Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 4D Rank-5 Depletion at 50% Depth (Super 6)
COMBINATORIAL DEPLETION · 4D · RANK-5 · 50% DEPTH

4-Deck Five-Pip Card Depletion at 50% Penetration (Super 6 Audit DEP229)

Removing 9 of 16 Five-Pip Card (Rank-5) cards at 50% penetration of a 4-deck (208-card) shoe leaves 7 Rank-5 cards inside a 104-card stub (DEP229), producing 45.8711% Banker wins, 44.5872% Player wins, 9.5417% Ties, and a 1.4091% Banker house edge under Super 6.

Banker EV (Super 6)
-1.4091%
Player EV (1:1)
-1.2839%
Rank-5 in 104-Card Stub
7/16
Single-Hand Std Dev
0.9360
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 DEP229 (4D Rank-5 at 50% 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 (DEP229)
104 / 208 Cards

50% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).

Rank-5 Remaining
7 of 16 Cards

9 5-pip cards (final mandatory Player draw threshold) removed from the 4D pack.

Banker EV (Super 6)
-1.4091%

Resolved at 45.8711% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.2839%

Resolved at 44.5872% Player win rate with 0.9360 unit standard deviation.

Tie Incidence (8:1)
9.5417%

Produces a 14.1243% house hold on the 8-to-1 Tie wager in state DEP229.

FINITE-SHOE ENUMERATION · DEP229

How Five-Pip Card Depletion at 50% Depth Impacts 4D (Super 6)

At 50% penetration of a 208-card (4D) shoe, state DEP229 isolates 9 dealt Rank-5 cards (7 remaining inside 104 stub cards), yielding 45.8711% Banker wins, 44.5872% Player wins, and 0.9360 per-hand standard deviation under Super 6.

Fewer 5s in the (DEP229-Rank-5) stub reduce Banker third-card improvements (104c) from 3 to 8 and (DEP229-Rank-5·104c) from 4 to 9. Because 9 of 16 Five-Pip Card cards are absent in DEP229 at 50% 4D penetration (104 cards left), per-card sensitivity (-0.84 bps) interacts directly with mid-shoe 50% penetration depth (DEP229) under Super 6 no-commission rules (Rank-5) (winning Banker 6 pays 0.50:1) (DEP229·Rank-5).

State DEP229 (4D, 50% depth, 7/16 Rank-5 left, Super 6)
Wager / MetricState DEP229 Value4D BaselineSettlement Note
DEP229 Banker (Super 6)45.8711% (-1.4091% EV)45.8732%DEP229 4D 50% (7 Rank-5)
DEP229 Player (1:1)44.5872% (-1.2839% EV)44.5850%DEP229 104-card 4D stub (0.9360 SD)
DEP229 Tie (8:1)9.5417% (-14.1243% EV)9.5418%DEP229 Rank-5 (9 out, 7 in)
TABLEAU & SCOREBOARD SEPARATION · DEP229

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP229 · 4D)

In DEP229, the 104-card 4D stub (50% penetration, 9 of 16 Rank-5 dealt) yields 45.8711% Banker, 44.5872% Player, and 9.5417% Tie outcomes with 0.9360 dispersion under Super 6.

  • DEP229 (4D 50%): 104/208 cards with 7/16 Rank-5 (2A).
  • DEP229 (Rank-5 split): 45.8711% Banker, 44.5872% Player, 9.5417% Tie in 104 4D cards (2B).
  • DEP229 (Super 6 EV): -1.4091% Banker, -1.2839% Player, -14.1243% Tie, 0.9360 SD at 50% (2C).
  • DEP229 (4D roads): red/blue marks log Big Road columns, never 7 Rank-5 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 9 Five-Pip Card cards leave a 4D shoe by 50% depth (DEP229), 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-5 stub counts (7/16 in 104 cards); Banker carries a -1.4091% expectation under Super 6.
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