Removing 4 of 8 Nine-Pip Card (Rank-9) cards at 40% penetration of a 2-deck (104-card) shoe leaves 4 Rank-9 cards inside a 62-card stub (DEP174), producing 45.8993% Banker wins, 44.5681% Player wins, 9.5326% Ties, and a 0.5048% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPBPPBBPBPPBBPB) illustrating derived-road symmetry checks alongside DEP174 (2D Rank-9 at 40% 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.
40% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).
4 9-pip cards (top Natural 9 generator) removed from the 2D pack.
Resolved at 45.8993% Banker win rate under 4% settlement.
Resolved at 44.5681% Player win rate with 0.9362 unit standard deviation.
Produces a 14.2068% house hold on the 8-to-1 Tie wager in state DEP174.
Under 4% settlement (4% Vig), combinatorial state DEP174 models a 2D carrier with 62 cards left (40% dealt) and 4/8 Nine-Pip Card cards remaining, producing a 0.5048% Banker edge versus 1.3312% on Player.
In six-card resolution tree DEP174 (2D at 40% depth, 62 cards left), when 9s are depleted (dep174-rank-9) late in the shoe, more (62c) hands bypass four-card natural resolution (dep174-rank-9·62c) and enter the five- and six-card tableau; removing 4 of 8 Rank-9 cards (-0.23 bps weight) leaves Banker at -0.5048% EV under 4%.
| Wager / Metric | State DEP174 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP174 Banker (4% Vig) | 45.8993% (-0.5048% EV) | 45.8998% | DEP174 2D 40% (4 Rank-9) |
| DEP174 Player (1:1) | 44.5681% (-1.3312% EV) | 44.5676% | DEP174 62-card 2D stub (0.9362 SD) |
| DEP174 Tie (8:1) | 9.5326% (-14.2068% EV) | 9.5326% | DEP174 Rank-9 (4 out, 4 in) |
Whether DEP174 is observed in double-deck European salon privé carriers and two-deck shoe pits at 40% depth (62/104 cards left, 4 Rank-9 remaining), 4% Vig settlement locks Banker EV at -0.5048% and Player EV at -1.3312% with 9.5326% Ties.
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