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How to use the probability distribution in slots
The probability distribution in the slots describes how often each type of outcome occurs: zero spin, small payout, medium, large, bonus, jackpot. By understanding the shape of this distribution, you can realistically plan the budget, session duration and expectations - without superstition and dogon.
1) What exactly is distributed
One spin can be looked at as a random variable (X) - a multiplier to the bet (how many bets will return in this back: 0, 0. 2, 1. 5, 10, 200, etc.). Then:- RTP = (\mathbb{E}[X]\times100%)
- Variance/volatility = (\mathrm {Var} (X) =\mathbb {E} [X ^ 2] -\mathbb {E} [X] ^ 2)
- Hit Frequency (HF) = (\mathbb{P}(X>0))
- A "significant event" (e.g. (X\ge 10)) has its probability (q =\mathbb {P} (X\ge 10))
Slots often have "heavy tails": very rare, but large values (X). Because of them, the average return is realized by "torn" bursts.
2) Mini example "probability passport"
Suppose 1 bet:- (P(X=0)=0. 70)
- (P(X=0. 5)=0. 20)
- (P(X=2)=0. 07)
- (P(X=10)=0. 02)
- (P(X=100)=0. 009)
- (P(X=1000)=0. 001)
- (\mathbb{E}[X]=0\cdot0. 70+0. 5\cdot0. 20+2\cdot0. 07+10\cdot0. 02+100\cdot0. 009+1000\cdot0. 001=0. 1+0. 14+0. 2+0. 9+1=2. 34).
- This is a hypothetical example (RTP 234%) only to illustrate techniques: the method is the same for any real set of probabilities.
- HF (=1-0. 70=30%)
- Chance ≥×10: (q = 0. 02+0. 009+0. 001=3%)
- Wait to ≥×10: average (\approach 1/q\approach 33) back; median (\approach\lceil\ln (0. 5 )/\ln (1-q )\rceil\approx 23) spin.
- (For small (q): median (\approach 0. 693/q).)
3) What exactly to count and how to use it
a) Average return ((\mathbb {E} [X])
Gives the "passport" RTP level. He doesn't say how often you'll see him. At short distances, deviations are normal.
b) Volatility ((\mathrm {Var} (X)))
The larger the proportion of rare large (X), the higher the dispersion - the longer the "deserts" and sharper the peaks.
c) Event frequencies
HF helps to understand the "liveliness" of the slot (how many small returns).
Threshold probabilities (for example, (X\ge 5,10,50)) give an idea of the rarity of "tangible" wins.
d) Waiting intervals
If an event with probability (q) occurs independently in each back, the expectation before it is the geometric distribution:- Average span (\approach 1/q) of spins
- Median (\approach\lceil\ln (0. 5)/\ln(1-q) \rceil)
- Plan a bankroll to survive multiple median intervals, not one.
- In addition to the average, it is useful to store percentiles by (X): 50th, 75th, 90th. This gives an honest answer "which payout is typical among winning spins."
4) "Passport of probabilities" for reviews and personal analytics
Assemble a block that can be inserted into each slot page:- HF (any win):...%
- Probabilities ≥×2/ ≥×5/ ≥×10/ ≥×50: .../.../.../...
- Expected interval to ≥×10: average... spins; median... (75-percentile...)
- Volatility comment: low/medium/high (which "deserts" are typical)
- Note: independence of spins; intervals - landmarks, not "timing."
Such a passport immediately removes false expectations and helps to choose the pace of the rate and the duration of the session.
5) How to get distribution if exact data is not available
1. From the provider's descriptions: there are HFs, a rarity of the bonus, ranges of multipliers - already enough to approach (q) by thresholds.
2. Empirically from the logs: fixed rate, 2-5 thousand spins, write (X) and build histograms and threshold frequencies.
3. Groups: combine "small" payments into baskets (≤×1, × 1- × 5, × 5- × 20, ≥×20), then - the same calculations.
4. Bootstrap: Re-sample your array (X) to get the uncertainty intervals for (\mathbb {E} [X]), HF, and (q).
6) Bankroll planning through probabilities
If (q =\mathbb {P} (X\ge 10) = 1%), the mean interval ≈ 100 spins, the median ≈ 69 spins. To "catch an event with a high probability," plan the stock for several such intervals.
Limits:- Stop loss on money (for example, 150-300 bets for high-volatility slots).
- Stop loss by back (for example, 2 median intervals without ≥×10 - break).
- Rate tempo: With aggressive tails, use a smaller base rate to withstand the characteristic "deserts."
7) What distribution does not give (and this is important)
You can't predict the next spin. Independence of outcomes is maintained.
You cannot "synchronize" luck by time of day. "Clusters" is a property of randomness, not a day mode.
You can not defeat the negative expectation of the bet management. Change the risk profile and form of drawdown, but not expectation.
8) Fast operating algorithm
1. Define the significance thresholds for yourself (≥×5, ≥×10, ≥×50).
2. Estimate their probabilities (q) (from descriptions/logs).
3. Calculate the expected intervals (mean, median, 75 percentile).
4. Rate your HF and shopping carts (up to × 1, × 1- × 5, × 5- × 20, ≥×20).
5. Set up bankroll and limits for these intervals.
6. In the report, show quantiles and bootstrap intervals, not just the average.
9) Frequent errors
Rely only on the mean (RTP). Ignoring tails leads to high expectations.
Consider HF a sign of "low risk." Many small returns do not negate long series of minuses.
Overestimate "rare big" as "should soon." The geometry of expectations knows no duty.
Mix slots/rates in one sample. The test conditions must be stable.
10) Ready-made template for your materials
Slot/Provider:...
Bet: ... (fix.)
HF (any win): ...%
Threshold probabilities (≥×2/ ≥×5/ ≥×10/ ≥×50): .../.../.../...
≥×10 waiting intervals: average...; median...; 75th percentile...
Volatility comment:...
Recommendations for limits: stop loss... rates; timeout after L-streak ≥...
Note: backs are independent; intervals are landmarks, not a prediction of "when the bonus will definitely come."
Bottom line: Probability distribution is your working tool for game planning. It does not "catch timing," but allows you to choose a slot for your goals, choose the size of the bet and the duration of the session, set realistic limits and talk about risks in the language of numbers, not sensations.