Removing 2 of 4 Three-Pip (Trey) (Rank-3) cards at 50% penetration of a 1-deck (52-card) shoe leaves 2 Rank-3 cards inside a 26-card stub (DEP031), producing 45.9610% Banker wins, 44.5234% Player wins, 9.5156% Ties, and a 1.2554% Banker house edge under Super 6.
Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP031 (1D Rank-3 at 50% 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 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.
50% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).
2 3-pip cards across all four suits removed from the 1D pack.
Resolved at 45.9610% Banker win rate under Super 6 settlement.
Resolved at 44.5234% Player win rate with 0.9354 unit standard deviation.
Produces a 14.3592% house hold on the 8-to-1 Tie wager in state DEP031.
When a 1D shoe reaches 50% cut-card depth (26 of 52 cards undealt, state DEP031) with 2 Three-Pip (Trey) cards removed and 2 remaining, Player wins 44.5234% (1.4376% edge) while Banker wins 45.9610% (1.2554% edge under Super 6).
Combinatorial weighting in DEP031 (26 cards left from 52 at 50% depth) is governed by two rules: banker total 4 draws (dep031) on player third-card 3, and (1d-50%) banker total 5 stands on (dep031·1d-50%) player third-card 3, creating asymmetric sensitivity, and banker wins on totals (dep031-1d) 1–5 and 7–9 pay 1:1 (2/4) while any winning 2-card or (dep031-1d·2/4) 3-card banker 6 pays 50 cents on the dollar (+0.65 bps per Rank-3 removed).
| Wager / Metric | State DEP031 Value | 1D Baseline | Settlement Note |
|---|---|---|---|
| DEP031 Banker (Super 6) | 45.9610% (-1.2554% EV) | 45.9595% | DEP031 1D 50% (2 Rank-3) |
| DEP031 Player (1:1) | 44.5234% (-1.4376% EV) | 44.5249% | DEP031 26-card 1D stub (0.9354 SD) |
| DEP031 Tie (8:1) | 9.5156% (-14.3592% EV) | 9.5156% | DEP031 Rank-3 (2 out, 2 in) |
On the electronic scoreboard for DEP031 (1D, 50% depth, 26 cards left), Bead Plate and Big Road circles record Banker (45.9610%) and Player (44.5234%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Rank-3 card counts (2/4).
Enter any sequence to inspect the Big Road, Big Eye Boy, Small Road, Cockroach Pig, and next-hand previews.
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.
Visual step-by-step breakdowns with closed captions, chapter markers, and full searchable transcripts.
Macau Cantonese, French, and mathematical table terms explained in plain English with road diagrams.
Direct answers to real student questions on dragon tails, tie handling, lookback rules, and table variants.
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