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COMBINATORIAL DEPLETION · 4D · RANK-2 · 70% DEPTH

4-Deck Two-Pip (Deuce) Depletion at 70% Penetration (5% Audit DEP204)

Removing 13 of 16 Two-Pip (Deuce) (Rank-2) cards at 70% penetration of a 4-deck (208-card) shoe leaves 3 Rank-2 cards inside a 62-card stub (DEP204), producing 45.8753% Banker wins, 44.5828% Player wins, 9.5419% Ties, and a 1.0012% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0012%
Player EV (1:1)
-1.2926%
Rank-2 in 62-Card Stub
3/16
Single-Hand Std Dev
0.9371
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPPPPBBBBPPBBPB) illustrating derived-road symmetry checks alongside DEP204 (4D Rank-2 at 70% 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 (DEP204)
62 / 208 Cards

70% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).

Rank-2 Remaining
3 of 16 Cards

13 2-pip cards across all four suits removed from the 4D pack.

Banker EV (5% Vig)
-1.0012%

Resolved at 45.8753% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2926%

Resolved at 44.5828% Player win rate with 0.9371 unit standard deviation.

Tie Incidence (8:1)
9.5419%

Produces a 14.1231% house hold on the 8-to-1 Tie wager in state DEP204.

FINITE-SHOE ENUMERATION · DEP204

How Two-Pip (Deuce) Depletion at 70% Depth Impacts 4D (5% Vig)

Within four-deck Asian VIP salons and compact automatic shuffler shoes, profile DEP204 examines 70% shoe depletion (62 of 208 cards remaining) after 13 Rank-2 cards exit, leaving 3 Two-Pip (Deuce) cards and a 1.0012% Banker house hold under 5%.

Comparing initial 208-card 4D weights against stub DEP204 (62 cards, 70% depth, 3 Rank-2 left) illustrates how on banker total 4, (dep204) banker draws against player third-card (4d-70%) 2 through 7; removing 2s (dep204·4d-70%) trims low-pip player third-card triggers (+0.52 bps slope, 1.0012% 5% Vig edge).

State DEP204 (4D, 70% depth, 3/16 Rank-2 left, 5% Vig)
Wager / MetricState DEP204 Value4D BaselineSettlement Note
DEP204 Banker (5% Vig)45.8753% (-1.0012% EV)45.8732%DEP204 4D 70% (3 Rank-2)
DEP204 Player (1:1)44.5828% (-1.2926% EV)44.5850%DEP204 62-card 4D stub (0.9371 SD)
DEP204 Tie (8:1)9.5419% (-14.1231% EV)9.5418%DEP204 Rank-2 (13 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP204

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP204 · 4D)

Across 100-hand session horizons at state DEP204 (4D 70% depth, 3/16 Rank-2 in 62 cards), single-hand dispersion (0.9371 SD) dominates the 1.0012% (5% Vig) Banker and 1.2926% Player expectation gap.

  • DEP204 (4D 70%): 62/208 cards with 3/16 Rank-2 (3A).
  • DEP204 (Rank-2 split): 45.8753% Banker, 44.5828% Player, 9.5419% Tie in 62 4D cards (3B).
  • DEP204 (5% Vig EV): -1.0012% Banker, -1.2926% Player, -14.1231% Tie, 0.9371 SD at 70% (3C).
  • DEP204 (4D roads): red/blue marks log Big Road columns, never 3 Rank-2 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 13 Two-Pip (Deuce) cards leave a 4D shoe by 70% depth (DEP204), 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-2 stub counts (3/16 in 62 cards); Banker carries a -1.0012% 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