Removing 4 of 8 Seven-Pip Card (Rank-7) cards at 40% penetration of a 2-deck (104-card) shoe leaves 4 Rank-7 cards inside a 62-card stub (DEP156), producing 45.8980% Banker wins, 44.5694% Player wins, 9.5326% Ties, and a 0.5073% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPPPPBBBBPPBBPB) illustrating derived-road symmetry checks alongside DEP156 (2D Rank-7 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 2D (double-deck European salon privé carriers and two-deck shoe pits).
4 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 2D pack.
Resolved at 45.8980% Banker win rate under 4% settlement.
Resolved at 44.5694% Player win rate with 0.9356 unit standard deviation.
Produces a 14.2070% house hold on the 8-to-1 Tie wager in state DEP156.
In combinatorial record DEP156, depleting 4 Rank-7 cards across 40% of a 2D (104-card) pack leaves 4 Seven-Pip Card cards among 62 remaining cards, setting Banker win probability to 45.8980% and house edge to 0.5073% (4% Vig).
For DEP156 (2-deck shoe, 40% dealt), player stands pat on (dep156) two-card 7, and a player (2d-40%) third-card 7 is the highest (dep156·2d-40%) card that forces banker 4, 5, and 6 to draw. Holding 4 of 8 Rank-7 cards in a 62-card stub with -0.83 bps rank slope yields 45.8980% Banker, 44.5694% Player, and 9.5326% Tie.
| Wager / Metric | State DEP156 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP156 Banker (4% Vig) | 45.8980% (-0.5073% EV) | 45.8998% | DEP156 2D 40% (4 Rank-7) |
| DEP156 Player (1:1) | 44.5694% (-1.3286% EV) | 44.5676% | DEP156 62-card 2D stub (0.9356 SD) |
| DEP156 Tie (8:1) | 9.5326% (-14.2070% EV) | 9.5326% | DEP156 Rank-7 (4 out, 4 in) |
Comparing DEP156 (40% 2D depth, 4 Rank-7 removed, 4 remaining in 62 cards) against fresh-shoe baselines shows how finite-stub variance (0.9356 SD) coexists with a 0.5073% 4% Banker house edge.
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