Removing 13 of 16 Five-Pip Card (Rank-5) cards at 70% penetration of a 4-deck (208-card) shoe leaves 3 Rank-5 cards inside a 62-card stub (DEP231), producing 45.8697% Banker wins, 44.5885% Player wins, 9.5417% Ties, and a 1.0123% Banker house edge under 5%.
Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP231 (4D Rank-5 at 70% 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.
70% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
13 5-pip cards (final mandatory Player draw threshold) removed from the 4D pack.
Resolved at 45.8697% Banker win rate under 5% settlement.
Resolved at 44.5885% Player win rate with 0.9380 unit standard deviation.
Produces a 14.1245% house hold on the 8-to-1 Tie wager in state DEP231.
Card-removal benchmark DEP231 measures Five-Pip Card (Rank-5) scarcity at 70% depth in a 4-deck shoe: 13 removed ranks leave 3 in the 62-card remainder, shifting Banker win share to 45.8697% (1.0123% edge, 5% Vig).
In 4D audit DEP231 (62/208 stub at 70% depth), fewer 5s in the (dep231-rank-5) stub reduce banker third-card improvements (62c) from 3 to 8 and (dep231-rank-5·62c) from 4 to 9. Removing 13 Rank-5 cards (-0.84 bps per card) alongside 5% Vig rules sets Tie hold to 14.1245% (9.5417% frequency).
| Wager / Metric | State DEP231 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP231 Banker (5% Vig) | 45.8697% (-1.0123% EV) | 45.8732% | DEP231 4D 70% (3 Rank-5) |
| DEP231 Player (1:1) | 44.5885% (-1.2812% EV) | 44.5850% | DEP231 62-card 4D stub (0.9380 SD) |
| DEP231 Tie (8:1) | 9.5417% (-14.1245% EV) | 9.5418% | DEP231 Rank-5 (13 out, 3 in) |
Statistical verification of DEP231 (4D, 70% penetration, 3 Five-Pip Card cards in 62 stub cards) demonstrates why single-rank depletion (13 Rank-5 dealt) shifts edges by basis points around -1.0123% (5% Vig).
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