Removing 4 of 8 Five-Pip Card (Rank-5) cards at 40% penetration of a 2-deck (104-card) shoe leaves 4 Rank-5 cards inside a 62-card stub (DEP138), producing 45.8980% Banker wins, 44.5694% Player wins, 9.5326% Ties, and a 0.5073% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPBTBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP138 (2D Rank-5 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 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.
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 5-pip cards (final mandatory Player draw threshold) removed from the 2D pack.
Resolved at 45.8980% Banker win rate under 4% settlement.
Resolved at 44.5694% Player win rate with 0.9350 unit standard deviation.
Produces a 14.2070% house hold on the 8-to-1 Tie wager in state DEP138.
Exact conditional enumeration DEP138 for a 2D shoe at 40% depth (62/104 cards undealt) with 4 remaining Rank-5 cards confirms a 0.5073% Banker edge (4% Vig), 1.3286% Player edge, and 14.2070% Tie edge.
Tableau audit DEP138 confirms that because player draws on (dep138) two-card 5 and stands on (2d-40%) 6, while banker 3, 4, (dep138·2d-40%) and 5 all draw against a player third-card 5, rank 5 favors player when depleted. Inside the 62-card 2D stub (40% depth, 4/8 Rank-5 remaining, -0.84 bps slope), standard deviation is 0.9350 under 4% Vig.
| Wager / Metric | State DEP138 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP138 Banker (4% Vig) | 45.8980% (-0.5073% EV) | 45.8998% | DEP138 2D 40% (4 Rank-5) |
| DEP138 Player (1:1) | 44.5694% (-1.3286% EV) | 44.5676% | DEP138 62-card 2D stub (0.9350 SD) |
| DEP138 Tie (8:1) | 9.5326% (-14.2070% EV) | 9.5326% | DEP138 Rank-5 (4 out, 4 in) |
For DEP138 (62 remaining cards in a 104-card 2D shoe at 40% depth), tracking all 4 exited Rank-5 cards moves Banker win rate to 45.8980% (-0.5073% EV, 4% Vig) and Player to 44.5694% (-1.3286% EV).
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