Removing 1 of 8 Nine-Pip Card (Rank-9) cards at 10% penetration of a 2-deck (104-card) shoe leaves 7 Rank-9 cards inside a 94-card stub (DEP172), producing 45.8997% Banker wins, 44.5677% Player wins, 9.5326% Ties, and a 0.9630% Banker house edge under 5%.
Reference shoe scoreboard (PPBBPPPPBBBBPPBBPB) illustrating derived-road symmetry checks alongside DEP172 (2D Rank-9 at 10% 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.
This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.
This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.
10% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).
1 9-pip cards (top Natural 9 generator) removed from the 2D pack.
Resolved at 45.8997% Banker win rate under 5% settlement.
Resolved at 44.5677% Player win rate with 0.9332 unit standard deviation.
Produces a 14.2066% house hold on the 8-to-1 Tie wager in state DEP172.
Finite-shoe specification DEP172 tracks Rank-9 removal at 10% depth in 2-deck play: with 7 of 8 Nine-Pip Card cards left in the 94-card stub, Tie incidence is 9.5326% and Banker expectation settles at -0.9630% (5% Vig).
Because when 9s are depleted (dep172-rank-9) late in the shoe, more (94c) hands bypass four-card natural resolution (dep172-rank-9·94c) and enter the five- and six-card tableau, state DEP172 (10% 2D depth, 1 Rank-9 removed, 7 in 94 cards) registers a -0.23 bps rank derivative and 0.9630% Banker house edge (5% Vig).
| Wager / Metric | State DEP172 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP172 Banker (5% Vig) | 45.8997% (-0.9630% EV) | 45.8998% | DEP172 2D 10% (7 Rank-9) |
| DEP172 Player (1:1) | 44.5677% (-1.3320% EV) | 44.5676% | DEP172 94-card 2D stub (0.9332 SD) |
| DEP172 Tie (8:1) | 9.5326% (-14.2066% EV) | 9.5326% | DEP172 Rank-9 (1 out, 7 in) |
Cut-card protocol at 10% depth in DEP172 (2D, 94 stub cards containing 7 Rank-9 cards) ensures the shoe reshuffles long before 5% house hold (0.9630% Banker / 1.3320% Player) is overturned.
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