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COMBINATORIAL DEPLETION · 2D · RANK-4 · 60% DEPTH

2-Deck Four-Pip Card Depletion at 60% Penetration (EZ Baccarat Audit DEP131)

Removing 6 of 8 Four-Pip Card (Rank-4) cards at 60% penetration of a 2-deck (104-card) shoe leaves 2 Rank-4 cards inside a 42-card stub (DEP131), producing 45.9041% Banker wins, 44.5632% Player wins, 9.5327% Ties, and a 0.9126% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.9126%
Player EV (1:1)
-1.3408%
Rank-4 in 42-Card Stub
2/8
Single-Hand Std Dev
0.9367
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBPBPBBPPBPBPBB) illustrating derived-road symmetry checks alongside DEP131 (2D Rank-4 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 (DEP131)
42 / 104 Cards

60% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Rank-4 Remaining
2 of 8 Cards

6 4-pip cards (strongest pro-Banker removal sensitivity) removed from the 2D pack.

Banker EV (EZ Bar-7)
-0.9126%

Resolved at 45.9041% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.3408%

Resolved at 44.5632% Player win rate with 0.9367 unit standard deviation.

Tie Incidence (8:1)
9.5327%

Produces a 14.2060% house hold on the 8-to-1 Tie wager in state DEP131.

FINITE-SHOE ENUMERATION · DEP131

How Four-Pip Card Depletion at 60% Depth Impacts 2D (EZ Bar-7)

At 60% penetration of a 104-card (2D) shoe, state DEP131 isolates 6 dealt Rank-4 cards (2 remaining inside 42 stub cards), yielding 45.9041% Banker wins, 44.5632% Player wins, and 0.9367 per-hand standard deviation under EZ Baccarat.

In 2D audit DEP131 (42/104 stub at 60% depth), removing 4s produces the (dep131-rank-4) single largest per-card shift toward (42c) banker (and away from player) (dep131-rank-4·42c) of any rank in the shoe. Removing 6 Rank-4 cards (+1.19 bps per card) alongside EZ Bar-7 rules sets Tie hold to 14.2060% (9.5327% frequency).

State DEP131 (2D, 60% depth, 2/8 Rank-4 left, EZ Bar-7)
Wager / MetricState DEP131 Value2D BaselineSettlement Note
DEP131 Banker (EZ Bar-7)45.9041% (-0.9126% EV)45.8998%DEP131 2D 60% (2 Rank-4)
DEP131 Player (1:1)44.5632% (-1.3408% EV)44.5676%DEP131 42-card 2D stub (0.9367 SD)
DEP131 Tie (8:1)9.5327% (-14.2060% EV)9.5326%DEP131 Rank-4 (6 out, 2 in)
TABLEAU & SCOREBOARD SEPARATION · DEP131

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP131 · 2D)

While DEP131 tracks 6 removed Four-Pip Card cards across 60% of a 104-card (2D) shoe (42 remaining, 0.9126% EZ Bar-7 edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP131 (2D 60%): 42/104 cards with 2/8 Rank-4 (2A).
  • DEP131 (Rank-4 split): 45.9041% Banker, 44.5632% Player, 9.5327% Tie in 42 2D cards (2B).
  • DEP131 (EZ Bar-7 EV): -0.9126% Banker, -1.3408% Player, -14.2060% Tie, 0.9367 SD at 60% (2C).
  • DEP131 (2D roads): red/blue marks log Big Road columns, never 2 Rank-4 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 6 Four-Pip Card cards leave a 2D shoe by 60% depth (DEP131), 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-4 stub counts (2/8 in 42 cards); Banker carries a -0.9126% 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