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

2-Deck Two-Pip (Deuce) Depletion at 85% Penetration (EZ Baccarat Audit DEP117)

Removing 7 of 8 Two-Pip (Deuce) (Rank-2) cards at 85% penetration of a 2-deck (104-card) shoe leaves 1 Rank-2 cards inside a 16-card stub (DEP117), producing 45.9023% Banker wins, 44.5650% Player wins, 9.5327% Ties, and a 0.9161% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.9161%
Player EV (1:1)
-1.3373%
Rank-2 in 16-Card Stub
1/8
Single-Hand Std Dev
0.9386
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPPBBBPPBPTBPBBP) illustrating derived-road symmetry checks alongside DEP117 (2D Rank-2 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

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 2 goes down to Row 3, so use Rule 2: look 1 column back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Small Road Mark #2

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 3 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

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 (DEP117)
16 / 104 Cards

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

Rank-2 Remaining
1 of 8 Cards

7 2-pip cards across all four suits removed from the 2D pack.

Banker EV (EZ Bar-7)
-0.9161%

Resolved at 45.9023% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.3373%

Resolved at 44.5650% Player win rate with 0.9386 unit standard deviation.

Tie Incidence (8:1)
9.5327%

Produces a 14.2057% house hold on the 8-to-1 Tie wager in state DEP117.

FINITE-SHOE ENUMERATION · DEP117

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

At 85% penetration of a 104-card (2D) shoe, state DEP117 isolates 7 dealt Rank-2 cards (1 remaining inside 16 stub cards), yielding 45.9023% Banker wins, 44.5650% Player wins, and 0.9386 per-hand standard deviation under EZ Baccarat.

On Banker total 4, (DEP117) Banker draws against Player third-card (2D-85%) 2 through 7; removing 2s (DEP117·2D-85%) trims low-pip Player third-card triggers. In state DEP117 (2D, 85% depth), each removed Rank-2 card applies a +0.52 bps baseline directional pressure before scaling to the 16-card remainder (1 Rank-2 left), while At 85% cut-card penetration, (DEP117-2D) only 15% of the pack (1/8) remains and winning 3-card Banker (DEP117-2D·1/8) 7 hands push.

State DEP117 (2D, 85% depth, 1/8 Rank-2 left, EZ Bar-7)
Wager / MetricState DEP117 Value2D BaselineSettlement Note
DEP117 Banker (EZ Bar-7)45.9023% (-0.9161% EV)45.8998%DEP117 2D 85% (1 Rank-2)
DEP117 Player (1:1)44.5650% (-1.3373% EV)44.5676%DEP117 16-card 2D stub (0.9386 SD)
DEP117 Tie (8:1)9.5327% (-14.2057% EV)9.5326%DEP117 Rank-2 (7 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP117

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP117 · 2D)

Statistical verification of DEP117 (2D, 85% penetration, 1 Two-Pip (Deuce) cards in 16 stub cards) demonstrates why single-rank depletion (7 Rank-2 dealt) shifts edges by basis points around -0.9161% (EZ Bar-7).

  • DEP117 (2D 85%): 16/104 cards with 1/8 Rank-2 (2A).
  • DEP117 (Rank-2 split): 45.9023% Banker, 44.5650% Player, 9.5327% Tie in 16 2D cards (2B).
  • DEP117 (EZ Bar-7 EV): -0.9161% Banker, -1.3373% Player, -14.2057% Tie, 0.9386 SD at 85% (2C).
  • DEP117 (2D roads): red/blue marks log Big Road columns, never 1 Rank-2 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Two-Pip (Deuce) cards leave a 2D shoe by 85% depth (DEP117), 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-2 stub counts (1/8 in 16 cards); Banker carries a -0.9161% 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