Removing 5 of 16 Three-Pip (Trey) (Rank-3) cards at 25% penetration of a 4-deck (208-card) shoe leaves 11 Rank-3 cards inside a 156-card stub (DEP209), producing 45.8740% Banker wins, 44.5842% Player wins, 9.5418% Ties, and a 1.0039% Banker house edge under 5%.
Reference shoe scoreboard (BBPPBBPPBPTBPBBPBP) illustrating derived-road symmetry checks alongside DEP209 (4D Rank-3 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 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.
25% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
5 3-pip cards across all four suits removed from the 4D pack.
Resolved at 45.8740% Banker win rate under 5% settlement.
Resolved at 44.5842% Player win rate with 0.9329 unit standard deviation.
Produces a 14.1236% house hold on the 8-to-1 Tie wager in state DEP209.
Shoe-stub analysis DEP209 inspects 156 remaining cards at 25% penetration of a 208-card (4D) pack after 5 Three-Pip (Trey) cards have cleared, leaving 11 Rank-3 cards and a 1.0039% 5% Banker edge.
In 4D audit DEP209 (156/208 stub at 25% depth), each removed 3-pip card (dep209-rank-3) modifies the boundary between banker (156c) standing on 5 and drawing (dep209-rank-3·156c) against mid-range player pulls. Removing 5 Rank-3 cards (+0.65 bps per card) alongside 5% Vig rules sets Tie hold to 14.1236% (9.5418% frequency).
| Wager / Metric | State DEP209 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP209 Banker (5% Vig) | 45.8740% (-1.0039% EV) | 45.8732% | DEP209 4D 25% (11 Rank-3) |
| DEP209 Player (1:1) | 44.5842% (-1.2898% EV) | 44.5850% | DEP209 156-card 4D stub (0.9329 SD) |
| DEP209 Tie (8:1) | 9.5418% (-14.1236% EV) | 9.5418% | DEP209 Rank-3 (5 out, 11 in) |
Comparing DEP209 (25% 4D depth, 5 Rank-3 removed, 11 remaining in 156 cards) against fresh-shoe baselines shows how finite-stub variance (0.9329 SD) coexists with a 1.0039% 5% Banker house edge.
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