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COMBINATORIAL DEPLETION · 4D · RANK-7 · 75% DEPTH

4-Deck Seven-Pip Card Depletion at 75% Penetration (4% Audit DEP250)

Removing 14 of 16 Seven-Pip Card (Rank-7) cards at 75% penetration of a 4-deck (208-card) shoe leaves 2 Rank-7 cards inside a 52-card stub (DEP250), producing 45.8694% Banker wins, 44.5889% Player wins, 9.5417% Ties, and a 0.5542% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5542%
Player EV (1:1)
-1.2806%
Rank-7 in 52-Card Stub
2/16
Single-Hand Std Dev
0.9391
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPBTBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP250 (4D Rank-7 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

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 columns back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 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 (DEP250)
52 / 208 Cards

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

Rank-7 Remaining
2 of 16 Cards

14 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 4D pack.

Banker EV (4% Vig)
-0.5542%

Resolved at 45.8694% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2806%

Resolved at 44.5889% Player win rate with 0.9391 unit standard deviation.

Tie Incidence (8:1)
9.5417%

Produces a 14.1246% house hold on the 8-to-1 Tie wager in state DEP250.

FINITE-SHOE ENUMERATION · DEP250

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

Exact conditional enumeration DEP250 for a 4D shoe at 75% depth (52/208 cards undealt) with 2 remaining Rank-7 cards confirms a 0.5542% Banker edge (4% Vig), 1.2806% Player edge, and 14.1246% Tie edge.

Because depleting 7s lowers the (dep250-rank-7) rate of winning three-card banker (52c) 7 hands (the barred push (dep250-rank-7·52c) total on ez baccarat tables), state DEP250 (75% 4D depth, 14 Rank-7 removed, 2 in 52 cards) registers a -0.83 bps rank derivative and 0.5542% Banker house edge (4% Vig).

State DEP250 (4D, 75% depth, 2/16 Rank-7 left, 4% Vig)
Wager / MetricState DEP250 Value4D BaselineSettlement Note
DEP250 Banker (4% Vig)45.8694% (-0.5542% EV)45.8732%DEP250 4D 75% (2 Rank-7)
DEP250 Player (1:1)44.5889% (-1.2806% EV)44.5850%DEP250 52-card 4D stub (0.9391 SD)
DEP250 Tie (8:1)9.5417% (-14.1246% EV)9.5418%DEP250 Rank-7 (14 out, 2 in)
TABLEAU & SCOREBOARD SEPARATION · DEP250

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP250 · 4D)

On the electronic scoreboard for DEP250 (4D, 75% depth, 52 cards left), Bead Plate and Big Road circles record Banker (45.8694%) and Player (44.5889%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Rank-7 card counts (2/16).

  • DEP250 (4D 75%): 52/208 cards with 2/16 Rank-7 (2A).
  • DEP250 (Rank-7 split): 45.8694% Banker, 44.5889% Player, 9.5417% Tie in 52 4D cards (2B).
  • DEP250 (4% Vig EV): -0.5542% Banker, -1.2806% Player, -14.1246% Tie, 0.9391 SD at 75% (2C).
  • DEP250 (4D roads): red/blue marks log Big Road columns, never 2 Rank-7 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 14 Seven-Pip Card cards leave a 4D shoe by 75% depth (DEP250), 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 (2/16 in 52 cards); Banker carries a -0.5542% 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