JONAH STUDY — CARD CLUSTERING SIMULATOR

K(t) = Σj [(Cj · Rj) / ΔSj] + ε | Testing clustering constant across card game simulations

K(t) = Σj [(Cj · Rj) / ΔSj] + ε
Cj = observed high-value cards in interval j / expected | Rj = recurrence ratio across simulated shoes | ΔSj = interval since last high-value cluster | ε = residual constant

Game Mode

Decks in Shoe

Simulations: 500

Interval Size (cards)

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ε (Epsilon)

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Peak Cluster %

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vs Null (Δ from 0.39)

Shoes Simulated

Epsilon Position on [0, 1] Scale — Red Line = 0.39 (Jonah Constant)

0.39

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Cluster Curve

Shoe Viz

K(t) Over Time

Compare Modes

Average high-value card density per deck position across all simulations. Red bar = 0.39 position.

High value (10,J,Q,K,A) Low value (2–6) Mid value (7–9)

K(t) value calculated at each deck position, averaged across simulations.

Run multiple modes to compare ε across game types.

Run simulations in different modes to populate comparison.

Current Simulation Stats

Mode—

Total cards per shoe—

High-value cards—

Expected ε (random)—

Observed ε—

Δ from Jonah constant—

Jonah match (±0.05)?—

Simulation Log

Awaiting simulation run...