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How to: Use Pay Tables for Analysis
The paytable is the "passport" of the slot: what combinations are paid and what are the rates. If you supplement it with information about reel strips or at least reasonable assumptions, you can evaluate the frequency of hits, the contribution of the base game to RTP, the strength of bonuses and the nature of volatility.
1) What exactly is in the paytable
Usually indicated:- Symbols and coefficients (x-multipliers to the bet/to the line) for 3/4/5 are the same.
- Wild (replacements, multipliers with participation).
- Scatter (payment "anywhere" and/or freespin trigger).
- Calculation type: lines (fix. lines, payment for "left-to-right") or ways (on each reel ≥1 a matching symbol, order from left to right; Megaways - variable drum height).
- Bonus rules: free spins, multipliers, sticky/walking wilds, hold & spin, wheels.
2) From the paytable - to the frequency of hits (basic game)
2. 1. Model lines (5 × 3, L lines)
On reel (r), let the fraction (or weight) of symbol (a) be (p_{a,r}) (one position per spin). For a combination of exactly k identical ones on a fixed line (without wild's for simplicity):[
P(a, k)=\Big(\prod_{r=1}^{k} p_{a,r}\Big)\cdot\Big(1-p_{a,k+1}\Big), ]where the multiplier on the right is "trims" the series on the next reel (so that it is exactly k, not k + 1).
Then the frequency of k matches of symbol (a) on one line is (P (a, k)). On all lines - multiply by (L) (adjusted for possible intersections, usually neglected at first approximation).
Hit of any type (no zeros):[
HF_{\text{base}}\approx 1-\prod _ {r = 1} ^ {R} (1 -\sum _ {a} p_{a,r} )\\text {(on the line is counted by the sum of events; in practice, sum the payoff probabilities for all symbols/k).}
]2. 2. Simplified approximation without tapes
If tapes are unknown, often assume uniform drums: (p_{a,r}\approx p_a). Combine weak symbols into "baskets": high/medium/low, assign them coarse fractions (for example, high = 5%, mid = 15%, low = 25%) and calculate (P (a, k)) - get the order of HF values and contributions.
3) From the paytable - to the expectation (EV) of the base game
If the payout for k matches of (a) equals (x_{a,k}) in line bets, then at (b) per line wait per line:[
EV_{\text{line}}=\sum_{a}\sum_{k\ge 3} x_{a,k}\cdot P(a,k)\cdot b.
][
EV_{\text{base}} = L\cdot EV_{\text{line}}.
]If payouts are "to total rate," remove (L).
Wild as a replacement. For accuracy, replace (p_{a,r}\to p_{a,r}+p_{w,r}) in places where wild can complement the combo (and separately take into account your own wild'a payments, if any). If wild multiplies the payout × 2/ × 3 when participating - multiply the corresponding probabilities of the participating combinations by the average participation multiplier.
4) Scatter and freespins: frequency and contribution to RTP
Scatter payment (anywhere): For the symbol s on the reel (r) with fraction (p_{s,r}), the probability is exactly m scatters:[
P_{s}(m)=\sum_{\substack{A\subset{1..R}\ A =m}}\ \prod_{i\in A} p_{s,i}\ \prod_{j\notin A}(1-p_{s,j}).
][
EV_{\text{scatter}}=\sum_{m} x_{s,m}\cdot P_{s}(m).
][
q_{\text{FS}}=\sum_{m\ge 3} P_{s}(m).
][
EV_{\text{bonus}}=q_{\text{FS}}\cdot EV_{\text{FS}}.
][
RTP \approx EV_{\text{base}} + EV_{\text{scatter}} + EV_{\text{bonus}}.
]5) Ways/Megaways: How to read the paytable
5. 1. Ways (e.g. 243 ways, fixed height 5 × 3)
The combination of the k matches of symbol (a) means "there is ≥1 such symbol on the first k reels." Probability on drum (r): (s_{a,r}=1- (1-p_{a,r}) ^ {h _ r}), where (h_r) is the number of rows (for example, 3). Then:[
P_{\text{ways}}(a,k)=\Big(\prod_{r=1}^{k} s_{a,r}\Big)\cdot(1-s_{a,k+1}), ]similar to the lines formula, but with (s_{a,r}) instead of (p_{a,r}). EV is considered the sum of payments by k with the weight of the number of paths (if the game pays "for each path," many tables immediately give an x-multiplier by the "combination," do not multiply again).
