Removing 2 of 4 Ace (1-Point Pip) (Ace-1) cards at 40% penetration of a 1-deck (52-card) shoe leaves 2 Ace-1 cards inside a 31-card stub (DEP012), producing 45.9604% Banker wins, 44.5239% Player wins, 9.5156% Ties, and a 0.4019% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPPPPBBBBPPBBPB) illustrating derived-road symmetry checks alongside DEP012 (1D Ace-1 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.
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.
40% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).
2 Ace cards valued at 1 modulo-10 point removed from the 1D pack.
Resolved at 45.9604% Banker win rate under 4% settlement.
Resolved at 44.5239% Player win rate with 0.9338 unit standard deviation.
Produces a 14.3594% house hold on the 8-to-1 Tie wager in state DEP012.
Exact conditional enumeration DEP012 for a 1D shoe at 40% depth (31/52 cards undealt) with 2 remaining Ace-1 cards confirms a 0.4019% Banker edge (4% Vig), 1.4365% Player edge, and 14.3594% Tie edge.
Because when fewer aces remain, (dep012-ace-1) player 7 and 8 third-card (31c) transitions from 6 and 7 (dep012-ace-1·31c) occur less often during six-card resolutions, state DEP012 (40% 1D depth, 2 Ace-1 removed, 2 in 31 cards) registers a +0.44 bps rank derivative and 0.4019% Banker house edge (4% Vig).
| Wager / Metric | State DEP012 Value | 1D Baseline | Settlement Note |
|---|---|---|---|
| DEP012 Banker (4% Vig) | 45.9604% (-0.4019% EV) | 45.9595% | DEP012 1D 40% (2 Ace-1) |
| DEP012 Player (1:1) | 44.5239% (-1.4365% EV) | 44.5249% | DEP012 31-card 1D stub (0.9338 SD) |
| DEP012 Tie (8:1) | 9.5156% (-14.3594% EV) | 9.5156% | DEP012 Ace-1 (2 out, 2 in) |
Synthesizing DEP012 (1D at 40% depth, 2 Ace (1-Point Pip) cards left inside 31 stub cards): 4% rules produce a 0.4019% Banker edge, 1.4365% Player edge, 14.3594% Tie edge, and 0.9338 unit volatility.
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