Removing 2 of 16 Ace (1-Point Pip) (Ace-1) cards at 10% penetration of a 4-deck (208-card) shoe leaves 14 Ace-1 cards inside a 187-card stub (DEP190), producing 45.8734% Banker wins, 44.5848% Player wins, 9.5418% Ties, and a 1.0051% Banker house edge under 5%.
Reference shoe scoreboard (PPBBPBPPBBPBPPBBPB) illustrating derived-road symmetry checks alongside DEP190 (4D 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 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.
10% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).
2 Ace cards valued at 1 modulo-10 point removed from the 4D pack.
Resolved at 45.8734% Banker win rate under 5% settlement.
Resolved at 44.5848% Player win rate with 0.9308 unit standard deviation.
Produces a 14.1238% house hold on the 8-to-1 Tie wager in state DEP190.
Within four-deck Asian VIP salons and compact automatic shuffler shoes, profile DEP190 examines 10% shoe depletion (187 of 208 cards remaining) after 2 Ace-1 cards exit, leaving 14 Ace (1-Point Pip) cards and a 1.0051% Banker house hold under 5%.
Why does Ace-1 carry a +0.44 bps per-card effect in DEP190? Removing Aces slightly favors (DEP190) Banker because Banker stands on (4D-10%) 6 against Player third-card Ace (DEP190·4D-10%) while Player must draw on 0–5, and at 10% penetration (14 Ace (1-Point Pip) cards left in 187 4D cards), winning banker tickets pay (dep190-4d) 0.95 units per unit staked (14/16) while 90% of the initial (dep190-4d·14/16) shoe remains undealt.
| Wager / Metric | State DEP190 Value | 4D Baseline | Settlement Note |
|---|---|---|---|
| DEP190 Banker (5% Vig) | 45.8734% (-1.0051% EV) | 45.8732% | DEP190 4D 10% (14 Ace-1) |
| DEP190 Player (1:1) | 44.5848% (-1.2886% EV) | 44.5850% | DEP190 187-card 4D stub (0.9308 SD) |
| DEP190 Tie (8:1) | 9.5418% (-14.1238% EV) | 9.5418% | DEP190 Ace-1 (2 out, 14 in) |
In DEP190, the 187-card 4D stub (10% penetration, 2 of 16 Ace-1 dealt) yields 45.8734% Banker, 44.5848% Player, and 9.5418% Tie outcomes with 0.9308 dispersion under 5% Vig.
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