Removing 3 of 4 Nine-Pip Card (Rank-9) cards at 75% penetration of a 1-deck (52-card) shoe leaves 1 Rank-9 cards inside a 13-card stub (DEP088), producing 45.9586% Banker wins, 44.5258% Player wins, 9.5156% Ties, and a 0.4056% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPPBPBPBBPPBBPB) illustrating derived-road symmetry checks alongside DEP088 (1D Rank-9 at 75% 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.
75% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).
3 9-pip cards (top Natural 9 generator) removed from the 1D pack.
Resolved at 45.9586% Banker win rate under 4% settlement.
Resolved at 44.5258% Player win rate with 0.9397 unit standard deviation.
Produces a 14.3600% house hold on the 8-to-1 Tie wager in state DEP088.
Finite-shoe specification DEP088 tracks Rank-9 removal at 75% depth in 1-deck play: with 1 of 4 Nine-Pip Card cards left in the 13-card stub, Tie incidence is 9.5156% and Banker expectation settles at -0.4056% (4% Vig).
Mechanical draw trees in DEP088 reflect how when 9s are depleted (dep088-rank-9) late in the shoe, more (13c) hands bypass four-card natural resolution (dep088-rank-9·13c) and enter the five- and six-card tableau. At 75% 1D depth (1 Rank-9 left of 4 in 13 cards, -0.23 bps slope), three-quarters of the shoe (dep088-1d) has been dealt and winning (1/4) banker wagers return 0.96 units (dep088-1d·1/4) net per unit risked.
| Wager / Metric | State DEP088 Value | 1D Baseline | Settlement Note |
|---|---|---|---|
| DEP088 Banker (4% Vig) | 45.9586% (-0.4056% EV) | 45.9595% | DEP088 1D 75% (1 Rank-9) |
| DEP088 Player (1:1) | 44.5258% (-1.4328% EV) | 44.5249% | DEP088 13-card 1D stub (0.9397 SD) |
| DEP088 Tie (8:1) | 9.5156% (-14.3600% EV) | 9.5156% | DEP088 Rank-9 (3 out, 1 in) |
Synthesizing DEP088 (1D at 75% depth, 1 Nine-Pip Card cards left inside 13 stub cards): 4% rules produce a 0.4056% Banker edge, 1.4328% Player edge, 14.3600% Tie edge, and 0.9397 unit volatility.
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