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COMBINATORIAL DEPLETION · 4D · RANK-6 · 85% DEPTH

4-Deck Six-Pip Card Depletion at 85% Penetration (EZ Baccarat Audit DEP243)

Removing 15 of 16 Six-Pip Card (Rank-6) cards at 85% penetration of a 4-deck (208-card) shoe leaves 1 Rank-6 cards inside a 31-card stub (DEP243), producing 45.8674% Banker wins, 44.5909% Player wins, 9.5417% Ties, and a 0.9769% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.9769%
Player EV (1:1)
-1.2765%
Rank-6 in 31-Card Stub
1/16
Single-Hand Std Dev
0.9398
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBPBPBBPPBPBPBB) illustrating derived-road symmetry checks alongside DEP243 (4D Rank-6 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

Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

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

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 (DEP243)
31 / 208 Cards

85% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).

Rank-6 Remaining
1 of 16 Cards

15 6-pip cards (standing threshold and Banker 6 trigger) removed from the 4D pack.

Banker EV (EZ Bar-7)
-0.9769%

Resolved at 45.8674% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.2765%

Resolved at 44.5909% Player win rate with 0.9398 unit standard deviation.

Tie Incidence (8:1)
9.5417%

Produces a 14.1247% house hold on the 8-to-1 Tie wager in state DEP243.

FINITE-SHOE ENUMERATION · DEP243

How Six-Pip Card Depletion at 85% Depth Impacts 4D (EZ Bar-7)

At 85% penetration of a 208-card (4D) shoe, state DEP243 isolates 15 dealt Rank-6 cards (1 remaining inside 31 stub cards), yielding 45.8674% Banker wins, 44.5909% Player wins, and 0.9398 per-hand standard deviation under EZ Baccarat.

Why does Rank-6 carry a -1.13 bps per-card effect in DEP243? Banker 6 only draws (DEP243) when Player pulls a third-card (4D-85%) 6 or 7; depleting 6s (DEP243·4D-85%) directly alters both Banker 6 draws and Super 6 settlement frequency, and at 85% penetration (1 Six-Pip Card cards left in 31 4D cards), at 85% cut-card penetration, (dep243-4d) only 15% of the pack (1/16) remains and winning 3-card banker (dep243-4d·1/16) 7 hands push.

State DEP243 (4D, 85% depth, 1/16 Rank-6 left, EZ Bar-7)
Wager / MetricState DEP243 Value4D BaselineSettlement Note
DEP243 Banker (EZ Bar-7)45.8674% (-0.9769% EV)45.8732%DEP243 4D 85% (1 Rank-6)
DEP243 Player (1:1)44.5909% (-1.2765% EV)44.5850%DEP243 31-card 4D stub (0.9398 SD)
DEP243 Tie (8:1)9.5417% (-14.1247% EV)9.5418%DEP243 Rank-6 (15 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP243

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP243 · 4D)

Whether DEP243 is observed in four-deck Asian VIP salons and compact automatic shuffler shoes at 85% depth (31/208 cards left, 1 Rank-6 remaining), EZ Bar-7 settlement locks Banker EV at -0.9769% and Player EV at -1.2765% with 9.5417% Ties.

  • DEP243 (4D 85%): 31/208 cards with 1/16 Rank-6 (2A).
  • DEP243 (Rank-6 split): 45.8674% Banker, 44.5909% Player, 9.5417% Tie in 31 4D cards (2B).
  • DEP243 (EZ Bar-7 EV): -0.9769% Banker, -1.2765% Player, -14.1247% Tie, 0.9398 SD at 85% (2C).
  • DEP243 (4D roads): red/blue marks log Big Road columns, never 1 Rank-6 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 15 Six-Pip Card cards leave a 4D shoe by 85% depth (DEP243), 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 Rank-6 stub counts (1/16 in 31 cards); Banker carries a -0.9769% 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