Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 8D Ace-1 Depletion at 85% Depth (EZ Bar-7)
COMBINATORIAL DEPLETION · 8D · ACE-1 · 85% DEPTH

8-Deck Ace (1-Point Pip) Depletion at 85% Penetration (EZ Baccarat Audit DEP378)

Removing 31 of 32 Ace (1-Point Pip) (Ace-1) cards at 85% penetration of a 8-deck (416-card) shoe leaves 1 Ace-1 cards inside a 62-card stub (DEP378), producing 45.8620% Banker wins, 44.6223% Player wins, 9.5157% Ties, and a 1.0137% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-1.0137%
Player EV (1:1)
-1.2397%
Ace-1 in 62-Card Stub
1/32
Single-Hand Std Dev
0.9383
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPBTBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP378 (8D Ace-1 at 85% 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

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 columns back, at Column 2.
  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.

Cockroach Pig Mark #2

Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. 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.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP378)
62 / 416 Cards

85% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Ace-1 Remaining
1 of 32 Cards

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

Banker EV (EZ Bar-7)
-1.0137%

Resolved at 45.8620% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.2397%

Resolved at 44.6223% Player win rate with 0.9383 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3591% house hold on the 8-to-1 Tie wager in state DEP378.

FINITE-SHOE ENUMERATION · DEP378

How Ace (1-Point Pip) Depletion at 85% Depth Impacts 8D (EZ Bar-7)

Quantitative proof DEP378 documents 8D rank depletion at 85% depth: 31 exited Ace-1 cards leave 1 of 32 in the 62-card stub, generating 45.8620% Banker wins (-1.0137% EV under EZ Bar-7) and 44.6223% Player wins.

Comparing initial 416-card 8D weights against stub DEP378 (62 cards, 85% depth, 1 Ace-1 left) illustrates how removing aces slightly favors (dep378) banker because banker stands on (8d-85%) 6 against player third-card ace (dep378·8d-85%) while player must draw on 0–5 (+0.44 bps slope, 1.0137% EZ Bar-7 edge).

State DEP378 (8D, 85% depth, 1/32 Ace-1 left, EZ Bar-7)
Wager / MetricState DEP378 Value8D BaselineSettlement Note
DEP378 Banker (EZ Bar-7)45.8620% (-1.0137% EV)45.8597%DEP378 8D 85% (1 Ace-1)
DEP378 Player (1:1)44.6223% (-1.2397% EV)44.6247%DEP378 62-card 8D stub (0.9383 SD)
DEP378 Tie (8:1)9.5157% (-14.3591% EV)9.5156%DEP378 Ace-1 (31 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP378

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP378 · 8D)

Whether DEP378 is observed in eight-deck Macau, Las Vegas Strip, and Singapore standard shoes at 85% depth (62/416 cards left, 1 Ace-1 remaining), EZ Bar-7 settlement locks Banker EV at -1.0137% and Player EV at -1.2397% with 9.5157% Ties.

  • DEP378 (8D 85%): 62/416 cards with 1/32 Ace-1 (5A).
  • DEP378 (Ace-1 split): 45.8620% Banker, 44.6223% Player, 9.5157% Tie in 62 8D cards (5B).
  • DEP378 (EZ Bar-7 EV): -1.0137% Banker, -1.2397% Player, -14.3591% Tie, 0.9383 SD at 85% (5C).
  • DEP378 (8D roads): red/blue marks log Big Road columns, never 1 Ace-1 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 31 Ace (1-Point Pip) cards leave a 8D shoe by 85% depth (DEP378), 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 (1/32 in 62 cards); Banker carries a -1.0137% expectation under EZ Baccarat.
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