Removing 1 of 4 Six-Pip Card (Rank-6) cards at 25% penetration of a 1-deck (52-card) shoe leaves 3 Rank-6 cards inside a 39-card stub (DEP056), producing 45.9584% Banker wins, 44.5260% Player wins, 9.5156% Ties, and a 0.8655% Banker house edge under 5%.
Reference shoe scoreboard (PPBBPPBPBPBBPPBBPB) illustrating derived-road symmetry checks alongside DEP056 (1D Rank-6 at 25% 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 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.
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.
25% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).
1 6-pip cards (standing threshold and Banker 6 trigger) removed from the 1D pack.
Resolved at 45.9584% Banker win rate under 5% settlement.
Resolved at 44.5260% Player win rate with 0.9338 unit standard deviation.
Produces a 14.3598% house hold on the 8-to-1 Tie wager in state DEP056.
Quantitative proof DEP056 documents 1D rank depletion at 25% depth: 1 exited Rank-6 cards leave 3 of 4 in the 39-card stub, generating 45.9584% Banker wins (-0.8655% EV under 5% Vig) and 44.5260% Player wins.
Combinatorial weighting in DEP056 (39 cards left from 52 at 25% depth) is governed by two rules: banker 6 only draws (dep056) when player pulls a third-card (1d-25%) 6 or 7; depleting 6s (dep056·1d-25%) directly alters both banker 6 draws and super 6 settlement frequency, and one-quarter of the shoe (dep056-1d) has exited the carrier and (3/4) winning banker wagers pay 0.95 (dep056-1d·3/4) to 1 after 5% house tax (-1.13 bps per Rank-6 removed).
| Wager / Metric | State DEP056 Value | 1D Baseline | Settlement Note |
|---|---|---|---|
| DEP056 Banker (5% Vig) | 45.9584% (-0.8655% EV) | 45.9595% | DEP056 1D 25% (3 Rank-6) |
| DEP056 Player (1:1) | 44.5260% (-1.4324% EV) | 44.5249% | DEP056 39-card 1D stub (0.9338 SD) |
| DEP056 Tie (8:1) | 9.5156% (-14.3598% EV) | 9.5156% | DEP056 Rank-6 (1 out, 3 in) |
Statistical verification of DEP056 (1D, 25% penetration, 3 Six-Pip Card cards in 39 stub cards) demonstrates why single-rank depletion (1 Rank-6 dealt) shifts edges by basis points around -0.8655% (5% Vig).
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