Removing 7 of 16 Nine-Pip Card (Rank-9) cards at 40% penetration of a 4-deck (208-card) shoe leaves 9 Rank-9 cards inside a 125-card stub (DEP264), producing 45.8728% Banker wins, 44.5854% Player wins, 9.5418% Ties, and a 0.5476% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPPBPBPBBPPBBPB) illustrating derived-road symmetry checks alongside DEP264 (4D Rank-9 at 40% 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.
40% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
7 9-pip cards (top Natural 9 generator) removed from the 4D pack.
Resolved at 45.8728% Banker win rate under 4% settlement.
Resolved at 44.5854% Player win rate with 0.9362 unit standard deviation.
Produces a 14.1240% house hold on the 8-to-1 Tie wager in state DEP264.
Exact conditional enumeration DEP264 for a 4D shoe at 40% depth (125/208 cards undealt) with 9 remaining Rank-9 cards confirms a 0.5476% Banker edge (4% Vig), 1.2873% Player edge, and 14.1240% Tie edge.
Rank 9 paired with (DEP264) any ten or face card (4D-40%) creates an unbeatable two-card Natural (DEP264·4D-40%) 9 that halts all third-card drawing on both sides. In state DEP264 (4D, 40% depth), each removed Rank-9 card applies a -0.23 bps baseline directional pressure before scaling to the 125-card remainder (9 Rank-9 left), while Winning Banker wagers collect (DEP264-4D) 0.96 units per unit staked (9/16) with 60% of the shoe (DEP264-4D·9/16) still inside the acrylic carrier.
| Wager / Metric | State DEP264 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP264 Banker (4% Vig) | 45.8728% (-0.5476% EV) | 45.8732% | DEP264 4D 40% (9 Rank-9) |
| DEP264 Player (1:1) | 44.5854% (-1.2873% EV) | 44.5850% | DEP264 125-card 4D stub (0.9362 SD) |
| DEP264 Tie (8:1) | 9.5418% (-14.1240% EV) | 9.5418% | DEP264 Rank-9 (7 out, 9 in) |
Across 100-hand session horizons at state DEP264 (4D 40% depth, 9/16 Rank-9 in 125 cards), single-hand dispersion (0.9362 SD) dominates the 0.5476% (4% Vig) Banker and 1.2873% Player expectation gap.
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About 64 minutes of lessons covering outcomes, the Bead Plate, Big Road columns, and dragon tails.
Train Third-Card Rule decisions, depth counting, lookback column references, and derived-road speed recognition.
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Direct answers to real student questions on dragon tails, tie handling, lookback rules, and table variants.
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