Removing 3 of 4 Four-Pip Card (Rank-4) cards at 70% penetration of a 1-deck (52-card) shoe leaves 1 Rank-4 cards inside a 16-card stub (DEP042), producing 45.9640% Banker wins, 44.5203% Player wins, 9.5157% Ties, and a 0.8545% Banker house edge under 5%.
Reference shoe scoreboard (PPBBPBTBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP042 (1D Rank-4 at 70% 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.
70% 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 45.9640% Banker win rate under 5% settlement.
Resolved at 44.5203% Player win rate with 0.9377 unit standard deviation.
Produces a 14.3589% house hold on the 8-to-1 Tie wager in state DEP042.
Quantitative proof DEP042 documents 1D rank depletion at 70% depth: 3 exited Rank-4 cards leave 1 of 4 in the 16-card stub, generating 45.9640% Banker wins (-0.8545% EV under 5% Vig) and 44.5203% Player wins.
Tracking DEP042 across 16 remaining 1D cards (70% depth) shows that removing 4s produces the (dep042-rank-4) single largest per-card shift toward (16c) banker (and away from player) (dep042-rank-4·16c) of any rank in the shoe. With 3 Rank-4 cards gone (+1.19 bps unit sensitivity), Banker expectation is -0.8545% (5% Vig) vs -1.4437% on Player.
| Wager / Metric | State DEP042 Value | 1D Baseline | Settlement Note |
|---|---|---|---|
| DEP042 Banker (5% Vig) | 45.9640% (-0.8545% EV) | 45.9595% | DEP042 1D 70% (1 Rank-4) |
| DEP042 Player (1:1) | 44.5203% (-1.4437% EV) | 44.5249% | DEP042 16-card 1D stub (0.9377 SD) |
| DEP042 Tie (8:1) | 9.5157% (-14.3589% EV) | 9.5156% | DEP042 Rank-4 (3 out, 1 in) |
Synthesizing DEP042 (1D at 70% depth, 1 Four-Pip Card cards left inside 16 stub cards): 5% rules produce a 0.8545% Banker edge, 1.4437% Player edge, 14.3589% Tie edge, and 0.9377 unit volatility.
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