Removing 26 of 32 Seven-Pip Card (Rank-7) cards at 70% penetration of a 8-deck (416-card) shoe leaves 6 Rank-7 cards inside a 125-card stub (DEP429), producing 45.8563% Banker wins, 44.6282% Player wins, 9.5155% Ties, and a 1.0647% Banker house edge under 5%.
Reference shoe scoreboard (BBPPBPBBPPBPBBPPBP) illustrating derived-road symmetry checks alongside DEP429 (8D Rank-7 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.
Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).
Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.
This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.
70% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).
26 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 8D pack.
Resolved at 45.8563% Banker win rate under 5% settlement.
Resolved at 44.6282% Player win rate with 0.9386 unit standard deviation.
Produces a 14.3603% house hold on the 8-to-1 Tie wager in state DEP429.
Across 4,998,398,275,503,360 initial 8D permutations, depletion node DEP429 narrows to a 125-card stub (70% depth) holding 6 of 32 Rank-7 cards, where Banker resolves at 45.8563% (-1.0647% EV) and Player at 44.6282% (-1.2281% EV).
Tableau audit DEP429 confirms that player stands pat on (dep429) two-card 7, and a player (8d-70%) third-card 7 is the highest (dep429·8d-70%) card that forces banker 4, 5, and 6 to draw. Inside the 125-card 8D stub (70% depth, 6/32 Rank-7 remaining, -0.83 bps slope), standard deviation is 0.9386 under 5% Vig.
| Wager / Metric | State DEP429 Value | 8D Baseline | Settlement Note |
|---|---|---|---|
| DEP429 Banker (5% Vig) | 45.8563% (-1.0647% EV) | 45.8597% | DEP429 8D 70% (6 Rank-7) |
| DEP429 Player (1:1) | 44.6282% (-1.2281% EV) | 44.6247% | DEP429 125-card 8D stub (0.9386 SD) |
| DEP429 Tie (8:1) | 9.5155% (-14.3603% EV) | 9.5156% | DEP429 Rank-7 (26 out, 6 in) |
Comparing DEP429 (70% 8D depth, 26 Rank-7 removed, 6 remaining in 125 cards) against fresh-shoe baselines shows how finite-stub variance (0.9386 SD) coexists with a 1.0647% 5% Banker house edge.
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