5. 2. Megaways (variable height)
Height (h_r) is random. First, the conditional calculation at fixed (h), then averaging by the distribution of heights:[
q_{\text{FS}}=\mathbb{E}h\big[q{\text{FS}}(h)\big],\quad EV_{\text{base}}=\mathbb{E}h\big[EV{\text{base}}(h)\big].
]It is practical to do Monte Carlo at the configuration level (h).
6) Mini example (5 × 3, 20 lines, no wild/scatter)
Let there be symbols A (high), B (mid), C (low) with the same fractions on the drums: (p_A=0{,}05,\ p_B=0{,}12,\ p_C=0{,}20) (the rest is "zero-symbols"). Payouts (to line rate): Probabilities "exactly k" in one line:- (P(a,3)=p_a^3(1-p_a)), (P(a,4)=p_a^4(1-p_a)), (P(a,5)=p_a^5).
[
EV_{\text{line}}=\sum_{a\in{A,B,C}}\sum_{k=3}^{5} x_{a,k},P(a,k).
]After counting (substitute numbers), multiply by (L = 20) - get the EV of the base game per spin (in bets per line). Add, if there is a scatter/bonus, their contribution according to the formulas above.
7) Volatility from paytable
Signs of high volatility: a large gap between 3-of-a-kind and 5-of-a-kind payments for high-symbols, a rare but bold bonus (small (q_{\text{FS}}), high (EV_{\text{FS}})), wild/freespin multipliers.
Variance estimate (approximation):[
\mathrm{Var} \approx \sum_{j} p_j x_j^2 - \Big(\sum_{j} p_j x_j\Big)^2, ]where (x_j) are all possible spin wins (in bets), (p_j) are their probabilities. In practice, baskets (0; ≤×1; × 1- × 5; × 5- × 20; ≥×20) and "representative" (x) are taken in each basket.
Event waiting intervals: if (q_{\text{FS}}) or (q_{\ge\times 10}) evaluated, mean interval (1/q), median (\approach 0 {,} 693/q).
8) What to do if data is scarce
Calibrate the p_{a,r} to the known RTP. Start with uniform (p_a), count the base EV. If you know (RTP) and the share of the bonus in it, trust the bonus with the remainder and correct (p_a) so that the "low" characters give a realistic HF (20-35% for "live" games).
Gather the empiricist. 5-10 thousand spins in the demo: rate HF, 3/4/5-combo share and bonus frequency - use as anchors for (p_{a,r}).
Simulate. Even rough imitation (uniform reels + paytable) gives plausible intervals and relative slot comparisons.
9) Frequent errors
Betting confusion. Payments "to the line" vs "to the total rate" - recalculate correctly.
Ignore the wild. They dramatically increase the frequency of 4/5 combos; consider as "substitution" in probabilities.
Adds disjoint events without checking. Combos intersect on the lines; at the first approximation, it is permissible to ignore overlaps, but remember this in the conclusions.
Megaways as regular ways. Here the key is the distribution of drum heights; without it, simulation is better right away.
Mixing RTP versions. One slot has several of them - one table, and the weights are different → the other RTP and frequencies.
10) "Payment Table Slot Passport" - ready-made template
Game type: lines/ways/Megaways; drums: 5 × 3/...; lines/ways:...
Key characters: high/mid/low with approximate fractions (p_a) (or "baskets").
HF (estimate): ...% (source: calculation/empirical)
Base game contribution to RTP:... p.p.
Scatter: rule, payments; q_FS: …%; EV_FS: … rates; bonus contribution:... p.p.
Intervals: median to frispins... spins; 75th percentile...
Volatility (qualitative): low/medium/high; features (bold 5-of-a-kind, multipliers, rare bonus).
Comment: strengths/weaknesses (frequent small things vs rare large ones), recommendations for session length and bet.
11) Quick checklist before publishing analysis
Are pay units (to line/to total rate) given?
Is the valuation method (p_{a,r}) (ribbons/empirics/assumptions) specified?
Does the total RTP converge with the passport (± a couple of pp)?
Are the waiting intervals and bonus role shown in RTP?
Is there a volatility assessment and practical conclusions (session length, limits)?
Bottom line: the paytable is not just "icon pictures," but a starting point for quantitative analysis. By comparing it with the fractions of the symbols on the reels (or reasonable approximations), you get HF, the contribution of the base game and bonus to RTP, waiting intervals and a qualitative assessment of volatility. This helps to compare slots, schedule sessions and write reviews in the language of numbers - without guesswork and "timing magic."