Removing 2 of 8 Three-Pip (Trey) (Rank-3) cards at 25% penetration of a 2-deck (104-card) shoe leaves 6 Rank-3 cards inside a 78-card stub (DEP119), producing 45.9004% Banker wins, 44.5670% Player wins, 9.5326% Ties, and a 0.9615% Banker house edge under 5%.
Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP119 (2D Rank-3 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 2D (double-deck European salon privé carriers and two-deck shoe pits).
2 3-pip cards across all four suits removed from the 2D pack.
Resolved at 45.9004% Banker win rate under 5% settlement.
Resolved at 44.5670% Player win rate with 0.9329 unit standard deviation.
Produces a 14.2064% house hold on the 8-to-1 Tie wager in state DEP119.
Card-removal benchmark DEP119 measures Three-Pip (Trey) (Rank-3) scarcity at 25% depth in a 2-deck shoe: 2 removed ranks leave 6 in the 78-card remainder, shifting Banker win share to 45.9004% (0.9615% edge, 5% Vig).
Under the fixed third-card tableau for DEP119, banker total 4 draws (dep119) on player third-card 3, and (2d-25%) banker total 5 stands on (dep119·2d-25%) player third-card 3, creating asymmetric sensitivity. With 6 Rank-3 cards inside 78 remaining 2D cards (25% dealt), single-card slope (+0.65 bps) keeps Banker house edge at 0.9615% and Player at 1.3335%.
| Wager / Metric | State DEP119 Value | 2D Baseline | Settlement Note |
|---|---|---|---|
| DEP119 Banker (5% Vig) | 45.9004% (-0.9615% EV) | 45.8998% | DEP119 2D 25% (6 Rank-3) |
| DEP119 Player (1:1) | 44.5670% (-1.3335% EV) | 44.5676% | DEP119 78-card 2D stub (0.9329 SD) |
| DEP119 Tie (8:1) | 9.5326% (-14.2064% EV) | 9.5326% | DEP119 Rank-3 (2 out, 6 in) |
Learners auditing DEP119 (2D at 25% depth, 6/8 Rank-3 in 78 stub cards) can verify that 5% house hold (0.9615% Banker, 1.3335% Player, 14.2064% Tie) operates independently of prior Big Road streaks.
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