Removing 7 of 8 Three-Pip (Trey) (Rank-3) cards at 85% penetration of a 2-deck (104-card) shoe leaves 1 Rank-3 cards inside a 16-card stub (DEP126), producing 45.9029% Banker wins, 44.5644% Player wins, 9.5327% Ties, and a 0.9149% Banker house edge under EZ Baccarat.
Reference shoe scoreboard (PPBBPBPPBBPBPPBBPB) illustrating derived-road symmetry checks alongside DEP126 (2D Rank-3 at 85% 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.
85% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).
7 3-pip cards across all four suits removed from the 2D pack.
Resolved at 45.9029% Banker win rate under EZ Baccarat settlement.
Resolved at 44.5644% Player win rate with 0.9389 unit standard deviation.
Produces a 14.2057% house hold on the 8-to-1 Tie wager in state DEP126.
Quantitative proof DEP126 documents 2D rank depletion at 85% depth: 7 exited Rank-3 cards leave 1 of 8 in the 16-card stub, generating 45.9029% Banker wins (-0.9149% EV under EZ Bar-7) and 44.5644% Player wins.
When 7 Rank-3 cards exit a 2D shoe by 85% penetration (DEP126, 1 left in 16 cards), each removed 3-pip card (dep126-rank-3) modifies the boundary between banker (16c) standing on 5 and drawing (dep126-rank-3·16c) against mid-range player pulls, combining a +0.65 bps rank vector with EZ Baccarat settlement (-0.9149% Banker EV).
| Wager / Metric | State DEP126 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP126 Banker (EZ Bar-7) | 45.9029% (-0.9149% EV) | 45.8998% | DEP126 2D 85% (1 Rank-3) |
| DEP126 Player (1:1) | 44.5644% (-1.3385% EV) | 44.5676% | DEP126 16-card 2D stub (0.9389 SD) |
| DEP126 Tie (8:1) | 9.5327% (-14.2057% EV) | 9.5326% | DEP126 Rank-3 (7 out, 1 in) |
Cut-card protocol at 85% depth in DEP126 (2D, 16 stub cards containing 1 Rank-3 cards) ensures the shoe reshuffles long before EZ Baccarat house hold (0.9149% Banker / 1.3385% Player) is overturned.
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