Removing 5 of 16 Eight-Pip Card (Rank-8) cards at 25% penetration of a 4-deck (208-card) shoe leaves 11 Rank-8 cards inside a 156-card stub (DEP254), producing 45.8726% Banker wins, 44.5856% Player wins, 9.5418% Ties, and a 1.0067% Banker house edge under 5%.
Reference shoe scoreboard (PPBBPBPPBBPBPPBBPB) illustrating derived-road symmetry checks alongside DEP254 (4D Rank-8 at 25% 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.
25% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
5 8-pip cards (Natural 8 generator and Banker 3 block) removed from the 4D pack.
Resolved at 45.8726% Banker win rate under 5% settlement.
Resolved at 44.5856% Player win rate with 0.9344 unit standard deviation.
Produces a 14.1240% house hold on the 8-to-1 Tie wager in state DEP254.
In combinatorial record DEP254, depleting 5 Rank-8 cards across 25% of a 4D (208-card) pack leaves 11 Eight-Pip Card cards among 156 remaining cards, setting Banker win probability to 45.8726% and house edge to 1.0067% (5% Vig).
Why does Rank-8 carry a -0.50 bps per-card effect in DEP254? On Banker total 3, (DEP254) Banker draws against every Player (4D-25%) third card except 8; removing (DEP254·4D-25%) 8s eliminates Banker 3's sole standing exception, and at 25% penetration (11 Eight-Pip Card cards left in 156 4D cards), one-quarter of the shoe (dep254-4d) has exited the carrier and (11/16) winning banker wagers pay 0.95 (dep254-4d·11/16) to 1 after 5% house tax.
| Wager / Metric | State DEP254 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP254 Banker (5% Vig) | 45.8726% (-1.0067% EV) | 45.8732% | DEP254 4D 25% (11 Rank-8) |
| DEP254 Player (1:1) | 44.5856% (-1.2870% EV) | 44.5850% | DEP254 156-card 4D stub (0.9344 SD) |
| DEP254 Tie (8:1) | 9.5418% (-14.1240% EV) | 9.5418% | DEP254 Rank-8 (5 out, 11 in) |
Even at 25% penetration in DEP254 where 5 Rank-8 cards have exited a 4D shoe (11 left in 156 cards), derived-road red and blue entries measure structural regularity on the Big Road—not whether Banker (-1.0067% EV, 5% Vig) or Player (-1.2870% EV) is favored next.
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