Removing 4 of 8 Eight-Pip Card (Rank-8) cards at 40% penetration of a 2-deck (104-card) shoe leaves 4 Rank-8 cards inside a 62-card stub (DEP165), producing 45.8987% Banker wins, 44.5687% Player wins, 9.5326% Ties, and a 0.5059% Banker house edge under 4%.
Reference shoe scoreboard (BBPPPBBBPPBPTBPBBP) illustrating derived-road symmetry checks alongside DEP165 (2D Rank-8 at 40% depth).
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.
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.
40% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).
4 8-pip cards (Natural 8 generator and Banker 3 block) removed from the 2D pack.
Resolved at 45.8987% Banker win rate under 4% settlement.
Resolved at 44.5687% Player win rate with 0.9359 unit standard deviation.
Produces a 14.2070% house hold on the 8-to-1 Tie wager in state DEP165.
Removing 4 of 8 Rank-8 cards by the 40% mark of a 2-deck shoe (DEP165, 62 cards left) leaves 4 Eight-Pip Card cards and adjusts conditional probabilities to 45.8987% Banker, 44.5687% Player, and 9.5326% Tie under 4%.
Depleting 8-pip cards also (DEP165-Rank-8) lowers two-card Natural 8 lockouts (62c) when paired with zero-point tens (DEP165-Rank-8·62c) and court cards. Because 4 of 8 Eight-Pip Card cards are absent in DEP165 at 40% 2D penetration (62 cards left), per-card sensitivity (-0.50 bps) interacts directly with mid-early 40% penetration depth (DEP165) under reduced 4% Banker commission (Rank-8) (0.96:1 payout).
| Wager / Metric | State DEP165 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP165 Banker (4% Vig) | 45.8987% (-0.5059% EV) | 45.8998% | DEP165 2D 40% (4 Rank-8) |
| DEP165 Player (1:1) | 44.5687% (-1.3300% EV) | 44.5676% | DEP165 62-card 2D stub (0.9359 SD) |
| DEP165 Tie (8:1) | 9.5326% (-14.2070% EV) | 9.5326% | DEP165 Rank-8 (4 out, 4 in) |
Across 100-hand session horizons at state DEP165 (2D 40% depth, 4/8 Rank-8 in 62 cards), single-hand dispersion (0.9359 SD) dominates the 0.5059% (4% Vig) Banker and 1.3300% Player expectation gap.
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