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COMBINATORIAL DEPLETION · 4D · RANK-3 · 60% DEPTH

4-Deck Three-Pip (Trey) Depletion at 60% Penetration (EZ Baccarat Audit DEP212)

Removing 11 of 16 Three-Pip (Trey) (Rank-3) cards at 60% penetration of a 4-deck (208-card) shoe leaves 5 Rank-3 cards inside a 83-card stub (DEP212), producing 45.8753% Banker wins, 44.5828% Player wins, 9.5419% Ties, and a 0.9608% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.9608%
Player EV (1:1)
-1.2926%
Rank-3 in 83-Card Stub
5/16
Single-Hand Std Dev
0.9364
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 B P P B B P B P B P P
Big Eye Boy = = ≠ = = = ≠ ≠ = = ≠ = = = ≠
Small Road ≠ ≠ = = ≠ ≠ ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ = ≠

Reference shoe scoreboard (PPBBPBPBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP212 (4D Rank-3 at 60% 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 (DEP212)
83 / 208 Cards

60% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).

Rank-3 Remaining
5 of 16 Cards

11 3-pip cards across all four suits removed from the 4D pack.

Banker EV (EZ Bar-7)
-0.9608%

Resolved at 45.8753% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.2926%

Resolved at 44.5828% Player win rate with 0.9364 unit standard deviation.

Tie Incidence (8:1)
9.5419%

Produces a 14.1232% house hold on the 8-to-1 Tie wager in state DEP212.

FINITE-SHOE ENUMERATION · DEP212

How Three-Pip (Trey) Depletion at 60% Depth Impacts 4D (EZ Bar-7)

In combinatorial record DEP212, depleting 11 Rank-3 cards across 60% of a 4D (208-card) pack leaves 5 Three-Pip (Trey) cards among 83 remaining cards, setting Banker win probability to 45.8753% and house edge to 0.9608% (EZ Bar-7).

When 11 Rank-3 cards exit a 4D shoe by 60% penetration (DEP212, 5 left in 83 cards), each removed 3-pip card (dep212-rank-3) modifies the boundary between banker (83c) standing on 5 and drawing (dep212-rank-3·83c) against mid-range player pulls, combining a +0.65 bps rank vector with EZ Baccarat settlement (-0.9608% Banker EV).

State DEP212 (4D, 60% depth, 5/16 Rank-3 left, EZ Bar-7)
Wager / MetricState DEP212 Value4D BaselineSettlement Note
DEP212 Banker (EZ Bar-7)45.8753% (-0.9608% EV)45.8732%DEP212 4D 60% (5 Rank-3)
DEP212 Player (1:1)44.5828% (-1.2926% EV)44.5850%DEP212 83-card 4D stub (0.9364 SD)
DEP212 Tie (8:1)9.5419% (-14.1232% EV)9.5418%DEP212 Rank-3 (11 out, 5 in)
TABLEAU & SCOREBOARD SEPARATION · DEP212

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP212 · 4D)

Scoreboard literacy in DEP212 separates two independent concepts: 4D card-removal math (5 Rank-3 left in 83 cards at 60% depth, 0.9364 volatility) and derived-road comparison rules (Rule 1 column-depth checks and Rule 2 two-cell lookbacks).

  • DEP212 (4D 60%): 83/208 cards with 5/16 Rank-3 (1A).
  • DEP212 (Rank-3 split): 45.8753% Banker, 44.5828% Player, 9.5419% Tie in 83 4D cards (1B).
  • DEP212 (EZ Bar-7 EV): -0.9608% Banker, -1.2926% Player, -14.1232% Tie, 0.9364 SD at 60% (1C).
  • DEP212 (4D roads): red/blue marks log Big Road columns, never 5 Rank-3 stub count (1D).
Table Reality Check

Myth vs. Truth

MythWhen 11 Three-Pip (Trey) cards leave a 4D shoe by 60% depth (DEP212), 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-3 stub counts (5/16 in 83 cards); Banker carries a -0.9608% 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