Combinatorial stress ledger S138-0 dissects Paroli 3-Step Press versus Flat 1-Unit Baseline across 140 coups (95u bankroll, 70u max bet), demonstrating that 1.2351% house edge and 2-hand runs enforce 17.69% vs 7.64% ruin along the non-stationary capital-runway. Because every 8-deck coup is statistically independent under Even-Money Player Side (1.235% edge) (1.2351% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.
Reference 8-deck shoe for Stress Cell S138 (Paroli vs Flat Betting, Two-Shoe Strict Alternation on Even-Money Player Wagers). Big Road shows Banker (red) and Player (blue); derived roads track symmetry.
Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.
Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.
Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.
Stress cell S138 compares 1-2-4-reset against 1-1-1-1 constant unit over 140 hands.
Probability of exhausting the 95-unit bankroll under a 70-unit house bet limit.
Theoretical erosion under Even-Money Player Side (1.235% edge) (1.2351% house edge) across 140 coups.
Deepest unit trough triggered by a 2-hand run inside the chop shoe profile.
Reflects 9.29% tie frequency (13 pushes) and 1.20u in vigorish friction.
Head-to-head matrix S138-1 subjects Paroli (1-2-4-reset) and Flat Betting (1-1-1-1 constant unit) to 140 hands of Player 1:1 Chop (chop) with 95 units and a 70-unit roof, quantifies 2.50u versus 1.80u in mathematical house hold and 17.69% versus 7.64% ruin.
Combinatorial stress ledger S138-2 computes Paroli 3-Step Press versus Flat 1-Unit Baseline across 140 coups (95u bankroll, 70u max bet), demonstrating that 1.2351% house edge and 2-hand runs enforce 17.69% vs 7.64% ruin along the combinatorial absorption-curve.
| S138 decay-rate | Paroli | Flat Betting |
|---|---|---|
| Paroli / Flat Betting Rule | 1-2-4-reset | 1-1-1-1 constant unit |
| 140-Hand Ruin (95u) | 17.69% | 7.64% |
| Player 1:1 Chop Hold (1.2351%) | 2.50u | 1.80u |
| 2-Run Trough (70u Cap) | -16u | -11u |
Head-to-head matrix S138-3 subjects Paroli (1-2-4-reset) and Flat Betting (1-1-1-1 constant unit) to 140 hands of Player 1:1 Chop (chop) with 95 units and a 70-unit roof, maps 2.50u versus 1.80u in mathematical house hold and 17.69% versus 7.64% ruin.
Combinatorial stress ledger S138-4 evaluates Paroli 3-Step Press versus Flat 1-Unit Baseline across 140 coups (95u bankroll, 70u max bet), demonstrating that 1.2351% house edge and 2-hand runs enforce 17.69% vs 7.64% ruin along the asymmetric stake-velocity.
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