Removing 9 of 32 Five-Pip Card (Rank-5) cards at 25% penetration of a 8-deck (416-card) shoe leaves 23 Rank-5 cards inside a 312-card stub (DEP407), producing 45.8588% Banker wins, 44.6256% Player wins, 9.5156% Ties, and a 1.0598% Banker house edge under 5%.
Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP407 (8D Rank-5 at 25% 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.
25% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).
9 5-pip cards (final mandatory Player draw threshold) removed from the 8D pack.
Resolved at 45.8588% Banker win rate under 5% settlement.
Resolved at 44.6256% Player win rate with 0.9335 unit standard deviation.
Produces a 14.3598% house hold on the 8-to-1 Tie wager in state DEP407.
Audit DEP407 evaluates a 8-deck (416-card) shoe at 25% penetration where 9 of 32 Five-Pip Card cards have exited, leaving 23 Rank-5 cards inside the 312-card stub with Banker EV at -1.0598% under 5%.
In six-card resolution tree DEP407 (8D at 25% depth, 312 cards left), fewer 5s in the (dep407-rank-5) stub reduce banker third-card improvements (312c) from 3 to 8 and (dep407-rank-5·312c) from 4 to 9; removing 9 of 32 Rank-5 cards (-0.84 bps weight) leaves Banker at -1.0598% EV under 5%.
| Wager / Metric | State DEP407 Value | 8D Baseline | Settlement Note |
|---|---|---|---|
| DEP407 Banker (5% Vig) | 45.8588% (-1.0598% EV) | 45.8597% | DEP407 8D 25% (23 Rank-5) |
| DEP407 Player (1:1) | 44.6256% (-1.2332% EV) | 44.6247% | DEP407 312-card 8D stub (0.9335 SD) |
| DEP407 Tie (8:1) | 9.5156% (-14.3598% EV) | 9.5156% | DEP407 Rank-5 (9 out, 23 in) |
Synthesizing DEP407 (8D at 25% depth, 23 Five-Pip Card cards left inside 312 stub cards): 5% rules produce a 1.0598% Banker edge, 1.2332% Player edge, 14.3598% Tie edge, and 0.9335 unit volatility.
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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.
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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