Removing 7 of 8 Nine-Pip Card (Rank-9) cards at 75% penetration of a 2-deck (104-card) shoe leaves 1 Rank-9 cards inside a 26-card stub (DEP178), producing 45.8988% Banker wins, 44.5687% Player wins, 9.5326% Ties, and a 0.5059% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPPBBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP178 (2D 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 2D (double-deck European salon privé carriers and two-deck shoe pits).
7 9-pip cards (top Natural 9 generator) removed from the 2D pack.
Resolved at 45.8988% Banker win rate under 4% settlement.
Resolved at 44.5687% Player win rate with 0.9397 unit standard deviation.
Produces a 14.2070% house hold on the 8-to-1 Tie wager in state DEP178.
Depletion matrix entry DEP178 pairs 2D (104 cards) at 75% penetration with 7 removed Nine-Pip Card cards (1 left in 26 cards), fixing per-hand volatility at 0.9397 and Banker house hold at 0.5059% (4% Vig).
In 2D audit DEP178 (26/104 stub at 75% depth), when 9s are depleted (dep178-rank-9) late in the shoe, more (26c) hands bypass four-card natural resolution (dep178-rank-9·26c) and enter the five- and six-card tableau. Removing 7 Rank-9 cards (-0.23 bps per card) alongside 4% Vig rules sets Tie hold to 14.2070% (9.5326% frequency).
| Wager / Metric | State DEP178 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP178 Banker (4% Vig) | 45.8988% (-0.5059% EV) | 45.8998% | DEP178 2D 75% (1 Rank-9) |
| DEP178 Player (1:1) | 44.5687% (-1.3301% EV) | 44.5676% | DEP178 26-card 2D stub (0.9397 SD) |
| DEP178 Tie (8:1) | 9.5326% (-14.2070% EV) | 9.5326% | DEP178 Rank-9 (7 out, 1 in) |
Synthesizing DEP178 (2D at 75% depth, 1 Nine-Pip Card cards left inside 26 stub cards): 4% rules produce a 0.5059% Banker edge, 1.3301% Player edge, 14.2070% Tie edge, and 0.9397 unit volatility.
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