Removing 1 of 4 Three-Pip (Trey) (Rank-3) cards at 25% penetration of a 1-deck (52-card) shoe leaves 3 Rank-3 cards inside a 39-card stub (DEP029), producing 45.9601% Banker wins, 44.5243% Player wins, 9.5156% Ties, and a 0.8621% Banker house edge under 5%.
Reference shoe scoreboard (BBPPBPBBPPBPBBPPBP) illustrating derived-road symmetry checks alongside DEP029 (1D 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 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.
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.
25% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).
1 3-pip cards across all four suits removed from the 1D pack.
Resolved at 45.9601% Banker win rate under 5% settlement.
Resolved at 44.5243% Player win rate with 0.9329 unit standard deviation.
Produces a 14.3594% house hold on the 8-to-1 Tie wager in state DEP029.
Audit DEP029 evaluates a 1-deck (52-card) shoe at 25% penetration where 1 of 4 Three-Pip (Trey) cards have exited, leaving 3 Rank-3 cards inside the 39-card stub with Banker EV at -0.8621% under 5%.
For DEP029 (1-deck shoe, 25% dealt), banker total 4 draws (dep029) on player third-card 3, and (1d-25%) banker total 5 stands on (dep029·1d-25%) player third-card 3, creating asymmetric sensitivity. Holding 3 of 4 Rank-3 cards in a 39-card stub with +0.65 bps rank slope yields 45.9601% Banker, 44.5243% Player, and 9.5156% Tie.
| Wager / Metric | State DEP029 Value | 1D Baseline | Settlement Note |
|---|---|---|---|
| DEP029 Banker (5% Vig) | 45.9601% (-0.8621% EV) | 45.9595% | DEP029 1D 25% (3 Rank-3) |
| DEP029 Player (1:1) | 44.5243% (-1.4359% EV) | 44.5249% | DEP029 39-card 1D stub (0.9329 SD) |
| DEP029 Tie (8:1) | 9.5156% (-14.3594% EV) | 9.5156% | DEP029 Rank-3 (1 out, 3 in) |
Learners auditing DEP029 (1D at 25% depth, 3/4 Rank-3 in 39 stub cards) can verify that 5% house hold (0.8621% Banker, 1.4359% Player, 14.3594% Tie) operates independently of prior Big Road streaks.
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