Three worked examples, start to finish
The arithmetic of game maths is simple enough to do on the back of an envelope. These three examples carry it from a single round, through a session, to the gap between the average and reality.
Example 1 — the cost of a single round
Start with one round. Everything else is this figure multiplied.
Stake 1 unit, published RTP 96%, so the house edge is 4%.
EV = 1 × (0.96 − 1.00) = −0.04 unitsOne round is worth, on average, four hundredths of a unit to the player. That is invisible in a single result, which is exactly why the edge is easy to forget.
Example 2 — the expected cost of a session
Now run the same round a large number of times at a fixed stake.
The expected cost of the session is 32 units. Note the shape of this: it is proportional to turnover, so doubling the rounds or the stake doubles the expected cost.
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Example 3 — how far a session can sit from the average
The expected cost is a centre, not a schedule. In a session of a few hundred rounds the realised result is a draw from a wide spread, and it can land on either side of the average by a large margin.
All three sessions below have identical stakes, identical rounds and identical RTP. Only the ordering of results differs.
Lucky session: returns +180 units against an expected −32 Typical session: returns roughly −30 units Unlucky session: returns −240 units against an expected −32Winning in a session is not evidence the RTP is higher than published; losing heavily is not evidence it is lower. Both are the spread doing what a spread does, and neither survives in the long run.
The lesson is not that any single session can be predicted — it cannot — but that the average accrue of cost is real, steady and proportional to how much is staked. That is the part the maths can promise, and the part worth planning around.
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