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COMBINATORIAL DEPLETION · 4D · RANK-2 · 85% DEPTH

4-Deck Two-Pip (Deuce) Depletion at 85% Penetration (EZ Baccarat Audit DEP207)

Removing 15 of 16 Two-Pip (Deuce) (Rank-2) cards at 85% penetration of a 4-deck (208-card) shoe leaves 1 Rank-2 cards inside a 31-card stub (DEP207), producing 45.8759% Banker wins, 44.5822% Player wins, 9.5419% Ties, and a 0.9598% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.9598%
Player EV (1:1)
-1.2936%
Rank-2 in 31-Card Stub
1/16
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 B B P P B B P P B B P B
Big Eye Boy = = = = = = ≠ = = = = = = =
Small Road = = = = = = ≠ ≠ = = = =
Cockroach Pig = = = = = = ≠ ≠ ≠ =

Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP207 (4D 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

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 (DEP207)
31 / 208 Cards

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

Rank-2 Remaining
1 of 16 Cards

15 2-pip cards across all four suits removed from the 4D pack.

Banker EV (EZ Bar-7)
-0.9598%

Resolved at 45.8759% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.2936%

Resolved at 44.5822% Player win rate with 0.9386 unit standard deviation.

Tie Incidence (8:1)
9.5419%

Produces a 14.1229% house hold on the 8-to-1 Tie wager in state DEP207.

FINITE-SHOE ENUMERATION · DEP207

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

Removing 15 of 16 Rank-2 cards by the 85% mark of a 4-deck shoe (DEP207, 31 cards left) leaves 1 Two-Pip (Deuce) cards and adjusts conditional probabilities to 45.8759% Banker, 44.5822% Player, and 9.5419% Tie under EZ Baccarat.

Depleting 2s shifts the (DEP207-Rank-2) probability of Banker converting a (31c) two-card 4 or 5 into (DEP207-Rank-2·31c) a winning three-card 6 or 7. Because 15 of 16 Two-Pip (Deuce) cards are absent in DEP207 at 85% 4D penetration (31 cards left), per-card sensitivity (+0.52 bps) interacts directly with cut-card boundary 85% penetration (DEP207) depth under EZ Baccarat barred (Rank-2) 3-card Banker 7 rules.

State DEP207 (4D, 85% depth, 1/16 Rank-2 left, EZ Bar-7)
Wager / MetricState DEP207 Value4D BaselineSettlement Note
DEP207 Banker (EZ Bar-7)45.8759% (-0.9598% EV)45.8732%DEP207 4D 85% (1 Rank-2)
DEP207 Player (1:1)44.5822% (-1.2936% EV)44.5850%DEP207 31-card 4D stub (0.9386 SD)
DEP207 Tie (8:1)9.5419% (-14.1229% EV)9.5418%DEP207 Rank-2 (15 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP207

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP207 · 4D)

For DEP207 (31 remaining cards in a 208-card 4D shoe at 85% depth), tracking all 15 exited Rank-2 cards moves Banker win rate to 45.8759% (-0.9598% EV, EZ Bar-7) and Player to 44.5822% (-1.2936% EV).

  • DEP207 (4D 85%): 31/208 cards with 1/16 Rank-2 (4A).
  • DEP207 (Rank-2 split): 45.8759% Banker, 44.5822% Player, 9.5419% Tie in 31 4D cards (4B).
  • DEP207 (EZ Bar-7 EV): -0.9598% Banker, -1.2936% Player, -14.1229% Tie, 0.9386 SD at 85% (4C).
  • DEP207 (4D roads): red/blue marks log Big Road columns, never 1 Rank-2 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 15 Two-Pip (Deuce) cards leave a 4D shoe by 85% depth (DEP207), 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 (1/16 in 31 cards); Banker carries a -0.9598% 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