Removing 15 of 32 Three-Pip (Trey) (Rank-3) cards at 40% penetration of a 8-deck (416-card) shoe leaves 17 Rank-3 cards inside a 250-card stub (DEP390), producing 45.8610% Banker wins, 44.6234% Player wins, 9.5156% Ties, and a 0.5968% Banker house edge under 4%.
Reference shoe scoreboard (PPBBBPPPBBPBTBPBPP) illustrating derived-road symmetry checks alongside DEP390 (8D Rank-3 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 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).
15 3-pip cards across all four suits removed from the 8D pack.
Resolved at 45.8610% Banker win rate under 4% settlement.
Resolved at 44.6234% Player win rate with 0.9344 unit standard deviation.
Produces a 14.3592% house hold on the 8-to-1 Tie wager in state DEP390.
Exact conditional enumeration DEP390 for a 8D shoe at 40% depth (250/416 cards undealt) with 17 remaining Rank-3 cards confirms a 0.5968% Banker edge (4% Vig), 1.2376% Player edge, and 14.3592% Tie edge.
In six-card resolution tree DEP390 (8D at 40% depth, 250 cards left), each removed 3-pip card (dep390-rank-3) modifies the boundary between banker (250c) standing on 5 and drawing (dep390-rank-3·250c) against mid-range player pulls; removing 15 of 32 Rank-3 cards (+0.65 bps weight) leaves Banker at -0.5968% EV under 4%.
| Wager / Metric | State DEP390 Value | 8D Baseline | Settlement Note |
|---|---|---|---|
| DEP390 Banker (4% Vig) | 45.8610% (-0.5968% EV) | 45.8597% | DEP390 8D 40% (17 Rank-3) |
| DEP390 Player (1:1) | 44.6234% (-1.2376% EV) | 44.6247% | DEP390 250-card 8D stub (0.9344 SD) |
| DEP390 Tie (8:1) | 9.5156% (-14.3592% EV) | 9.5156% | DEP390 Rank-3 (15 out, 17 in) |
Comparing DEP390 (40% 8D depth, 15 Rank-3 removed, 17 remaining in 250 cards) against fresh-shoe baselines shows how finite-stub variance (0.9344 SD) coexists with a 0.5968% 4% Banker house edge.
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