Removing 4 of 32 Ace (1-Point Pip) (Ace-1) cards at 10% penetration of a 8-deck (416-card) shoe leaves 28 Ace-1 cards inside a 374-card stub (DEP370), producing 45.8599% Banker wins, 44.6245% Player wins, 9.5156% Ties, and a 1.0576% Banker house edge under 5%.
Reference shoe scoreboard (PPBBPPBBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP370 (8D Ace-1 at 10% 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 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.
10% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).
4 Ace cards valued at 1 modulo-10 point removed from the 8D pack.
Resolved at 45.8599% Banker win rate under 5% settlement.
Resolved at 44.6245% Player win rate with 0.9308 unit standard deviation.
Produces a 14.3596% house hold on the 8-to-1 Tie wager in state DEP370.
Under 5% settlement (5% Vig), combinatorial state DEP370 models a 8D carrier with 374 cards left (10% dealt) and 28/32 Ace (1-Point Pip) cards remaining, producing a 1.0576% Banker edge versus 1.2354% on Player.
Why does Ace-1 carry a +0.44 bps per-card effect in DEP370? Removing Aces slightly favors (DEP370) Banker because Banker stands on (8D-10%) 6 against Player third-card Ace (DEP370·8D-10%) while Player must draw on 0–5, and at 10% penetration (28 Ace (1-Point Pip) cards left in 374 8D cards), winning banker tickets pay (dep370-8d) 0.95 units per unit staked (28/32) while 90% of the initial (dep370-8d·28/32) shoe remains undealt.
| Wager / Metric | State DEP370 Value | 8D Baseline | Settlement Note |
|---|---|---|---|
| DEP370 Banker (5% Vig) | 45.8599% (-1.0576% EV) | 45.8597% | DEP370 8D 10% (28 Ace-1) |
| DEP370 Player (1:1) | 44.6245% (-1.2354% EV) | 44.6247% | DEP370 374-card 8D stub (0.9308 SD) |
| DEP370 Tie (8:1) | 9.5156% (-14.3596% EV) | 9.5156% | DEP370 Ace-1 (4 out, 28 in) |
Across 100-hand session horizons at state DEP370 (8D 10% depth, 28/32 Ace-1 in 374 cards), single-hand dispersion (0.9308 SD) dominates the 1.0576% (5% Vig) Banker and 1.2354% Player expectation gap.
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