Removing 2 of 4 Nine-Pip Card (Rank-9) cards at 40% penetration of a 1-deck (52-card) shoe leaves 2 Rank-9 cards inside a 31-card stub (DEP084), producing 45.9590% Banker wins, 44.5254% Player wins, 9.5156% Ties, and a 0.4048% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPBPBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP084 (1D Rank-9 at 40% 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.
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.
40% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).
2 9-pip cards (top Natural 9 generator) removed from the 1D pack.
Resolved at 45.9590% Banker win rate under 4% settlement.
Resolved at 44.5254% Player win rate with 0.9362 unit standard deviation.
Produces a 14.3598% house hold on the 8-to-1 Tie wager in state DEP084.
Quantitative proof DEP084 documents 1D rank depletion at 40% depth: 2 exited Rank-9 cards leave 2 of 4 in the 31-card stub, generating 45.9590% Banker wins (-0.4048% EV under 4% Vig) and 44.5254% Player wins.
Rank 9 paired with (DEP084) any ten or face card (1D-40%) creates an unbeatable two-card Natural (DEP084·1D-40%) 9 that halts all third-card drawing on both sides. In state DEP084 (1D, 40% depth), each removed Rank-9 card applies a -0.23 bps baseline directional pressure before scaling to the 31-card remainder (2 Rank-9 left), while Winning Banker wagers collect (DEP084-1D) 0.96 units per unit staked (2/4) with 60% of the shoe (DEP084-1D·2/4) still inside the acrylic carrier.
| Wager / Metric | State DEP084 Value | 1D Baseline | Settlement Note |
|---|---|---|---|
| DEP084 Banker (4% Vig) | 45.9590% (-0.4048% EV) | 45.9595% | DEP084 1D 40% (2 Rank-9) |
| DEP084 Player (1:1) | 44.5254% (-1.4336% EV) | 44.5249% | DEP084 31-card 1D stub (0.9362 SD) |
| DEP084 Tie (8:1) | 9.5156% (-14.3598% EV) | 9.5156% | DEP084 Rank-9 (2 out, 2 in) |
In DEP084, the 31-card 1D stub (40% penetration, 2 of 4 Rank-9 dealt) yields 45.9590% Banker, 44.5254% Player, and 9.5156% Tie outcomes with 0.9362 dispersion under 4% Vig.
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