Removing 4 of 8 Ace (1-Point Pip) (Ace-1) cards at 40% penetration of a 2-deck (104-card) shoe leaves 4 Ace-1 cards inside a 62-card stub (DEP102), producing 45.9007% Banker wins, 44.5666% Player wins, 9.5326% Ties, and a 0.5019% Banker house edge under 4%.
Reference shoe scoreboard (PPBBBPPPBBPBTBPBPP) illustrating derived-road symmetry checks alongside DEP102 (2D Ace-1 at 40% depth).
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.
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.
40% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).
4 Ace cards valued at 1 modulo-10 point removed from the 2D pack.
Resolved at 45.9007% Banker win rate under 4% settlement.
Resolved at 44.5666% Player win rate with 0.9338 unit standard deviation.
Produces a 14.2064% house hold on the 8-to-1 Tie wager in state DEP102.
Finite-shoe specification DEP102 tracks Ace-1 removal at 40% depth in 2-deck play: with 4 of 8 Ace (1-Point Pip) cards left in the 62-card stub, Tie incidence is 9.5326% and Banker expectation settles at -0.5019% (4% Vig).
Tableau audit DEP102 confirms that removing aces slightly favors (dep102) banker because banker stands on (2d-40%) 6 against player third-card ace (dep102·2d-40%) while player must draw on 0–5. Inside the 62-card 2D stub (40% depth, 4/8 Ace-1 remaining, +0.44 bps slope), standard deviation is 0.9338 under 4% Vig.
| Wager / Metric | State DEP102 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP102 Banker (4% Vig) | 45.9007% (-0.5019% EV) | 45.8998% | DEP102 2D 40% (4 Ace-1) |
| DEP102 Player (1:1) | 44.5666% (-1.3341% EV) | 44.5676% | DEP102 62-card 2D stub (0.9338 SD) |
| DEP102 Tie (8:1) | 9.5326% (-14.2064% EV) | 9.5326% | DEP102 Ace-1 (4 out, 4 in) |
Statistical verification of DEP102 (2D, 40% penetration, 4 Ace (1-Point Pip) cards in 62 stub cards) demonstrates why single-rank depletion (4 Ace-1 dealt) shifts edges by basis points around -0.5019% (4% Vig).
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