Removing 1 of 8 Ace (1-Point Pip) (Ace-1) cards at 10% penetration of a 2-deck (104-card) shoe leaves 7 Ace-1 cards inside a 94-card stub (DEP100), producing 45.9000% Banker wins, 44.5674% Player wins, 9.5326% Ties, and a 0.9624% Banker house edge under 5%.
Reference shoe scoreboard (PPBBPBPBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP100 (2D Ace-1 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.
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.
Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).
Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.
10% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).
1 Ace cards valued at 1 modulo-10 point removed from the 2D pack.
Resolved at 45.9000% Banker win rate under 5% settlement.
Resolved at 44.5674% Player win rate with 0.9308 unit standard deviation.
Produces a 14.2066% house hold on the 8-to-1 Tie wager in state DEP100.
In combinatorial record DEP100, depleting 1 Ace-1 cards across 10% of a 2D (104-card) pack leaves 7 Ace (1-Point Pip) cards among 94 remaining cards, setting Banker win probability to 45.9000% and house edge to 0.9624% (5% Vig).
Combinatorial weighting in DEP100 (94 cards left from 104 at 10% depth) is governed by two rules: removing aces slightly favors (dep100) banker because banker stands on (2d-10%) 6 against player third-card ace (dep100·2d-10%) while player must draw on 0–5, and winning banker tickets pay (dep100-2d) 0.95 units per unit staked (7/8) while 90% of the initial (dep100-2d·7/8) shoe remains undealt (+0.44 bps per Ace-1 removed).
| Wager / Metric | State DEP100 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP100 Banker (5% Vig) | 45.9000% (-0.9624% EV) | 45.8998% | DEP100 2D 10% (7 Ace-1) |
| DEP100 Player (1:1) | 44.5674% (-1.3326% EV) | 44.5676% | DEP100 94-card 2D stub (0.9308 SD) |
| DEP100 Tie (8:1) | 9.5326% (-14.2066% EV) | 9.5326% | DEP100 Ace-1 (1 out, 7 in) |
In DEP100, the 94-card 2D stub (10% penetration, 1 of 8 Ace-1 dealt) yields 45.9000% Banker, 44.5674% Player, and 9.5326% Tie outcomes with 0.9308 dispersion under 5% Vig.
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