Removing 2 of 4 Three-Pip (Trey) (Rank-3) cards at 40% penetration of a 1-deck (52-card) shoe leaves 2 Rank-3 cards inside a 31-card stub (DEP030), producing 45.9609% Banker wins, 44.5235% Player wins, 9.5156% Ties, and a 0.4010% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPBPPBBPBPPBBPB) illustrating derived-road symmetry checks alongside DEP030 (1D Rank-3 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.
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.
40% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).
2 3-pip cards across all four suits removed from the 1D pack.
Resolved at 45.9609% Banker win rate under 4% settlement.
Resolved at 44.5235% Player win rate with 0.9344 unit standard deviation.
Produces a 14.3592% house hold on the 8-to-1 Tie wager in state DEP030.
In combinatorial record DEP030, depleting 2 Rank-3 cards across 40% of a 1D (52-card) pack leaves 2 Three-Pip (Trey) cards among 31 remaining cards, setting Banker win probability to 45.9609% and house edge to 0.4010% (4% Vig).
Mechanical draw trees in DEP030 reflect how each removed 3-pip card (dep030-rank-3) modifies the boundary between banker (31c) standing on 5 and drawing (dep030-rank-3·31c) against mid-range player pulls. At 40% 1D depth (2 Rank-3 left of 4 in 31 cards, +0.65 bps slope), winning banker wagers collect (dep030-1d) 0.96 units per unit staked (2/4) with 60% of the shoe (dep030-1d·2/4) still inside the acrylic carrier.
| Wager / Metric | State DEP030 Value | 1D Baseline | Settlement Note |
|---|---|---|---|
| DEP030 Banker (4% Vig) | 45.9609% (-0.4010% EV) | 45.9595% | DEP030 1D 40% (2 Rank-3) |
| DEP030 Player (1:1) | 44.5235% (-1.4374% EV) | 44.5249% | DEP030 31-card 1D stub (0.9344 SD) |
| DEP030 Tie (8:1) | 9.5156% (-14.3592% EV) | 9.5156% | DEP030 Rank-3 (2 out, 2 in) |
Across 100-hand session horizons at state DEP030 (1D 40% depth, 2/4 Rank-3 in 31 cards), single-hand dispersion (0.9344 SD) dominates the 0.4010% (4% Vig) Banker and 1.4374% Player expectation gap.
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