Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 4D Rank-0 Depletion at 60% Depth (EZ Bar-7)
COMBINATORIAL DEPLETION · 4D · RANK-0 · 60% DEPTH

4-Deck 0-Value Tens & Faces Depletion at 60% Penetration (EZ Baccarat Audit DEP185)

Removing 44 of 64 0-Value Tens & Faces (Rank-0) cards at 60% penetration of a 4-deck (208-card) shoe leaves 20 Rank-0 cards inside a 83-card stub (DEP185), producing 45.8756% Banker wins, 44.5825% Player wins, 9.5419% Ties, and a 0.9603% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.9603%
Player EV (1:1)
-1.2931%
Rank-0 in 83-Card Stub
20/64
Single-Hand Std Dev
0.9355
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 B P B B P
Big Eye Boy = = ≠ = = ≠ ≠ = = ≠ = = ≠ ≠
Small Road ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠
Cockroach Pig ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ ≠ ≠

Reference shoe scoreboard (BBPPBPTBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP185 (4D Rank-0 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 (DEP185)
83 / 208 Cards

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

Rank-0 Remaining
20 of 64 Cards

44 10, Jack, Queen, and King (zero-point cards) removed from the 4D pack.

Banker EV (EZ Bar-7)
-0.9603%

Resolved at 45.8756% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.2931%

Resolved at 44.5825% Player win rate with 0.9355 unit standard deviation.

Tie Incidence (8:1)
9.5419%

Produces a 14.1226% house hold on the 8-to-1 Tie wager in state DEP185.

FINITE-SHOE ENUMERATION · DEP185

How 0-Value Tens & Faces Depletion at 60% Depth Impacts 4D (EZ Bar-7)

When a 4D shoe reaches 60% cut-card depth (83 of 208 cards undealt, state DEP185) with 44 0-Value Tens & Faces cards removed and 20 remaining, Player wins 44.5825% (1.2931% edge) while Banker wins 45.8756% (0.9603% edge under EZ Baccarat).

In six-card resolution tree DEP185 (4D at 60% depth, 83 cards left), fewer zero-value draws mean (dep185-rank-0) third-card pulls change running totals (83c) more frequently instead of leaving (dep185-rank-0·83c) totals unchanged; removing 44 of 64 Rank-0 cards (+0.18 bps weight) leaves Banker at -0.9603% EV under EZ Baccarat.

State DEP185 (4D, 60% depth, 20/64 Rank-0 left, EZ Bar-7)
Wager / MetricState DEP185 Value4D BaselineSettlement Note
DEP185 Banker (EZ Bar-7)45.8756% (-0.9603% EV)45.8732%DEP185 4D 60% (20 Rank-0)
DEP185 Player (1:1)44.5825% (-1.2931% EV)44.5850%DEP185 83-card 4D stub (0.9355 SD)
DEP185 Tie (8:1)9.5419% (-14.1226% EV)9.5418%DEP185 Rank-0 (44 out, 20 in)
TABLEAU & SCOREBOARD SEPARATION · DEP185

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP185 · 4D)

Even at 60% penetration in DEP185 where 44 Rank-0 cards have exited a 4D shoe (20 left in 83 cards), derived-road red and blue entries measure structural regularity on the Big Road—not whether Banker (-0.9603% EV, EZ Bar-7) or Player (-1.2931% EV) is favored next.

  • DEP185 (4D 60%): 83/208 cards with 20/64 Rank-0 (6A).
  • DEP185 (Rank-0 split): 45.8756% Banker, 44.5825% Player, 9.5419% Tie in 83 4D cards (6B).
  • DEP185 (EZ Bar-7 EV): -0.9603% Banker, -1.2931% Player, -14.1226% Tie, 0.9355 SD at 60% (6C).
  • DEP185 (4D roads): red/blue marks log Big Road columns, never 20 Rank-0 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 44 0-Value Tens & Faces cards leave a 4D shoe by 60% depth (DEP185), 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-0 stub counts (20/64 in 83 cards); Banker carries a -0.9603% 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