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COMBINATORIAL DEPLETION · 6D · RANK-6 · 40% DEPTH

6-Deck Six-Pip Card Depletion at 40% Penetration (4% Audit DEP327)

Removing 11 of 24 Six-Pip Card (Rank-6) cards at 40% penetration of a 6-deck (312-card) shoe leaves 13 Rank-6 cards inside a 187-card stub (DEP327), producing 45.8626% Banker wins, 44.5925% Player wins, 9.5449% Ties, and a 0.5645% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5645%
Player EV (1:1)
-1.2700%
Rank-6 in 187-Card Stub
13/24
Single-Hand Std Dev
0.9353
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 B P B P P B B P P B P
Big Eye Boy = = = = ≠ = = = ≠ ≠ = = = = ≠
Small Road = = ≠ ≠ = = ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP327 (6D Rank-6 at 40% 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 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP327)
187 / 312 Cards

40% penetration depth in 6D (six-deck Mini-Baccarat and Midi-Baccarat North American floors).

Rank-6 Remaining
13 of 24 Cards

11 6-pip cards (standing threshold and Banker 6 trigger) removed from the 6D pack.

Banker EV (4% Vig)
-0.5645%

Resolved at 45.8626% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2700%

Resolved at 44.5925% Player win rate with 0.9353 unit standard deviation.

Tie Incidence (8:1)
9.5449%

Produces a 14.0963% house hold on the 8-to-1 Tie wager in state DEP327.

FINITE-SHOE ENUMERATION · DEP327

How Six-Pip Card Depletion at 40% Depth Impacts 6D (4% Vig)

At 40% penetration of a 312-card (6D) shoe, state DEP327 isolates 11 dealt Rank-6 cards (13 remaining inside 187 stub cards), yielding 45.8626% Banker wins, 44.5925% Player wins, and 0.9353 per-hand standard deviation under 4%.

Combinatorial weighting in DEP327 (187 cards left from 312 at 40% depth) is governed by two rules: banker 6 only draws (dep327) when player pulls a third-card (6d-40%) 6 or 7; depleting 6s (dep327·6d-40%) directly alters both banker 6 draws and super 6 settlement frequency, and winning banker wagers collect (dep327-6d) 0.96 units per unit staked (13/24) with 60% of the shoe (dep327-6d·13/24) still inside the acrylic carrier (-1.13 bps per Rank-6 removed).

State DEP327 (6D, 40% depth, 13/24 Rank-6 left, 4% Vig)
Wager / MetricState DEP327 Value6D BaselineSettlement Note
DEP327 Banker (4% Vig)45.8626% (-0.5645% EV)45.8648%DEP327 6D 40% (13 Rank-6)
DEP327 Player (1:1)44.5925% (-1.2700% EV)44.5903%DEP327 187-card 6D stub (0.9353 SD)
DEP327 Tie (8:1)9.5449% (-14.0963% EV)9.5449%DEP327 Rank-6 (11 out, 13 in)
TABLEAU & SCOREBOARD SEPARATION · DEP327

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP327 · 6D)

In studio and floor audits of DEP327 (187 cards undealt out of 312 in 6D at 40% depth), a 0.9353 unit standard deviation accompanies the 13-card Rank-6 stub under 4% Vig (45.8626% Banker vs 44.5925% Player).

  • DEP327 (6D 40%): 187/312 cards with 13/24 Rank-6 (2A).
  • DEP327 (Rank-6 split): 45.8626% Banker, 44.5925% Player, 9.5449% Tie in 187 6D cards (2B).
  • DEP327 (4% Vig EV): -0.5645% Banker, -1.2700% Player, -14.0963% Tie, 0.9353 SD at 40% (2C).
  • DEP327 (6D roads): red/blue marks log Big Road columns, never 13 Rank-6 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 11 Six-Pip Card cards leave a 6D shoe by 40% depth (DEP327), 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-6 stub counts (13/24 in 187 cards); Banker carries a -0.5645% expectation under 4%.
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  • 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