Removing 7 of 8 Five-Pip Card (Rank-5) cards at 75% penetration of a 2-deck (104-card) shoe leaves 1 Rank-5 cards inside a 26-card stub (DEP142), producing 45.8960% Banker wins, 44.5715% Player wins, 9.5325% Ties, and a 0.5114% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPBPPBBPBPPBBPB) illustrating derived-road symmetry checks alongside DEP142 (2D Rank-5 at 75% 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.
75% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).
7 5-pip cards (final mandatory Player draw threshold) removed from the 2D pack.
Resolved at 45.8960% Banker win rate under 4% settlement.
Resolved at 44.5715% Player win rate with 0.9385 unit standard deviation.
Produces a 14.2074% house hold on the 8-to-1 Tie wager in state DEP142.
In combinatorial record DEP142, depleting 7 Rank-5 cards across 75% of a 2D (104-card) pack leaves 1 Five-Pip Card cards among 26 remaining cards, setting Banker win probability to 45.8960% and house edge to 0.5114% (4% Vig).
In 2D audit DEP142 (26/104 stub at 75% depth), fewer 5s in the (dep142-rank-5) stub reduce banker third-card improvements (26c) from 3 to 8 and (dep142-rank-5·26c) from 4 to 9. Removing 7 Rank-5 cards (-0.84 bps per card) alongside 4% Vig rules sets Tie hold to 14.2074% (9.5325% frequency).
| Wager / Metric | State DEP142 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP142 Banker (4% Vig) | 45.8960% (-0.5114% EV) | 45.8998% | DEP142 2D 75% (1 Rank-5) |
| DEP142 Player (1:1) | 44.5715% (-1.3245% EV) | 44.5676% | DEP142 26-card 2D stub (0.9385 SD) |
| DEP142 Tie (8:1) | 9.5325% (-14.2074% EV) | 9.5326% | DEP142 Rank-5 (7 out, 1 in) |
Cut-card protocol at 75% depth in DEP142 (2D, 26 stub cards containing 1 Rank-5 cards) ensures the shoe reshuffles long before 4% house hold (0.5114% Banker / 1.3245% Player) is overturned.
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