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COMBINATORIAL DEPLETION · 1D · RANK-6 · 60% DEPTH

1-Deck Six-Pip Card Depletion at 60% Penetration (EZ Baccarat Audit DEP059)

Removing 3 of 4 Six-Pip Card (Rank-6) cards at 60% penetration of a 1-deck (52-card) shoe leaves 1 Rank-6 cards inside a 21-card stub (DEP059), producing 45.9554% Banker wins, 44.5290% Player wins, 9.5155% Ties, and a 0.8270% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.8270%
Player EV (1:1)
-1.4264%
Rank-6 in 21-Card Stub
1/4
Single-Hand Std Dev
0.9373
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBBBBPPPPBBPPBP) illustrating derived-road symmetry checks alongside DEP059 (1D Rank-6 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

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

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

  1. Column 4 goes down to Row 3, so use Rule 2: look 3 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.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP059)
21 / 52 Cards

60% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-6 Remaining
1 of 4 Cards

3 6-pip cards (standing threshold and Banker 6 trigger) removed from the 1D pack.

Banker EV (EZ Bar-7)
-0.8270%

Resolved at 45.9554% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.4264%

Resolved at 44.5290% Player win rate with 0.9373 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3602% house hold on the 8-to-1 Tie wager in state DEP059.

FINITE-SHOE ENUMERATION · DEP059

How Six-Pip Card Depletion at 60% Depth Impacts 1D (EZ Bar-7)

When a 1D shoe reaches 60% cut-card depth (21 of 52 cards undealt, state DEP059) with 3 Six-Pip Card cards removed and 1 remaining, Player wins 44.5290% (1.4264% edge) while Banker wins 45.9554% (0.8270% edge under EZ Baccarat).

Banker 6 only draws (DEP059) when Player pulls a third-card (1D-60%) 6 or 7; depleting 6s (DEP059·1D-60%) directly alters both Banker 6 draws and Super 6 settlement frequency. In state DEP059 (1D, 60% depth), each removed Rank-6 card applies a -1.13 bps baseline directional pressure before scaling to the 21-card remainder (1 Rank-6 left), while Banker wins pay 1:1 (DEP059-1D) with zero commission except when (1/4) Banker wins with a three-card (DEP059-1D·1/4) total of 7, which pushes.

State DEP059 (1D, 60% depth, 1/4 Rank-6 left, EZ Bar-7)
Wager / MetricState DEP059 Value1D BaselineSettlement Note
DEP059 Banker (EZ Bar-7)45.9554% (-0.8270% EV)45.9595%DEP059 1D 60% (1 Rank-6)
DEP059 Player (1:1)44.5290% (-1.4264% EV)44.5249%DEP059 21-card 1D stub (0.9373 SD)
DEP059 Tie (8:1)9.5155% (-14.3602% EV)9.5156%DEP059 Rank-6 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP059

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP059 · 1D)

Learners auditing DEP059 (1D at 60% depth, 1/4 Rank-6 in 21 stub cards) can verify that EZ Baccarat house hold (0.8270% Banker, 1.4264% Player, 14.3602% Tie) operates independently of prior Big Road streaks.

  • DEP059 (1D 60%): 21/52 cards with 1/4 Rank-6 (6A).
  • DEP059 (Rank-6 split): 45.9554% Banker, 44.5290% Player, 9.5155% Tie in 21 1D cards (6B).
  • DEP059 (EZ Bar-7 EV): -0.8270% Banker, -1.4264% Player, -14.3602% Tie, 0.9373 SD at 60% (6C).
  • DEP059 (1D roads): red/blue marks log Big Road columns, never 1 Rank-6 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Six-Pip Card cards leave a 1D shoe by 60% depth (DEP059), 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-6 stub counts (1/4 in 21 cards); Banker carries a -0.8270% 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