Removing 2 of 8 Two-Pip (Deuce) (Rank-2) cards at 25% penetration of a 2-deck (104-card) shoe leaves 6 Rank-2 cards inside a 78-card stub (DEP110), producing 45.9003% Banker wins, 44.5671% Player wins, 9.5326% Ties, and a 0.9618% Banker house edge under 5%.
Reference shoe scoreboard (PPBBPBPPBBPBPPBBPB) illustrating derived-road symmetry checks alongside DEP110 (2D Rank-2 at 25% 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.
Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).
Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.
This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.
25% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).
2 2-pip cards across all four suits removed from the 2D pack.
Resolved at 45.9003% Banker win rate under 5% settlement.
Resolved at 44.5671% Player win rate with 0.9326 unit standard deviation.
Produces a 14.2064% house hold on the 8-to-1 Tie wager in state DEP110.
Exact conditional enumeration DEP110 for a 2D shoe at 25% depth (78/104 cards undealt) with 6 remaining Rank-2 cards confirms a 0.9618% Banker edge (5% Vig), 1.3332% Player edge, and 14.2064% Tie edge.
Why does Rank-2 carry a +0.52 bps per-card effect in DEP110? On Banker total 4, (DEP110) Banker draws against Player third-card (2D-25%) 2 through 7; removing 2s (DEP110·2D-25%) trims low-pip Player third-card triggers, and at 25% penetration (6 Two-Pip (Deuce) cards left in 78 2D cards), one-quarter of the shoe (dep110-2d) has exited the carrier and (6/8) winning banker wagers pay 0.95 (dep110-2d·6/8) to 1 after 5% house tax.
| Wager / Metric | State DEP110 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP110 Banker (5% Vig) | 45.9003% (-0.9618% EV) | 45.8998% | DEP110 2D 25% (6 Rank-2) |
| DEP110 Player (1:1) | 44.5671% (-1.3332% EV) | 44.5676% | DEP110 78-card 2D stub (0.9326 SD) |
| DEP110 Tie (8:1) | 9.5326% (-14.2064% EV) | 9.5326% | DEP110 Rank-2 (2 out, 6 in) |
Comparing DEP110 (25% 2D depth, 2 Rank-2 removed, 6 remaining in 78 cards) against fresh-shoe baselines shows how finite-stub variance (0.9326 SD) coexists with a 0.9618% 5% Banker house edge.
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