Removing 14 of 16 Nine-Pip Card (Rank-9) cards at 75% penetration of a 4-deck (208-card) shoe leaves 2 Rank-9 cards inside a 52-card stub (DEP268), producing 45.8722% Banker wins, 44.5861% Player wins, 9.5418% Ties, and a 0.5488% Banker house edge under 4%.
Reference shoe scoreboard (PPBBPPPPBBBBPPBBPB) illustrating derived-road symmetry checks alongside DEP268 (4D 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.
This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.
This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.
75% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
14 9-pip cards (top Natural 9 generator) removed from the 4D pack.
Resolved at 45.8722% Banker win rate under 4% settlement.
Resolved at 44.5861% Player win rate with 0.9397 unit standard deviation.
Produces a 14.1242% house hold on the 8-to-1 Tie wager in state DEP268.
In combinatorial record DEP268, depleting 14 Rank-9 cards across 75% of a 4D (208-card) pack leaves 2 Nine-Pip Card cards among 52 remaining cards, setting Banker win probability to 45.8722% and house edge to 0.5488% (4% Vig).
Mechanical draw trees in DEP268 reflect how when 9s are depleted (dep268-rank-9) late in the shoe, more (52c) hands bypass four-card natural resolution (dep268-rank-9·52c) and enter the five- and six-card tableau. At 75% 4D depth (2 Rank-9 left of 16 in 52 cards, -0.23 bps slope), three-quarters of the shoe (dep268-4d) has been dealt and winning (2/16) banker wagers return 0.96 units (dep268-4d·2/16) net per unit risked.
| Wager / Metric | State DEP268 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP268 Banker (4% Vig) | 45.8722% (-0.5488% EV) | 45.8732% | DEP268 4D 75% (2 Rank-9) |
| DEP268 Player (1:1) | 44.5861% (-1.2861% EV) | 44.5850% | DEP268 52-card 4D stub (0.9397 SD) |
| DEP268 Tie (8:1) | 9.5418% (-14.1242% EV) | 9.5418% | DEP268 Rank-9 (14 out, 2 in) |
For DEP268 (52 remaining cards in a 208-card 4D shoe at 75% depth), tracking all 14 exited Rank-9 cards moves Banker win rate to 45.8722% (-0.5488% EV, 4% Vig) and Player to 44.5861% (-1.2861% EV).
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