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COMBINATORIAL DEPLETION · 4D · RANK-4 · 75% DEPTH

4-Deck Four-Pip Card Depletion at 75% Penetration (4% Audit DEP223)

Removing 14 of 16 Four-Pip Card (Rank-4) cards at 75% penetration of a 4-deck (208-card) shoe leaves 2 Rank-4 cards inside a 52-card stub (DEP223), producing 45.8786% Banker wins, 44.5795% Player wins, 9.5419% Ties, and a 0.5360% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5360%
Player EV (1:1)
-1.2991%
Rank-4 in 52-Card Stub
2/16
Single-Hand Std Dev
0.9382
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 P B B P B
Big Eye Boy = = = = = = ≠ = = = = = = =
Small Road = = = = = = ≠ ≠ = = = =
Cockroach Pig = = = = = = ≠ ≠ ≠ =

Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP223 (4D Rank-4 at 75% 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 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 4 starts, so use Rule 1: compare Column 3 with Column 1, 2 columns further back.
  2. Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.

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 (DEP223)
52 / 208 Cards

75% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).

Rank-4 Remaining
2 of 16 Cards

14 4-pip cards (strongest pro-Banker removal sensitivity) removed from the 4D pack.

Banker EV (4% Vig)
-0.5360%

Resolved at 45.8786% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2991%

Resolved at 44.5795% Player win rate with 0.9382 unit standard deviation.

Tie Incidence (8:1)
9.5419%

Produces a 14.1230% house hold on the 8-to-1 Tie wager in state DEP223.

FINITE-SHOE ENUMERATION · DEP223

How Four-Pip Card Depletion at 75% Depth Impacts 4D (4% Vig)

Shoe-stub analysis DEP223 inspects 52 remaining cards at 75% penetration of a 208-card (4D) pack after 14 Four-Pip Card cards have cleared, leaving 2 Rank-4 cards and a 0.5360% 4% Banker edge.

For DEP223 (4-deck shoe, 75% dealt), rank 4 sits at (dep223) the exact pivot where banker (4d-75%) 5 begins drawing (player third (dep223·4d-75%) card 4–7) while banker 3 and 4 also draw. Holding 2 of 16 Rank-4 cards in a 52-card stub with +1.19 bps rank slope yields 45.8786% Banker, 44.5795% Player, and 9.5419% Tie.

State DEP223 (4D, 75% depth, 2/16 Rank-4 left, 4% Vig)
Wager / MetricState DEP223 Value4D BaselineSettlement Note
DEP223 Banker (4% Vig)45.8786% (-0.5360% EV)45.8732%DEP223 4D 75% (2 Rank-4)
DEP223 Player (1:1)44.5795% (-1.2991% EV)44.5850%DEP223 52-card 4D stub (0.9382 SD)
DEP223 Tie (8:1)9.5419% (-14.1230% EV)9.5418%DEP223 Rank-4 (14 out, 2 in)
TABLEAU & SCOREBOARD SEPARATION · DEP223

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP223 · 4D)

Even at 75% penetration in DEP223 where 14 Rank-4 cards have exited a 4D shoe (2 left in 52 cards), derived-road red and blue entries measure structural regularity on the Big Road—not whether Banker (-0.5360% EV, 4% Vig) or Player (-1.2991% EV) is favored next.

  • DEP223 (4D 75%): 52/208 cards with 2/16 Rank-4 (7A).
  • DEP223 (Rank-4 split): 45.8786% Banker, 44.5795% Player, 9.5419% Tie in 52 4D cards (7B).
  • DEP223 (4% Vig EV): -0.5360% Banker, -1.2991% Player, -14.1230% Tie, 0.9382 SD at 75% (7C).
  • DEP223 (4D roads): red/blue marks log Big Road columns, never 2 Rank-4 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 14 Four-Pip Card cards leave a 4D shoe by 75% depth (DEP223), 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-4 stub counts (2/16 in 52 cards); Banker carries a -0.5360% expectation under 4%.
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