Removing 28 of 32 Nine-Pip Card (Rank-9) cards at 75% penetration of a 8-deck (416-card) shoe leaves 4 Rank-9 cards inside a 104-card stub (DEP448), producing 45.8587% Banker wins, 44.6258% Player wins, 9.5156% Ties, and a 0.6015% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPPBBPPBBPBTBPB) illustrating derived-road symmetry checks alongside DEP448 (8D Rank-9 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.
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.
75% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).
28 9-pip cards (top Natural 9 generator) removed from the 8D pack.
Resolved at 45.8587% Banker win rate under 4% settlement.
Resolved at 44.6258% Player win rate with 0.9397 unit standard deviation.
Produces a 14.3600% house hold on the 8-to-1 Tie wager in state DEP448.
Quantitative proof DEP448 documents 8D rank depletion at 75% depth: 28 exited Rank-9 cards leave 4 of 32 in the 104-card stub, generating 45.8587% Banker wins (-0.6015% EV under 4% Vig) and 44.6258% Player wins.
Why does Rank-9 carry a -0.23 bps per-card effect in DEP448? Rank 9 paired with (DEP448) any ten or face card (8D-75%) creates an unbeatable two-card Natural (DEP448·8D-75%) 9 that halts all third-card drawing on both sides, and at 75% penetration (4 Nine-Pip Card cards left in 104 8D cards), three-quarters of the shoe (dep448-8d) has been dealt and winning (4/32) banker wagers return 0.96 units (dep448-8d·4/32) net per unit risked.
| Wager / Metric | State DEP448 Value | 8D Baseline | Settlement Note |
|---|---|---|---|
| DEP448 Banker (4% Vig) | 45.8587% (-0.6015% EV) | 45.8597% | DEP448 8D 75% (4 Rank-9) |
| DEP448 Player (1:1) | 44.6258% (-1.2329% EV) | 44.6247% | DEP448 104-card 8D stub (0.9397 SD) |
| DEP448 Tie (8:1) | 9.5156% (-14.3600% EV) | 9.5156% | DEP448 Rank-9 (28 out, 4 in) |
In DEP448, the 104-card 8D stub (75% penetration, 28 of 32 Rank-9 dealt) yields 45.8587% Banker, 44.6258% Player, and 9.5156% Tie outcomes with 0.9397 dispersion under 4% Vig.
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