Removing 14 of 16 Three-Pip (Trey) (Rank-3) cards at 75% penetration of a 4-deck (208-card) shoe leaves 2 Rank-3 cards inside a 52-card stub (DEP214), producing 45.8762% Banker wins, 44.5820% Player wins, 9.5419% Ties, and a 0.5408% Banker house edge under 4%.
Reference shoe scoreboard (PPBBBPPPBBPBTBPBPP) illustrating derived-road symmetry checks alongside DEP214 (4D Rank-3 at 75% 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.
75% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
14 3-pip cards across all four suits removed from the 4D pack.
Resolved at 45.8762% Banker win rate under 4% settlement.
Resolved at 44.5820% Player win rate with 0.9379 unit standard deviation.
Produces a 14.1230% house hold on the 8-to-1 Tie wager in state DEP214.
Finite-shoe specification DEP214 tracks Rank-3 removal at 75% depth in 4-deck play: with 2 of 16 Three-Pip (Trey) cards left in the 52-card stub, Tie incidence is 9.5419% and Banker expectation settles at -0.5408% (4% Vig).
Because each removed 3-pip card (dep214-rank-3) modifies the boundary between banker (52c) standing on 5 and drawing (dep214-rank-3·52c) against mid-range player pulls, state DEP214 (75% 4D depth, 14 Rank-3 removed, 2 in 52 cards) registers a +0.65 bps rank derivative and 0.5408% Banker house edge (4% Vig).
| Wager / Metric | State DEP214 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP214 Banker (4% Vig) | 45.8762% (-0.5408% EV) | 45.8732% | DEP214 4D 75% (2 Rank-3) |
| DEP214 Player (1:1) | 44.5820% (-1.2942% EV) | 44.5850% | DEP214 52-card 4D stub (0.9379 SD) |
| DEP214 Tie (8:1) | 9.5419% (-14.1230% EV) | 9.5418% | DEP214 Rank-3 (14 out, 2 in) |
In DEP214, the 52-card 4D stub (75% penetration, 14 of 16 Rank-3 dealt) yields 45.8762% Banker, 44.5820% Player, and 9.5419% Tie outcomes with 0.9379 dispersion under 4% Vig.
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