Removing 3 of 4 Four-Pip Card (Rank-4) cards at 85% penetration of a 1-deck (52-card) shoe leaves 1 Rank-4 cards inside a 8-card stub (DEP045), producing 45.9644% Banker wins, 44.5199% Player wins, 9.5157% Ties, and a 0.8090% Banker house edge under EZ Baccarat.
Reference shoe scoreboard (BBPPBPBBPPBPBBPPBP) illustrating derived-road symmetry checks alongside DEP045 (1D Rank-4 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 1D (single-deck laboratory benchmarks and historical pitch audits).
3 4-pip cards (strongest pro-Banker removal sensitivity) removed from the 1D pack.
Resolved at 45.9644% Banker win rate under EZ Baccarat settlement.
Resolved at 44.5199% Player win rate with 0.9392 unit standard deviation.
Produces a 14.3589% house hold on the 8-to-1 Tie wager in state DEP045.
When a 1D shoe reaches 85% cut-card depth (8 of 52 cards undealt, state DEP045) with 3 Four-Pip Card cards removed and 1 remaining, Player wins 44.5199% (1.4444% edge) while Banker wins 45.9644% (0.8090% edge under EZ Baccarat).
Because removing 4s produces the (dep045-rank-4) single largest per-card shift toward (8c) banker (and away from player) (dep045-rank-4·8c) of any rank in the shoe, state DEP045 (85% 1D depth, 3 Rank-4 removed, 1 in 8 cards) registers a +1.19 bps rank derivative and 0.8090% Banker house edge (EZ Bar-7).
| Wager / Metric | State DEP045 Value | 1D Baseline | Settlement Note |
|---|---|---|---|
| DEP045 Banker (EZ Bar-7) | 45.9644% (-0.8090% EV) | 45.9595% | DEP045 1D 85% (1 Rank-4) |
| DEP045 Player (1:1) | 44.5199% (-1.4444% EV) | 44.5249% | DEP045 8-card 1D stub (0.9392 SD) |
| DEP045 Tie (8:1) | 9.5157% (-14.3589% EV) | 9.5156% | DEP045 Rank-4 (3 out, 1 in) |
Across 100-hand session horizons at state DEP045 (1D 85% depth, 1/4 Rank-4 in 8 cards), single-hand dispersion (0.9392 SD) dominates the 0.8090% (EZ Bar-7) Banker and 1.4444% Player expectation gap.
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