Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 4D Rank-7 Depletion at 60% Depth (EZ Bar-7)
COMBINATORIAL DEPLETION · 4D · RANK-7 · 60% DEPTH

4-Deck Seven-Pip Card Depletion at 60% Penetration (EZ Baccarat Audit DEP248)

Removing 11 of 16 Seven-Pip Card (Rank-7) cards at 60% penetration of a 4-deck (208-card) shoe leaves 5 Rank-7 cards inside a 83-card stub (DEP248), producing 45.8705% Banker wins, 44.5878% Player wins, 9.5417% Ties, and a 0.9707% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.9707%
Player EV (1:1)
-1.2827%
Rank-7 in 83-Card Stub
5/16
Single-Hand Std Dev
0.9376
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 P B P B B P P B B P B
Big Eye Boy = = = = ≠ = = = ≠ ≠ = = = = ≠
Small Road = = ≠ ≠ = = ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (PPBBPPBPBPBBPPBBPB) illustrating derived-road symmetry checks alongside DEP248 (4D Rank-7 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 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 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 (DEP248)
83 / 208 Cards

60% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).

Rank-7 Remaining
5 of 16 Cards

11 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 4D pack.

Banker EV (EZ Bar-7)
-0.9707%

Resolved at 45.8705% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.2827%

Resolved at 44.5878% Player win rate with 0.9376 unit standard deviation.

Tie Incidence (8:1)
9.5417%

Produces a 14.1244% house hold on the 8-to-1 Tie wager in state DEP248.

FINITE-SHOE ENUMERATION · DEP248

How Seven-Pip Card Depletion at 60% Depth Impacts 4D (EZ Bar-7)

Depletion matrix entry DEP248 pairs 4D (208 cards) at 60% penetration with 11 removed Seven-Pip Card cards (5 left in 83 cards), fixing per-hand volatility at 0.9376 and Banker house hold at 0.9707% (EZ Bar-7).

When 11 Rank-7 cards exit a 4D shoe by 60% penetration (DEP248, 5 left in 83 cards), depleting 7s lowers the (dep248-rank-7) rate of winning three-card banker (83c) 7 hands (the barred push (dep248-rank-7·83c) total on ez baccarat tables), combining a -0.83 bps rank vector with EZ Baccarat settlement (-0.9707% Banker EV).

State DEP248 (4D, 60% depth, 5/16 Rank-7 left, EZ Bar-7)
Wager / MetricState DEP248 Value4D BaselineSettlement Note
DEP248 Banker (EZ Bar-7)45.8705% (-0.9707% EV)45.8732%DEP248 4D 60% (5 Rank-7)
DEP248 Player (1:1)44.5878% (-1.2827% EV)44.5850%DEP248 83-card 4D stub (0.9376 SD)
DEP248 Tie (8:1)9.5417% (-14.1244% EV)9.5418%DEP248 Rank-7 (11 out, 5 in)
TABLEAU & SCOREBOARD SEPARATION · DEP248

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP248 · 4D)

Learners auditing DEP248 (4D at 60% depth, 5/16 Rank-7 in 83 stub cards) can verify that EZ Baccarat house hold (0.9707% Banker, 1.2827% Player, 14.1244% Tie) operates independently of prior Big Road streaks.

  • DEP248 (4D 60%): 83/208 cards with 5/16 Rank-7 (6A).
  • DEP248 (Rank-7 split): 45.8705% Banker, 44.5878% Player, 9.5417% Tie in 83 4D cards (6B).
  • DEP248 (EZ Bar-7 EV): -0.9707% Banker, -1.2827% Player, -14.1244% Tie, 0.9376 SD at 60% (6C).
  • DEP248 (4D roads): red/blue marks log Big Road columns, never 5 Rank-7 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 11 Seven-Pip Card cards leave a 4D shoe by 60% depth (DEP248), 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 (5/16 in 83 cards); Banker carries a -0.9707% 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