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COMBINATORIAL DEPLETION · 4D · RANK-3 · 85% DEPTH

4-Deck Three-Pip (Trey) Depletion at 85% Penetration (EZ Baccarat Audit DEP216)

Removing 15 of 16 Three-Pip (Trey) (Rank-3) cards at 85% penetration of a 4-deck (208-card) shoe leaves 1 Rank-3 cards inside a 31-card stub (DEP216), producing 45.8765% Banker wins, 44.5816% Player wins, 9.5419% Ties, and a 0.9584% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.9584%
Player EV (1:1)
-1.2950%
Rank-3 in 31-Card Stub
1/16
Single-Hand Std Dev
0.9389
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 DEP216 (4D Rank-3 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 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 (DEP216)
31 / 208 Cards

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

Rank-3 Remaining
1 of 16 Cards

15 3-pip cards across all four suits removed from the 4D pack.

Banker EV (EZ Bar-7)
-0.9584%

Resolved at 45.8765% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.2950%

Resolved at 44.5816% Player win rate with 0.9389 unit standard deviation.

Tie Incidence (8:1)
9.5419%

Produces a 14.1229% house hold on the 8-to-1 Tie wager in state DEP216.

FINITE-SHOE ENUMERATION · DEP216

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

Under EZ Baccarat settlement (EZ Bar-7), combinatorial state DEP216 models a 4D carrier with 31 cards left (85% dealt) and 1/16 Three-Pip (Trey) cards remaining, producing a 0.9584% Banker edge versus 1.2950% on Player.

In six-card resolution tree DEP216 (4D at 85% depth, 31 cards left), each removed 3-pip card (dep216-rank-3) modifies the boundary between banker (31c) standing on 5 and drawing (dep216-rank-3·31c) against mid-range player pulls; removing 15 of 16 Rank-3 cards (+0.65 bps weight) leaves Banker at -0.9584% EV under EZ Baccarat.

State DEP216 (4D, 85% depth, 1/16 Rank-3 left, EZ Bar-7)
Wager / MetricState DEP216 Value4D BaselineSettlement Note
DEP216 Banker (EZ Bar-7)45.8765% (-0.9584% EV)45.8732%DEP216 4D 85% (1 Rank-3)
DEP216 Player (1:1)44.5816% (-1.2950% EV)44.5850%DEP216 31-card 4D stub (0.9389 SD)
DEP216 Tie (8:1)9.5419% (-14.1229% EV)9.5418%DEP216 Rank-3 (15 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP216

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP216 · 4D)

Statistical verification of DEP216 (4D, 85% penetration, 1 Three-Pip (Trey) cards in 31 stub cards) demonstrates why single-rank depletion (15 Rank-3 dealt) shifts edges by basis points around -0.9584% (EZ Bar-7).

  • DEP216 (4D 85%): 31/208 cards with 1/16 Rank-3 (7A).
  • DEP216 (Rank-3 split): 45.8765% Banker, 44.5816% Player, 9.5419% Tie in 31 4D cards (7B).
  • DEP216 (EZ Bar-7 EV): -0.9584% Banker, -1.2950% Player, -14.1229% Tie, 0.9389 SD at 85% (7C).
  • DEP216 (4D roads): red/blue marks log Big Road columns, never 1 Rank-3 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 15 Three-Pip (Trey) cards leave a 4D shoe by 85% depth (DEP216), 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 (1/16 in 31 cards); Banker carries a -0.9584% 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