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COMBINATORIAL DEPLETION · 2D · RANK-7 · 85% DEPTH

2-Deck Seven-Pip Card Depletion at 85% Penetration (EZ Baccarat Audit DEP162)

Removing 7 of 8 Seven-Pip Card (Rank-7) cards at 85% penetration of a 2-deck (104-card) shoe leaves 1 Rank-7 cards inside a 16-card stub (DEP162), producing 45.8958% Banker wins, 44.5717% Player wins, 9.5325% Ties, and a 0.9292% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.9292%
Player EV (1:1)
-1.3242%
Rank-7 in 16-Card Stub
1/8
Single-Hand Std Dev
0.9401
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 B P P B B P B P B B P
Big Eye Boy = = = = = = ≠ = = = = ≠ ≠ = =
Small Road = = = = = = ≠ ≠ = = = ≠ ≠
Cockroach Pig = = = = = = ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (PPBBPPBBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP162 (2D Rank-7 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 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 (DEP162)
16 / 104 Cards

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

Rank-7 Remaining
1 of 8 Cards

7 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 2D pack.

Banker EV (EZ Bar-7)
-0.9292%

Resolved at 45.8958% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.3242%

Resolved at 44.5717% Player win rate with 0.9401 unit standard deviation.

Tie Incidence (8:1)
9.5325%

Produces a 14.2075% house hold on the 8-to-1 Tie wager in state DEP162.

FINITE-SHOE ENUMERATION · DEP162

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

Within double-deck European salon privé carriers and two-deck shoe pits, profile DEP162 examines 85% shoe depletion (16 of 104 cards remaining) after 7 Rank-7 cards exit, leaving 1 Seven-Pip Card cards and a 0.9292% Banker house hold under EZ Baccarat.

Comparing initial 104-card 2D weights against stub DEP162 (16 cards, 85% depth, 1 Rank-7 left) illustrates how player stands pat on (dep162) two-card 7, and a player (2d-85%) third-card 7 is the highest (dep162·2d-85%) card that forces banker 4, 5, and 6 to draw (-0.83 bps slope, 0.9292% EZ Bar-7 edge).

State DEP162 (2D, 85% depth, 1/8 Rank-7 left, EZ Bar-7)
Wager / MetricState DEP162 Value2D BaselineSettlement Note
DEP162 Banker (EZ Bar-7)45.8958% (-0.9292% EV)45.8998%DEP162 2D 85% (1 Rank-7)
DEP162 Player (1:1)44.5717% (-1.3242% EV)44.5676%DEP162 16-card 2D stub (0.9401 SD)
DEP162 Tie (8:1)9.5325% (-14.2075% EV)9.5326%DEP162 Rank-7 (7 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP162

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP162 · 2D)

Statistical verification of DEP162 (2D, 85% penetration, 1 Seven-Pip Card cards in 16 stub cards) demonstrates why single-rank depletion (7 Rank-7 dealt) shifts edges by basis points around -0.9292% (EZ Bar-7).

  • DEP162 (2D 85%): 16/104 cards with 1/8 Rank-7 (3A).
  • DEP162 (Rank-7 split): 45.8958% Banker, 44.5717% Player, 9.5325% Tie in 16 2D cards (3B).
  • DEP162 (EZ Bar-7 EV): -0.9292% Banker, -1.3242% Player, -14.2075% Tie, 0.9401 SD at 85% (3C).
  • DEP162 (2D roads): red/blue marks log Big Road columns, never 1 Rank-7 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Seven-Pip Card cards leave a 2D shoe by 85% depth (DEP162), 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-7 stub counts (1/8 in 16 cards); Banker carries a -0.9292% 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