Removing 5 of 16 Nine-Pip Card (Rank-9) cards at 25% penetration of a 4-deck (208-card) shoe leaves 11 Rank-9 cards inside a 156-card stub (DEP263), producing 45.8729% Banker wins, 44.5853% Player wins, 9.5418% Ties, and a 1.0060% Banker house edge under 5%.
Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP263 (4D Rank-9 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 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.
Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).
Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.
25% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
5 9-pip cards (top Natural 9 generator) removed from the 4D pack.
Resolved at 45.8729% Banker win rate under 5% settlement.
Resolved at 44.5853% Player win rate with 0.9347 unit standard deviation.
Produces a 14.1239% house hold on the 8-to-1 Tie wager in state DEP263.
Removing 5 of 16 Rank-9 cards by the 25% mark of a 4-deck shoe (DEP263, 156 cards left) leaves 11 Nine-Pip Card cards and adjusts conditional probabilities to 45.8729% Banker, 44.5853% Player, and 9.5418% Tie under 5%.
In six-card resolution tree DEP263 (4D at 25% depth, 156 cards left), when 9s are depleted (dep263-rank-9) late in the shoe, more (156c) hands bypass four-card natural resolution (dep263-rank-9·156c) and enter the five- and six-card tableau; removing 5 of 16 Rank-9 cards (-0.23 bps weight) leaves Banker at -1.0060% EV under 5%.
| Wager / Metric | State DEP263 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP263 Banker (5% Vig) | 45.8729% (-1.0060% EV) | 45.8732% | DEP263 4D 25% (11 Rank-9) |
| DEP263 Player (1:1) | 44.5853% (-1.2876% EV) | 44.5850% | DEP263 156-card 4D stub (0.9347 SD) |
| DEP263 Tie (8:1) | 9.5418% (-14.1239% EV) | 9.5418% | DEP263 Rank-9 (5 out, 11 in) |
Learners auditing DEP263 (4D at 25% depth, 11/16 Rank-9 in 156 stub cards) can verify that 5% house hold (1.0060% Banker, 1.2876% Player, 14.1239% Tie) operates independently of prior Big Road streaks.
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