Removing 13 of 16 Three-Pip (Trey) (Rank-3) cards at 70% penetration of a 4-deck (208-card) shoe leaves 3 Rank-3 cards inside a 62-card stub (DEP213), producing 45.8759% Banker wins, 44.5822% Player wins, 9.5419% Ties, and a 1.0002% Banker house edge under 5%.
Reference shoe scoreboard (BBPPPBBBPPBPTBPBBP) illustrating derived-road symmetry checks alongside DEP213 (4D Rank-3 at 70% 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.
70% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
13 3-pip cards across all four suits removed from the 4D pack.
Resolved at 45.8759% Banker win rate under 5% settlement.
Resolved at 44.5822% Player win rate with 0.9374 unit standard deviation.
Produces a 14.1231% house hold on the 8-to-1 Tie wager in state DEP213.
When a 4D shoe reaches 70% cut-card depth (62 of 208 cards undealt, state DEP213) with 13 Three-Pip (Trey) cards removed and 3 remaining, Player wins 44.5822% (1.2936% edge) while Banker wins 45.8759% (1.0002% edge under 5%).
Tableau audit DEP213 confirms that banker total 4 draws (dep213) on player third-card 3, and (4d-70%) banker total 5 stands on (dep213·4d-70%) player third-card 3, creating asymmetric sensitivity. Inside the 62-card 4D stub (70% depth, 3/16 Rank-3 remaining, +0.65 bps slope), standard deviation is 0.9374 under 5% Vig.
| Wager / Metric | State DEP213 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP213 Banker (5% Vig) | 45.8759% (-1.0002% EV) | 45.8732% | DEP213 4D 70% (3 Rank-3) |
| DEP213 Player (1:1) | 44.5822% (-1.2936% EV) | 44.5850% | DEP213 62-card 4D stub (0.9374 SD) |
| DEP213 Tie (8:1) | 9.5419% (-14.1231% EV) | 9.5418% | DEP213 Rank-3 (13 out, 3 in) |
Whether DEP213 is observed in four-deck Asian VIP salons and compact automatic shuffler shoes at 70% depth (62/208 cards left, 3 Rank-3 remaining), 5% Vig settlement locks Banker EV at -1.0002% and Player EV at -1.2936% with 9.5419% Ties.
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