How to estimate the actual return per 1000 spins

You can estimate the "real return" (that is, the actual RTP of your session) for 1000 spins without complex statistics. It is important to correctly collect data, calculate basic metrics and honestly assess the error: 1000 spins is a short distance, and the spread will be noticeable, especially in highly volatile slots.

1) What exactly we estimate

Actual RTP of the sample: the ratio of the total payment to the total rate for N spins.

Fixed rate formula (b):

[
\widehat{RTP}=\frac{\sum_{i=1}^{N} \text{win}_i}{N\cdot b}\times100%
]

Hit Frequency (HF): the proportion of spins with any payout ((\text {win} _ i> 0)).

Variance and "ragging": how unevenly the winnings are distributed over time (series of empty spins, "bursts").

2) How to collect data per 1000 spins (minimum)

Start a simple table (one row = one spin):

Spin no., rate (b) (better fixed), payout (\text {win} _ i).
Flags (optional): "significant win" (for example, ≥×10 to bet), bonus round, etc.

This is enough to:

count (\widehat {RTP}) and HF;
estimate variance from empirical data;
build a confidence interval or make a bootstrap.

3) Basic calculations on your data

Let (N = 1000), the rate is fixed (b).

1. Actual RTP:

[
\widehat{RTP}=\frac{\sum \text{win}_i}{N\cdot b}\times100%
]

Example: for 1000 spins at a rate of 1, a total of 940 ⇒ returned (\widehat {RTP} = 94%).

2. Hit Frequency (HF):

[
HF=\frac{#{i:\text{win}_i>0}}{N}\times100%
]

3. The empirical variance of a "bet win" is: Consider (X_i=\frac{\text{win}_i}{b}) (multiplier per spin). Then:

[
\bar{X}=\frac{1}{N}\sum X_i,\quad s^2=\frac{1}{N-1}\sum (X_i-\bar{X})^2
]

Here (\bar {X }\times100% =\widehat {RTP}).

4) Confidence interval for RTP (fast method)

If you have (s) (empirical MSE multiplier), then the standard error is:

[
SE=\frac{s}{\sqrt{N}}
]

And the approximate 95% confidence interval for the multiplier:

[
\bar{X}\ \pm\ 1{,}96\cdot SE
]

Converting to percentages (multiplying by 100%), we get the interval for RTP.

💡 Practical note: slots have a "heavy" distribution (long tails due to rare large winnings). Therefore, bootstrap is usually more reliable.

5) Confidence interval through bootstrap (without formulas)

1. From your array ({X _ i}) repeatedly (for example, 5000 times) "randomly re-sample" 1000 values with return.

2. For each re-sampled sample, calculate the mean (\bar {X} ^) (and convert to%).

3. Take the 2.5th and 97.5th percentiles of the received (\bar {X} ^) - this is the bootstrap interval for the actual RTP.

This interval reflects the real "ragging" of your data and is usually more honest than the classic approach.

6) What counts as a "normal" spread of 1,000 spins

The correct answer depends on the volatility of the slot. Rough:

Low/medium volatility: the spread of the actual RTP per 1000 spins is often within ± 5-10 percentage points of the "passport" RTP.
High volatility: deviations ± 10-20 + pp - a common thing at a short distance.
Therefore, 1000 spins is an express assessment, not a "verdict of honesty."

7) Interpretation of the result: how not to make a mistake

94% with a passport of 96-97% for 1000 spins - not a reason to draw conclusions. See the confidence interval: it easily "covers" the passport RTP.

80-85% at a very "evil" distance (without bonuses/hits) is possible even on fair play. Check tail events: could simply not happen.

💡 120% per 1000 spins - also normal: hit the "good window" with a major hit/bonus.

Key: Don't confuse session and long term. Passport RTP is implemented at very large volumes.

8) 3 more useful metrics

Median multiplier by winning backs (without zeros): shows a "typical" payout not covered by rare kh≈1000.

Intervals between significant events (for example, ≥×10): the median and 75th percentile will give a realistic expectation of "how much to wait."

Maximum series of losses (L-streak): useful for setting up stop losses not only for money, but also for the number of spins.

9) Mini calculation checklist (can be inserted into any article/report)

1. Collect 1000 lines: rate, payment.

2. Count: (\widehat {RTP}), HF, (\bar {X}), (s), (SE).

3. Plot the 95% interval (classic and/or bootstrap).

4. Write: median interval between "significant" events and top 3 L-streak.

5. Draw a brief conclusion: "The result fits/does not fit into the expected spread for such volatility."

10) Ready-made template "passport 1000 spins"

Slot/Provider:...

Bet: ... (fix.)

Spins: 1,000

Actual RTP: ...%

95% CI (bootstrap): ... -...%

HF (any win): ...%

Median ≥×10 interval: ... spins (75th percentile:...)

Max L-streak: ... spins

Volatility comment: low/medium/high; expected "empty" segments...

Conclusion: does it fit into a reasonable spread relative to the passport RTP (yes/no), is there a reason to increase the amount of data.

11) Frequent mistakes and how to avoid them

Mid-Test bet/slot change. Keep conditions steady.

Conclusions without error. Always show an interval, not just a period.

Ignoring tails. One × 300 can pull RTP; no bonus - "drown." This is a feature, not a "twist."

Gambler’s fallacy. The long desert doesn't "boost the chance" of the next spin.

12) What to do if you want to be more accurate

Increase the volume to 10,000 + spins or combine several independent sessions.

Use bootstrap regularly and store source data.

For HF, you can apply a Bayesian estimate (β a priori) - it will give accurate intervals for rare events.

With a fixed bank - compare not only RTP, but also drawdowns (max drawdown) in order to understand the "price" of volatility.

Bottom line: 1,000 spins is a quick "thermometer," not a diagnosis. Correctly collected data, calculation of the actual RTP, HF and confidence interval (preferably bootstrap) allow you to understand whether you are in the expected corridor for this level of volatility. All that goes beyond the scope is a reason not to make hasty conclusions, but to expand the sample and double-check the methodology.