, so it's worth its face value. A free bet (bonus funds,
stake not returned) must be played through โ and every pass through the reward game shrinks
it by that game's RTP:
cash value = R
free-bet value = R ร rrWR
where rr is the reward game's RTP and WR is the wagering
requirement (how many times the bonus must be re-bet). A ยฃ1 free bet at 96% RTP with
1ร wagering is worth 96p; at 3ร it's worth ~88p.
The verdict
The promo is worth it when the reward beats the stake cost:
session EV = reward value โ stake cost
Positive EV means the offer pays you to play. Equivalently, your session RTP
โ everything returned divided by everything staked โ climbs above 100%.
Model simplifications: it ignores min-odds rules, game weighting
toward wagering, max-win caps, variance and risk of busting a free bet before clearing.
Treat it as an upper-bound sanity check, not a guarantee.