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COMBINATORIAL DEPLETION · 4D · RANK-0 · 10% DEPTH

4-Deck 0-Value Tens & Faces Depletion at 10% Penetration (5% Audit DEP181)

Removing 7 of 64 0-Value Tens & Faces (Rank-0) cards at 10% penetration of a 4-deck (208-card) shoe leaves 57 Rank-0 cards inside a 187-card stub (DEP181), producing 45.8735% Banker wins, 44.5847% Player wins, 9.5418% Ties, and a 1.0049% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0049%
Player EV (1:1)
-1.2888%
Rank-0 in 187-Card Stub
57/64
Single-Hand Std Dev
0.9305
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPPBBBPPBPTBPBBP) illustrating derived-road symmetry checks alongside DEP181 (4D Rank-0 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

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

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

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

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 (DEP181)
187 / 208 Cards

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

Rank-0 Remaining
57 of 64 Cards

7 10, Jack, Queen, and King (zero-point cards) removed from the 4D pack.

Banker EV (5% Vig)
-1.0049%

Resolved at 45.8735% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2888%

Resolved at 44.5847% Player win rate with 0.9305 unit standard deviation.

Tie Incidence (8:1)
9.5418%

Produces a 14.1237% house hold on the 8-to-1 Tie wager in state DEP181.

FINITE-SHOE ENUMERATION · DEP181

How 0-Value Tens & Faces Depletion at 10% Depth Impacts 4D (5% Vig)

Shoe-stub analysis DEP181 inspects 187 remaining cards at 10% penetration of a 208-card (4D) pack after 7 0-Value Tens & Faces cards have cleared, leaving 57 Rank-0 cards and a 1.0049% 5% Banker edge.

For DEP181 (4-deck shoe, 10% dealt), depleting zero-point cards reduces (dep181) modulo-10 standoffs and alters two-card (4d-10%) natural combinations paired with 8s (dep181·4d-10%) and 9s. Holding 57 of 64 Rank-0 cards in a 187-card stub with +0.18 bps rank slope yields 45.8735% Banker, 44.5847% Player, and 9.5418% Tie.

State DEP181 (4D, 10% depth, 57/64 Rank-0 left, 5% Vig)
Wager / MetricState DEP181 Value4D BaselineSettlement Note
DEP181 Banker (5% Vig)45.8735% (-1.0049% EV)45.8732%DEP181 4D 10% (57 Rank-0)
DEP181 Player (1:1)44.5847% (-1.2888% EV)44.5850%DEP181 187-card 4D stub (0.9305 SD)
DEP181 Tie (8:1)9.5418% (-14.1237% EV)9.5418%DEP181 Rank-0 (7 out, 57 in)
TABLEAU & SCOREBOARD SEPARATION · DEP181

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP181 · 4D)

On the electronic scoreboard for DEP181 (4D, 10% depth, 187 cards left), Bead Plate and Big Road circles record Banker (45.8735%) and Player (44.5847%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Rank-0 card counts (57/64).

  • DEP181 (4D 10%): 187/208 cards with 57/64 Rank-0 (7A).
  • DEP181 (Rank-0 split): 45.8735% Banker, 44.5847% Player, 9.5418% Tie in 187 4D cards (7B).
  • DEP181 (5% Vig EV): -1.0049% Banker, -1.2888% Player, -14.1237% Tie, 0.9305 SD at 10% (7C).
  • DEP181 (4D roads): red/blue marks log Big Road columns, never 57 Rank-0 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 7 0-Value Tens & Faces cards leave a 4D shoe by 10% depth (DEP181), 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 (57/64 in 187 cards); Banker carries a -1.0049% 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