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COMBINATORIAL DEPLETION · 8D · ACE-1 · 75% DEPTH

8-Deck Ace (1-Point Pip) Depletion at 75% Penetration (4% Audit DEP376)

Removing 28 of 32 Ace (1-Point Pip) (Ace-1) cards at 75% penetration of a 8-deck (416-card) shoe leaves 4 Ace-1 cards inside a 104-card stub (DEP376), producing 45.8617% Banker wins, 44.6227% Player wins, 9.5156% Ties, and a 0.5954% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5954%
Player EV (1:1)
-1.2390%
Ace-1 in 104-Card Stub
4/32
Single-Hand Std Dev
0.9373
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road P P B B P P B P B P B B P P B B P B
Big Eye Boy = = = = ≠ = = = ≠ ≠ = = = = ≠
Small Road = = ≠ ≠ = = ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (PPBBPPBPBPBBPPBBPB) illustrating derived-road symmetry checks alongside DEP376 (8D Ace-1 at 75% depth).

Big Road B is Banker, P is Player Roads under it Red (=): repeating Blue (≠): breaking
Step-by-Step Mark Proofs (Rule 1 & Rule 2)
Big Eye Boy Mark #2

Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 3 starts, so use Rule 1: compare Column 2 with Column 1, 1 column further back.
  2. 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.

Small Road Mark #2

Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 4 starts, so use Rule 1: compare Column 3 with Column 1, 2 columns further back.
  2. 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.

Cockroach Pig Mark #2

Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. 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.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP376)
104 / 416 Cards

75% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Ace-1 Remaining
4 of 32 Cards

28 Ace cards valued at 1 modulo-10 point removed from the 8D pack.

Banker EV (4% Vig)
-0.5954%

Resolved at 45.8617% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2390%

Resolved at 44.6227% Player win rate with 0.9373 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3592% house hold on the 8-to-1 Tie wager in state DEP376.

FINITE-SHOE ENUMERATION · DEP376

How Ace (1-Point Pip) Depletion at 75% Depth Impacts 8D (4% Vig)

Exact conditional enumeration DEP376 for a 8D shoe at 75% depth (104/416 cards undealt) with 4 remaining Ace-1 cards confirms a 0.5954% Banker edge (4% Vig), 1.2390% Player edge, and 14.3592% Tie edge.

Tableau audit DEP376 confirms that removing aces slightly favors (dep376) banker because banker stands on (8d-75%) 6 against player third-card ace (dep376·8d-75%) while player must draw on 0–5. Inside the 104-card 8D stub (75% depth, 4/32 Ace-1 remaining, +0.44 bps slope), standard deviation is 0.9373 under 4% Vig.

State DEP376 (8D, 75% depth, 4/32 Ace-1 left, 4% Vig)
Wager / MetricState DEP376 Value8D BaselineSettlement Note
DEP376 Banker (4% Vig)45.8617% (-0.5954% EV)45.8597%DEP376 8D 75% (4 Ace-1)
DEP376 Player (1:1)44.6227% (-1.2390% EV)44.6247%DEP376 104-card 8D stub (0.9373 SD)
DEP376 Tie (8:1)9.5156% (-14.3592% EV)9.5156%DEP376 Ace-1 (28 out, 4 in)
TABLEAU & SCOREBOARD SEPARATION · DEP376

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP376 · 8D)

Cut-card protocol at 75% depth in DEP376 (8D, 104 stub cards containing 4 Ace-1 cards) ensures the shoe reshuffles long before 4% house hold (0.5954% Banker / 1.2390% Player) is overturned.

  • DEP376 (8D 75%): 104/416 cards with 4/32 Ace-1 (2A).
  • DEP376 (Ace-1 split): 45.8617% Banker, 44.6227% Player, 9.5156% Tie in 104 8D cards (2B).
  • DEP376 (4% Vig EV): -0.5954% Banker, -1.2390% Player, -14.3592% Tie, 0.9373 SD at 75% (2C).
  • DEP376 (8D roads): red/blue marks log Big Road columns, never 4 Ace-1 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 28 Ace (1-Point Pip) cards leave a 8D shoe by 75% depth (DEP376), Big Eye Boy red or blue marks show whether Banker or Player will win next.
TruthDerived-road red and blue marks only compare Big Road column lengths and never track Ace-1 stub counts (4/32 in 104 cards); Banker carries a -0.5954% expectation under 4%.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

Read Every Derived Road at Table Speed

Every reference guide, glossary definition, and road calculator on Baccarat Smart is open for everyone. When you want all 6 modules and 36 lessons (about 5.5 hours of lessons) organized in structured step-by-step order with 74 hands-on boards, 94 quiz checks along the way, and Cloud Shoe Log sync across web, iPhone, and Android, start Module 1 (10 lessons, about 64 minutes of lessons) free or unlock full membership for $25 a month.

  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android