Removing 7 of 8 Three-Pip (Trey) (Rank-3) cards at 75% penetration of a 2-deck (104-card) shoe leaves 1 Rank-3 cards inside a 26-card stub (DEP124), producing 45.9028% Banker wins, 44.5646% Player wins, 9.5327% Ties, and a 0.4979% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPPPPBBBBPPBBPB) illustrating derived-road symmetry checks alongside DEP124 (2D Rank-3 at 75% 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.
75% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).
7 3-pip cards across all four suits removed from the 2D pack.
Resolved at 45.9028% Banker win rate under 4% settlement.
Resolved at 44.5646% Player win rate with 0.9379 unit standard deviation.
Produces a 14.2058% house hold on the 8-to-1 Tie wager in state DEP124.
Exact conditional enumeration DEP124 for a 2D shoe at 75% depth (26/104 cards undealt) with 1 remaining Rank-3 cards confirms a 0.4979% Banker edge (4% Vig), 1.3382% Player edge, and 14.2058% Tie edge.
Mechanical draw trees in DEP124 reflect how each removed 3-pip card (dep124-rank-3) modifies the boundary between banker (26c) standing on 5 and drawing (dep124-rank-3·26c) against mid-range player pulls. At 75% 2D depth (1 Rank-3 left of 8 in 26 cards, +0.65 bps slope), three-quarters of the shoe (dep124-2d) has been dealt and winning (1/8) banker wagers return 0.96 units (dep124-2d·1/8) net per unit risked.
| Wager / Metric | State DEP124 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP124 Banker (4% Vig) | 45.9028% (-0.4979% EV) | 45.8998% | DEP124 2D 75% (1 Rank-3) |
| DEP124 Player (1:1) | 44.5646% (-1.3382% EV) | 44.5676% | DEP124 26-card 2D stub (0.9379 SD) |
| DEP124 Tie (8:1) | 9.5327% (-14.2058% EV) | 9.5326% | DEP124 Rank-3 (7 out, 1 in) |
Even at 75% penetration in DEP124 where 7 Rank-3 cards have exited a 2D shoe (1 left in 26 cards), derived-road red and blue entries measure structural regularity on the Big Road—not whether Banker (-0.4979% EV, 4% Vig) or Player (-1.3382% EV) is favored next.
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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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