Removing 13 of 16 Nine-Pip Card (Rank-9) cards at 70% penetration of a 4-deck (208-card) shoe leaves 3 Rank-9 cards inside a 62-card stub (DEP267), producing 45.8723% Banker wins, 44.5860% Player wins, 9.5418% Ties, and a 1.0073% Banker house edge under 5%.
Reference shoe scoreboard (BBPPBBBBPPPPBBPPBP) illustrating derived-road symmetry checks alongside DEP267 (4D Rank-9 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.
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.
70% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
13 9-pip cards (top Natural 9 generator) removed from the 4D pack.
Resolved at 45.8723% Banker win rate under 5% settlement.
Resolved at 44.5860% Player win rate with 0.9392 unit standard deviation.
Produces a 14.1242% house hold on the 8-to-1 Tie wager in state DEP267.
Audit DEP267 evaluates a 4-deck (208-card) shoe at 70% penetration where 13 of 16 Nine-Pip Card cards have exited, leaving 3 Rank-9 cards inside the 62-card stub with Banker EV at -1.0073% under 5%.
For DEP267 (4-deck shoe, 70% dealt), rank 9 paired with (dep267) any ten or face card (4d-70%) creates an unbeatable two-card natural (dep267·4d-70%) 9 that halts all third-card drawing on both sides. Holding 3 of 16 Rank-9 cards in a 62-card stub with -0.23 bps rank slope yields 45.8723% Banker, 44.5860% Player, and 9.5418% Tie.
| Wager / Metric | State DEP267 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP267 Banker (5% Vig) | 45.8723% (-1.0073% EV) | 45.8732% | DEP267 4D 70% (3 Rank-9) |
| DEP267 Player (1:1) | 44.5860% (-1.2863% EV) | 44.5850% | DEP267 62-card 4D stub (0.9392 SD) |
| DEP267 Tie (8:1) | 9.5418% (-14.1242% EV) | 9.5418% | DEP267 Rank-9 (13 out, 3 in) |
In studio and floor audits of DEP267 (62 cards undealt out of 208 in 4D at 70% depth), a 0.9392 unit standard deviation accompanies the 3-card Rank-9 stub under 5% Vig (45.8723% Banker vs 44.5860% Player).
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