When the arithmetic stops producing a number
You hold 50 SC with a 30x requirement on a game you assume returns 95%. What is the expected balance at the end?
Inputs
| Input | Value | Unit |
|---|---|---|
| Starting Sweeps Coins | 50 | SC |
| Playthrough multiplier | 30 | x |
| Game contribution | 100 | % |
| Assumed RTP | 95 | % |
Working
- The requirement is 50 x 30 = 1,500 SC of wagering, all of which must actually be staked at full contribution.
- At a 5% house edge the expected loss over that wagering is 1,500 x 0.05 = 75 SC.
- The balance is 50 SC. The model's expected loss exceeds it by 25 SC, so subtracting gives -25 SC — and a balance cannot be negative.
- This calculator does not print that number. A negative expected balance is not a smaller balance; it is a signal that the model's central assumption has broken, because the model keeps staking in states where a real balance would already be gone.
- What can be said honestly is this: the break-even multiplier is 1 / 0.05 = 20x, the requirement is 30x, and the unrestricted expected remainder B − T×h is negative. That is not a probability that a session finishes above average.
Result
| Output | Value |
|---|---|
| Status | exhausted |
| Requirement (credited) | 1,500.00 SC |
| Must actually stake | 1,500.00 SC |
| Expected loss | 75.00 SC |
| Shortfall | 25.00 SC |
| Break-even multiplier | 20x |
Takeaway
Where the arithmetic runs past the edge of its assumptions, the honest output is a statement of what broke, not a confidently negative number.
The formula behind it
h = 1 − r
T = (B × m) ÷ c
E[loss] = T × h
E[balance] = B − (T × h)
m* = c ÷ h (the multiplier at which the expected balance reaches zero)
Assumptions
- Every coin staked is staked at the same assumed RTP r. Switching games changes r and therefore changes the result.
- With predetermined turnover T held fixed, expected value is linear in T. This follows from the linearity of expectation and holds regardless of how that wagering is split into individual bets — bet sizing does not change the expected total loss when T is unchanged, only how the results spread out around it.
- The full requirement is actually staked. The model does not stop when the balance runs out, which is why it is only valid while the expected balance stays above zero.
- No jackpot contribution, side bet, rake, or promotional credit sits outside the stated RTP.
Limitations
- This is an average over an extremely large number of repetitions, not a forecast of one session. Half of all real sessions finish below the average, and for a high-volatility game most finish well below it while a few finish far above.
- Because the model keeps staking after a real balance would be gone, B − T×h is usually a lower bound on the true expected balance rather than an exact figure. The published simulator can overshoot required turnover T by up to one stake on the last bet, so that bound is not a theorem under the simulator. Once the result reaches zero the model stops reporting a number, because a balance cannot go negative and a false precision there would be misleading.
- It cannot produce the probability of completing a requirement. That depends on the game’s full payout distribution and bet size, neither of which is an input here.
- Published RTP is a long-run property of a game’s design. It does not describe, predict, or guarantee any individual result.
This is a theoretical calculation, not a prediction. It describes an average over a very large number of repetitions and says nothing about what will happen in any particular session.
Run these numbers yourself · All worked examples · Methodology