Removing 21 of 24 Ace (1-Point Pip) (Ace-1) cards at 75% penetration of a 6-deck (312-card) shoe leaves 3 Ace-1 cards inside a 78-card stub (DEP286), producing 45.8668% Banker wins, 44.5883% Player wins, 9.5449% Ties, and a 0.5561% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPBPPBBPBPPBBPB) illustrating derived-road symmetry checks alongside DEP286 (6D Ace-1 at 75% 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.
75% penetration depth in 6D (six-deck Mini-Baccarat and Midi-Baccarat North American floors).
21 Ace cards valued at 1 modulo-10 point removed from the 6D pack.
Resolved at 45.8668% Banker win rate under 4% settlement.
Resolved at 44.5883% Player win rate with 0.9373 unit standard deviation.
Produces a 14.0955% house hold on the 8-to-1 Tie wager in state DEP286.
Under 4% settlement (4% Vig), combinatorial state DEP286 models a 6D carrier with 78 cards left (75% dealt) and 3/24 Ace (1-Point Pip) cards remaining, producing a 0.5561% Banker edge versus 1.2785% on Player.
Removing Aces slightly favors (DEP286) Banker because Banker stands on (6D-75%) 6 against Player third-card Ace (DEP286·6D-75%) while Player must draw on 0–5. In state DEP286 (6D, 75% depth), each removed Ace-1 card applies a +0.44 bps baseline directional pressure before scaling to the 78-card remainder (3 Ace-1 left), while Three-quarters of the shoe (DEP286-6D) has been dealt and winning (3/24) Banker wagers return 0.96 units (DEP286-6D·3/24) net per unit risked.
| Wager / Metric | State DEP286 Value | 6D Baseline | Settlement Note |
|---|---|---|---|
| DEP286 Banker (4% Vig) | 45.8668% (-0.5561% EV) | 45.8648% | DEP286 6D 75% (3 Ace-1) |
| DEP286 Player (1:1) | 44.5883% (-1.2785% EV) | 44.5903% | DEP286 78-card 6D stub (0.9373 SD) |
| DEP286 Tie (8:1) | 9.5449% (-14.0955% EV) | 9.5449% | DEP286 Ace-1 (21 out, 3 in) |
Cut-card protocol at 75% depth in DEP286 (6D, 78 stub cards containing 3 Ace-1 cards) ensures the shoe reshuffles long before 4% house hold (0.5561% Banker / 1.2785% Player) is overturned.
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