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COMBINATORIAL DEPLETION · 4D · RANK-6 · 10% DEPTH

4-Deck Six-Pip Card Depletion at 10% Penetration (5% Audit DEP235)

Removing 2 of 16 Six-Pip Card (Rank-6) cards at 10% penetration of a 4-deck (208-card) shoe leaves 14 Rank-6 cards inside a 187-card stub (DEP235), producing 45.8727% Banker wins, 44.5855% Player wins, 9.5418% Ties, and a 1.0064% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0064%
Player EV (1:1)
-1.2872%
Rank-6 in 187-Card Stub
14/16
Single-Hand Std Dev
0.9323
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 DEP235 (4D Rank-6 at 10% 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 (DEP235)
187 / 208 Cards

10% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).

Rank-6 Remaining
14 of 16 Cards

2 6-pip cards (standing threshold and Banker 6 trigger) removed from the 4D pack.

Banker EV (5% Vig)
-1.0064%

Resolved at 45.8727% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2872%

Resolved at 44.5855% Player win rate with 0.9323 unit standard deviation.

Tie Incidence (8:1)
9.5418%

Produces a 14.1239% house hold on the 8-to-1 Tie wager in state DEP235.

FINITE-SHOE ENUMERATION · DEP235

How Six-Pip Card Depletion at 10% Depth Impacts 4D (5% Vig)

Removing 2 of 16 Rank-6 cards by the 10% mark of a 4-deck shoe (DEP235, 187 cards left) leaves 14 Six-Pip Card cards and adjusts conditional probabilities to 45.8727% Banker, 44.5855% Player, and 9.5418% Tie under 5%.

Mechanical draw trees in DEP235 reflect how removing 6-pip cards produces (dep235-rank-6) the strongest per-card shift toward (187c) the player side and reduces (dep235-rank-6·187c) barred banker 6 incidence. At 10% 4D depth (14 Rank-6 left of 16 in 187 cards, -1.13 bps slope), winning banker tickets pay (dep235-4d) 0.95 units per unit staked (14/16) while 90% of the initial (dep235-4d·14/16) shoe remains undealt.

State DEP235 (4D, 10% depth, 14/16 Rank-6 left, 5% Vig)
Wager / MetricState DEP235 Value4D BaselineSettlement Note
DEP235 Banker (5% Vig)45.8727% (-1.0064% EV)45.8732%DEP235 4D 10% (14 Rank-6)
DEP235 Player (1:1)44.5855% (-1.2872% EV)44.5850%DEP235 187-card 4D stub (0.9323 SD)
DEP235 Tie (8:1)9.5418% (-14.1239% EV)9.5418%DEP235 Rank-6 (2 out, 14 in)
TABLEAU & SCOREBOARD SEPARATION · DEP235

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP235 · 4D)

On the electronic scoreboard for DEP235 (4D, 10% depth, 187 cards left), Bead Plate and Big Road circles record Banker (45.8727%) and Player (44.5855%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Rank-6 card counts (14/16).

  • DEP235 (4D 10%): 187/208 cards with 14/16 Rank-6 (4A).
  • DEP235 (Rank-6 split): 45.8727% Banker, 44.5855% Player, 9.5418% Tie in 187 4D cards (4B).
  • DEP235 (5% Vig EV): -1.0064% Banker, -1.2872% Player, -14.1239% Tie, 0.9323 SD at 10% (4C).
  • DEP235 (4D roads): red/blue marks log Big Road columns, never 14 Rank-6 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 2 Six-Pip Card cards leave a 4D shoe by 10% depth (DEP235), 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 (14/16 in 187 cards); Banker carries a -1.0064% expectation under 5%.
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