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COMBINATORIAL DEPLETION · 2D · RANK-6 · 85% DEPTH

2-Deck Six-Pip Card Depletion at 85% Penetration (EZ Baccarat Audit DEP153)

Removing 7 of 8 Six-Pip Card (Rank-6) cards at 85% penetration of a 2-deck (104-card) shoe leaves 1 Rank-6 cards inside a 16-card stub (DEP153), producing 45.8944% Banker wins, 44.5731% Player wins, 9.5325% Ties, and a 0.9321% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.9321%
Player EV (1:1)
-1.3213%
Rank-6 in 16-Card Stub
1/8
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 B P P B B P B P B B P
Big Eye Boy = = ≠ = = ≠ ≠ = = ≠ = = ≠ ≠
Small Road ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠
Cockroach Pig ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ ≠ ≠

Reference shoe scoreboard (BBPPBPTBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP153 (2D 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 (DEP153)
16 / 104 Cards

85% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Rank-6 Remaining
1 of 8 Cards

7 6-pip cards (standing threshold and Banker 6 trigger) removed from the 2D pack.

Banker EV (EZ Bar-7)
-0.9321%

Resolved at 45.8944% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.3213%

Resolved at 44.5731% Player win rate with 0.9398 unit standard deviation.

Tie Incidence (8:1)
9.5325%

Produces a 14.2075% house hold on the 8-to-1 Tie wager in state DEP153.

FINITE-SHOE ENUMERATION · DEP153

How Six-Pip Card Depletion at 85% Depth Impacts 2D (EZ Bar-7)

Shoe-stub analysis DEP153 inspects 16 remaining cards at 85% penetration of a 104-card (2D) pack after 7 Six-Pip Card cards have cleared, leaving 1 Rank-6 cards and a 0.9321% EZ Baccarat Banker edge.

Banker 6 only draws (DEP153) when Player pulls a third-card (2D-85%) 6 or 7; depleting 6s (DEP153·2D-85%) directly alters both Banker 6 draws and Super 6 settlement frequency. In state DEP153 (2D, 85% depth), each removed Rank-6 card applies a -1.13 bps baseline directional pressure before scaling to the 16-card remainder (1 Rank-6 left), while At 85% cut-card penetration, (DEP153-2D) only 15% of the pack (1/8) remains and winning 3-card Banker (DEP153-2D·1/8) 7 hands push.

State DEP153 (2D, 85% depth, 1/8 Rank-6 left, EZ Bar-7)
Wager / MetricState DEP153 Value2D BaselineSettlement Note
DEP153 Banker (EZ Bar-7)45.8944% (-0.9321% EV)45.8998%DEP153 2D 85% (1 Rank-6)
DEP153 Player (1:1)44.5731% (-1.3213% EV)44.5676%DEP153 16-card 2D stub (0.9398 SD)
DEP153 Tie (8:1)9.5325% (-14.2075% EV)9.5326%DEP153 Rank-6 (7 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP153

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP153 · 2D)

For DEP153 (16 remaining cards in a 104-card 2D shoe at 85% depth), tracking all 7 exited Rank-6 cards moves Banker win rate to 45.8944% (-0.9321% EV, EZ Bar-7) and Player to 44.5731% (-1.3213% EV).

  • DEP153 (2D 85%): 16/104 cards with 1/8 Rank-6 (7A).
  • DEP153 (Rank-6 split): 45.8944% Banker, 44.5731% Player, 9.5325% Tie in 16 2D cards (7B).
  • DEP153 (EZ Bar-7 EV): -0.9321% Banker, -1.3213% Player, -14.2075% Tie, 0.9398 SD at 85% (7C).
  • DEP153 (2D roads): red/blue marks log Big Road columns, never 1 Rank-6 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Six-Pip Card cards leave a 2D shoe by 85% depth (DEP153), 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 (1/8 in 16 cards); Banker carries a -0.9321% 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