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COMBINATORIAL DEPLETION · 4D · RANK-7 · 25% DEPTH

4-Deck Seven-Pip Card Depletion at 25% Penetration (5% Audit DEP245)

Removing 5 of 16 Seven-Pip Card (Rank-7) cards at 25% penetration of a 4-deck (208-card) shoe leaves 11 Rank-7 cards inside a 156-card stub (DEP245), producing 45.8722% Banker wins, 44.5860% Player wins, 9.5418% Ties, and a 1.0074% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0074%
Player EV (1:1)
-1.2862%
Rank-7 in 156-Card Stub
11/16
Single-Hand Std Dev
0.9341
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 DEP245 (4D Rank-7 at 25% 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 (DEP245)
156 / 208 Cards

25% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).

Rank-7 Remaining
11 of 16 Cards

5 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 4D pack.

Banker EV (5% Vig)
-1.0074%

Resolved at 45.8722% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2862%

Resolved at 44.5860% Player win rate with 0.9341 unit standard deviation.

Tie Incidence (8:1)
9.5418%

Produces a 14.1240% house hold on the 8-to-1 Tie wager in state DEP245.

FINITE-SHOE ENUMERATION · DEP245

How Seven-Pip Card Depletion at 25% Depth Impacts 4D (5% Vig)

Card-removal benchmark DEP245 measures Seven-Pip Card (Rank-7) scarcity at 25% depth in a 4-deck shoe: 5 removed ranks leave 11 in the 156-card remainder, shifting Banker win share to 45.8722% (1.0074% edge, 5% Vig).

For DEP245 (4-deck shoe, 25% dealt), player stands pat on (dep245) two-card 7, and a player (4d-25%) third-card 7 is the highest (dep245·4d-25%) card that forces banker 4, 5, and 6 to draw. Holding 11 of 16 Rank-7 cards in a 156-card stub with -0.83 bps rank slope yields 45.8722% Banker, 44.5860% Player, and 9.5418% Tie.

State DEP245 (4D, 25% depth, 11/16 Rank-7 left, 5% Vig)
Wager / MetricState DEP245 Value4D BaselineSettlement Note
DEP245 Banker (5% Vig)45.8722% (-1.0074% EV)45.8732%DEP245 4D 25% (11 Rank-7)
DEP245 Player (1:1)44.5860% (-1.2862% EV)44.5850%DEP245 156-card 4D stub (0.9341 SD)
DEP245 Tie (8:1)9.5418% (-14.1240% EV)9.5418%DEP245 Rank-7 (5 out, 11 in)
TABLEAU & SCOREBOARD SEPARATION · DEP245

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP245 · 4D)

While DEP245 tracks 5 removed Seven-Pip Card cards across 25% of a 208-card (4D) shoe (156 remaining, 1.0074% 5% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP245 (4D 25%): 156/208 cards with 11/16 Rank-7 (5A).
  • DEP245 (Rank-7 split): 45.8722% Banker, 44.5860% Player, 9.5418% Tie in 156 4D cards (5B).
  • DEP245 (5% Vig EV): -1.0074% Banker, -1.2862% Player, -14.1240% Tie, 0.9341 SD at 25% (5C).
  • DEP245 (4D roads): red/blue marks log Big Road columns, never 11 Rank-7 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 5 Seven-Pip Card cards leave a 4D shoe by 25% depth (DEP245), 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-7 stub counts (11/16 in 156 cards); Banker carries a -1.0074% 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