#Slot Math Specification — Template

Цей документ визначає математичний контракт гри. Автоматично згенерований PAR sheet є доказовим артефактом, але не замінює правил, targets, tuning history та approval gates у цьому Math Spec.

#1. Identity and provenance

#Change log

#2. Math status

#3. Bet and payout units

Include conversion equations:

<win multiplier → credit win → monetary win>

#4. Target math profile

Definitions:

[ RTP = E[X] = \sum_i p_i x_i ]

[ Var(X) = \sum_i p_i(x_i - RTP)^2, \qquad \sigma = \sqrt{Var(X)} ]

#5. RTP decomposition

The decomposition must reconcile to total RTP within <numerical tolerance>.

#6. Mathematical model

#State-space size

[ N = \prod_{r=1}^{R} L_r ]

Explain whether entry weights represent repeated probability mass and how visible rows are derived from a selected entry.

#7. Symbols and paytable

#Scatter payouts

#Paylines

For ways/cluster games, replace this table with the exact adjacency, minimum-count, direction and aggregation rules.

#8. Reel strips / weights

Canonical machine-readable reels remain in the versioned configuration. This section may embed them or link to the exact artifact and hash.

#Symbol counts and expected visibility

#9. Evaluation order

This must match the GDD and production evaluator.

<Normative payout pseudocode>

#10. Feature model

Copy per feature.

#Feature: <name/type>

#Feature state transitions

#Closed-form derivation where available

For a simple trigger-and-award feature:

[ RTP_{feature} = P(trigger) \times E[feature\ payout] ]

Document the actual derivation, including retrigger limits and caps.

#11. RNG and mapping contract

No secret production seed material belongs in this document.

#12. Exact calculation

Do not silently replace exact calculation with simulation. Record the boundary explicitly.

#13. Monte Carlo specification

Required sample size for a desired RTP half-width (\varepsilon):

[ n \ge \left(\frac{z\sigma}{\varepsilon}\right)^2 ]

Report:

[ SE = \frac{s}{\sqrt{n}}, \qquad CI = \bar X \pm zSE ]

#Simulation results

#14. Win distribution

Add game-specific thresholds required for Big/Ultra/Mega presentation and marketing claims.

#15. Max-win analysis

Clearly distinguish a reachable value from a mathematical upper bound.

#16. Test vectors and parity

Required scenarios:

• No win
• Single win
• Simultaneous wins
• Wild substitution and exclusions
• Scatter trigger
• Multiplier order
• Feature trigger/retrigger
• Cascade/respin termination where applicable
• Max-win cap
• Interrupted-round replay where applicable

#17. Draft Math handoff

#Open and locked parameters

Draft handoff criteria:

• All payout-affecting rules are defined.
• Draft metrics meet draft tolerances.
• Config and evidence are versioned and hashed.
• Test vectors cover critical paths.
• Unsupported mechanics are rejected or explicitly excluded.

#18. Tuning record

Add one entry per tuning revision. Never overwrite the baseline.

#Tuning request <ID>

#19. Lifecycle and freeze

stateDiagram-v2
    [*] --> Draft
    Draft --> Integration: Draft gate
    Integration --> Tuning: Measured change request
    Tuning --> Integration: New candidate
    Integration --> Frozen: Exact/sim/parity gates
    Frozen --> Certification: Immutable package
    Certification --> Certified: External/internal approval
    Certification --> Tuning: Rejected with new revision
    Certified --> Retired

Frozen parameters:

• reel strips/weights;
• paytable;
• feature probabilities;
• evaluation and multiplier order;
• RTP split;
• rounding;
• RNG algorithm/version and mapping;
• max win and cap;
• bet-dependent behavior.

Any mathematical change after freeze requires a new math version and full regression evidence.

#20. Certification evidence bundle

#21. Risks and limitations

#22. Final sign-off

Final conditions:

• Total RTP and decomposition reconcile.
• Exact and simulated results agree within the justified interval where both apply.
• Max-win claims are proven and consistent with the GDD/help content.
• Reference/runtime parity passes.
• Config, reports and build identities are immutable and reproducible.
• No unresolved release-blocking risk remains.