Removing 1 of 8 Seven-Pip Card (Rank-7) cards at 10% penetration of a 2-deck (104-card) shoe leaves 7 Rank-7 cards inside a 94-card stub (DEP154), producing 45.8994% Banker wins, 44.5680% Player wins, 9.5326% Ties, and a 0.9635% Banker house edge under 5%.
Reference shoe scoreboard (PPBBPBTBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP154 (2D Rank-7 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.
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.
Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.
10% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).
1 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 2D pack.
Resolved at 45.8994% Banker win rate under 5% settlement.
Resolved at 44.5680% Player win rate with 0.9326 unit standard deviation.
Produces a 14.2067% house hold on the 8-to-1 Tie wager in state DEP154.
Quantitative proof DEP154 documents 2D rank depletion at 10% depth: 1 exited Rank-7 cards leave 7 of 8 in the 94-card stub, generating 45.8994% Banker wins (-0.9635% EV under 5% Vig) and 44.5680% Player wins.
Depleting 7s lowers the (DEP154-Rank-7) rate of winning three-card Banker (94c) 7 hands (the barred push (DEP154-Rank-7·94c) total on EZ Baccarat tables). Because 1 of 8 Seven-Pip Card cards are absent in DEP154 at 10% 2D penetration (94 cards left), per-card sensitivity (-0.83 bps) interacts directly with early-shoe 10% penetration depth (DEP154) under standard 5% Banker commission (Rank-7) (0.95:1 payout).
| Wager / Metric | State DEP154 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP154 Banker (5% Vig) | 45.8994% (-0.9635% EV) | 45.8998% | DEP154 2D 10% (7 Rank-7) |
| DEP154 Player (1:1) | 44.5680% (-1.3315% EV) | 44.5676% | DEP154 94-card 2D stub (0.9326 SD) |
| DEP154 Tie (8:1) | 9.5326% (-14.2067% EV) | 9.5326% | DEP154 Rank-7 (1 out, 7 in) |
Even at 10% penetration in DEP154 where 1 Rank-7 cards have exited a 2D shoe (7 left in 94 cards), derived-road red and blue entries measure structural regularity on the Big Road—not whether Banker (-0.9635% EV, 5% Vig) or Player (-1.3315% EV) is favored next.
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