Removing 1 of 4 Seven-Pip Card (Rank-7) cards at 25% penetration of a 1-deck (52-card) shoe leaves 3 Rank-7 cards inside a 39-card stub (DEP065), producing 45.9587% Banker wins, 44.5257% Player wins, 9.5156% Ties, and a 0.8650% Banker house edge under 5%.
Reference shoe scoreboard (BBPPBBPPBPTBPBBPBP) illustrating derived-road symmetry checks alongside DEP065 (1D Rank-7 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 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.
25% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).
1 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 1D pack.
Resolved at 45.9587% Banker win rate under 5% settlement.
Resolved at 44.5257% Player win rate with 0.9341 unit standard deviation.
Produces a 14.3598% house hold on the 8-to-1 Tie wager in state DEP065.
Across 14,658,134,400 initial 1D permutations, depletion node DEP065 narrows to a 39-card stub (25% depth) holding 3 of 4 Rank-7 cards, where Banker resolves at 45.9587% (-0.8650% EV) and Player at 44.5257% (-1.4330% EV).
For DEP065 (1-deck shoe, 25% dealt), player stands pat on (dep065) two-card 7, and a player (1d-25%) third-card 7 is the highest (dep065·1d-25%) card that forces banker 4, 5, and 6 to draw. Holding 3 of 4 Rank-7 cards in a 39-card stub with -0.83 bps rank slope yields 45.9587% Banker, 44.5257% Player, and 9.5156% Tie.
| Wager / Metric | State DEP065 Value | 1D Baseline | Settlement Note |
|---|---|---|---|
| DEP065 Banker (5% Vig) | 45.9587% (-0.8650% EV) | 45.9595% | DEP065 1D 25% (3 Rank-7) |
| DEP065 Player (1:1) | 44.5257% (-1.4330% EV) | 44.5249% | DEP065 39-card 1D stub (0.9341 SD) |
| DEP065 Tie (8:1) | 9.5156% (-14.3598% EV) | 9.5156% | DEP065 Rank-7 (1 out, 3 in) |
Comparing DEP065 (25% 1D depth, 1 Rank-7 removed, 3 remaining in 39 cards) against fresh-shoe baselines shows how finite-stub variance (0.9341 SD) coexists with a 0.8650% 5% Banker house edge.
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