Removing 7 of 16 Four-Pip Card (Rank-4) cards at 40% penetration of a 4-deck (208-card) shoe leaves 9 Rank-4 cards inside a 125-card stub (DEP219), producing 45.8754% Banker wins, 44.5827% Player wins, 9.5418% Ties, and a 0.5423% Banker house edge under 4%.
Reference shoe scoreboard (BBPPBBBBPPPPBBPPBP) illustrating derived-road symmetry checks alongside DEP219 (4D Rank-4 at 40% depth).
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.
This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.
This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.
40% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
7 4-pip cards (strongest pro-Banker removal sensitivity) removed from the 4D pack.
Resolved at 45.8754% Banker win rate under 4% settlement.
Resolved at 44.5827% Player win rate with 0.9347 unit standard deviation.
Produces a 14.1235% house hold on the 8-to-1 Tie wager in state DEP219.
Across 7,673,190,695,193,600 initial 4D permutations, depletion node DEP219 narrows to a 125-card stub (40% depth) holding 9 of 16 Rank-4 cards, where Banker resolves at 45.8754% (-0.5423% EV) and Player at 44.5827% (-1.2927% EV).
Under the fixed third-card tableau for DEP219, rank 4 sits at (dep219) the exact pivot where banker (4d-40%) 5 begins drawing (player third (dep219·4d-40%) card 4–7) while banker 3 and 4 also draw. With 9 Rank-4 cards inside 125 remaining 4D cards (40% dealt), single-card slope (+1.19 bps) keeps Banker house edge at 0.5423% and Player at 1.2927%.
| Wager / Metric | State DEP219 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP219 Banker (4% Vig) | 45.8754% (-0.5423% EV) | 45.8732% | DEP219 4D 40% (9 Rank-4) |
| DEP219 Player (1:1) | 44.5827% (-1.2927% EV) | 44.5850% | DEP219 125-card 4D stub (0.9347 SD) |
| DEP219 Tie (8:1) | 9.5418% (-14.1235% EV) | 9.5418% | DEP219 Rank-4 (7 out, 9 in) |
Across 100-hand session horizons at state DEP219 (4D 40% depth, 9/16 Rank-4 in 125 cards), single-hand dispersion (0.9347 SD) dominates the 0.5423% (4% Vig) Banker and 1.2927% Player expectation gap.
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