In head-to-head trial S208-0 across 140 deals (Player 1:1 Chop, 1.2351% edge), D'Alembert records a -21u peak footprint and 18.31% ruin probability on a 95-unit stack, whereas Flat Betting logs a -11u trough and 7.64% ruin under the 70-unit limit. 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 S208 (D'Alembert 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 S208 compares +1 on loss / -1 on win 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 1.67u in vigorish friction.
Within variance-scaled testbed S208-1, a 95-unit bankroll facing 140 coups of Player 1:1 Chop (chop) and a 70-unit maximum wager models 18.31% ruin (3.47u expected loss) on D'Alembert Pyramid versus 7.64% ruin (1.80u expected loss) on Flat 1-Unit Baseline.
In head-to-head trial S208-2 across 140 deals (Player 1:1 Chop, 1.2351% edge), D'Alembert records a -21u peak cadence and 18.31% ruin probability on a 95-unit stack, whereas Flat Betting logs a -11u trough and 7.64% ruin under the 70-unit limit.
| S208 capital-runway | D'Alembert | Flat Betting |
|---|---|---|
| D'Alembert / Flat Betting Rule | +1 on loss / -1 on win | 1-1-1-1 constant unit |
| 140-Hand Ruin (95u) | 18.31% | 7.64% |
| Player 1:1 Chop Hold (1.2351%) | 3.47u | 1.80u |
| 2-Run Trough (70u Cap) | -21u | -11u |
Within session-bounded testbed S208-3, a 95-unit bankroll facing 140 coups of Player 1:1 Chop (chop) and a 70-unit maximum wager dissects 18.31% ruin (3.47u expected loss) on D'Alembert Pyramid versus 7.64% ruin (1.80u expected loss) on Flat 1-Unit Baseline.
In head-to-head trial S208-4 across 140 deals (Player 1:1 Chop, 1.2351% edge), D'Alembert records a -21u peak escalation and 18.31% ruin probability on a 95-unit stack, whereas Flat Betting logs a -11u trough and 7.64% ruin under the 70-unit limit.
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