Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 2D Rank-4 Depletion at 80% Depth (Super 6)
COMBINATORIAL DEPLETION · 2D · RANK-4 · 80% DEPTH

2-Deck Four-Pip Card Depletion at 80% Penetration (Super 6 Audit DEP134)

Removing 7 of 8 Four-Pip Card (Rank-4) cards at 80% penetration of a 2-deck (104-card) shoe leaves 1 Rank-4 cards inside a 21-card stub (DEP134), producing 45.9054% Banker wins, 44.5620% Player wins, 9.5327% Ties, and a 1.3496% Banker house edge under Super 6.

Banker EV (Super 6)
-1.3496%
Player EV (1:1)
-1.3434%
Rank-4 in 21-Card Stub
1/8
Single-Hand Std Dev
0.9387
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBBPPPBBPBTBPBPP) illustrating derived-road symmetry checks alongside DEP134 (2D Rank-4 at 80% 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 (DEP134)
21 / 104 Cards

80% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Rank-4 Remaining
1 of 8 Cards

7 4-pip cards (strongest pro-Banker removal sensitivity) removed from the 2D pack.

Banker EV (Super 6)
-1.3496%

Resolved at 45.9054% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.3434%

Resolved at 44.5620% Player win rate with 0.9387 unit standard deviation.

Tie Incidence (8:1)
9.5327%

Produces a 14.2058% house hold on the 8-to-1 Tie wager in state DEP134.

FINITE-SHOE ENUMERATION · DEP134

How Four-Pip Card Depletion at 80% Depth Impacts 2D (Super 6)

Within double-deck European salon privé carriers and two-deck shoe pits, profile DEP134 examines 80% shoe depletion (21 of 104 cards remaining) after 7 Rank-4 cards exit, leaving 1 Four-Pip Card cards and a 1.3496% Banker house hold under Super 6.

For DEP134 (2-deck shoe, 80% dealt), rank 4 sits at (dep134) the exact pivot where banker (2d-80%) 5 begins drawing (player third (dep134·2d-80%) card 4–7) while banker 3 and 4 also draw. Holding 1 of 8 Rank-4 cards in a 21-card stub with +1.19 bps rank slope yields 45.9054% Banker, 44.5620% Player, and 9.5327% Tie.

State DEP134 (2D, 80% depth, 1/8 Rank-4 left, Super 6)
Wager / MetricState DEP134 Value2D BaselineSettlement Note
DEP134 Banker (Super 6)45.9054% (-1.3496% EV)45.8998%DEP134 2D 80% (1 Rank-4)
DEP134 Player (1:1)44.5620% (-1.3434% EV)44.5676%DEP134 21-card 2D stub (0.9387 SD)
DEP134 Tie (8:1)9.5327% (-14.2058% EV)9.5326%DEP134 Rank-4 (7 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP134

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP134 · 2D)

Learners auditing DEP134 (2D at 80% depth, 1/8 Rank-4 in 21 stub cards) can verify that Super 6 house hold (1.3496% Banker, 1.3434% Player, 14.2058% Tie) operates independently of prior Big Road streaks.

  • DEP134 (2D 80%): 21/104 cards with 1/8 Rank-4 (3A).
  • DEP134 (Rank-4 split): 45.9054% Banker, 44.5620% Player, 9.5327% Tie in 21 2D cards (3B).
  • DEP134 (Super 6 EV): -1.3496% Banker, -1.3434% Player, -14.2058% Tie, 0.9387 SD at 80% (3C).
  • DEP134 (2D roads): red/blue marks log Big Road columns, never 1 Rank-4 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Four-Pip Card cards leave a 2D shoe by 80% depth (DEP134), 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 (1/8 in 21 cards); Banker carries a -1.3496% 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