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COMBINATORIAL DEPLETION · 6D · RANK-8 · 75% DEPTH

6-Deck Eight-Pip Card Depletion at 75% Penetration (4% Audit DEP349)

Removing 21 of 24 Eight-Pip Card (Rank-8) cards at 75% penetration of a 6-deck (312-card) shoe leaves 3 Rank-8 cards inside a 78-card stub (DEP349), producing 45.8625% Banker wins, 44.5927% Player wins, 9.5448% Ties, and a 0.5646% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5646%
Player EV (1:1)
-1.2699%
Rank-8 in 78-Card Stub
3/24
Single-Hand Std Dev
0.9394
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBPBBPPBPBBPPBP) illustrating derived-road symmetry checks alongside DEP349 (6D Rank-8 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

Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #2

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

  1. Column 5 goes down to Row 2, so use Rule 2: look 3 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.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP349)
78 / 312 Cards

75% penetration depth in 6D (six-deck Mini-Baccarat and Midi-Baccarat North American floors).

Rank-8 Remaining
3 of 24 Cards

21 8-pip cards (Natural 8 generator and Banker 3 block) removed from the 6D pack.

Banker EV (4% Vig)
-0.5646%

Resolved at 45.8625% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2699%

Resolved at 44.5927% Player win rate with 0.9394 unit standard deviation.

Tie Incidence (8:1)
9.5448%

Produces a 14.0967% house hold on the 8-to-1 Tie wager in state DEP349.

FINITE-SHOE ENUMERATION · DEP349

How Eight-Pip Card Depletion at 75% Depth Impacts 6D (4% Vig)

Shoe-stub analysis DEP349 inspects 78 remaining cards at 75% penetration of a 312-card (6D) pack after 21 Eight-Pip Card cards have cleared, leaving 3 Rank-8 cards and a 0.5646% 4% Banker edge.

Tracking DEP349 across 78 remaining 6D cards (75% depth) shows that depleting 8-pip cards also (dep349-rank-8) lowers two-card natural 8 lockouts (78c) when paired with zero-point tens (dep349-rank-8·78c) and court cards. With 21 Rank-8 cards gone (-0.50 bps unit sensitivity), Banker expectation is -0.5646% (4% Vig) vs -1.2699% on Player.

State DEP349 (6D, 75% depth, 3/24 Rank-8 left, 4% Vig)
Wager / MetricState DEP349 Value6D BaselineSettlement Note
DEP349 Banker (4% Vig)45.8625% (-0.5646% EV)45.8648%DEP349 6D 75% (3 Rank-8)
DEP349 Player (1:1)44.5927% (-1.2699% EV)44.5903%DEP349 78-card 6D stub (0.9394 SD)
DEP349 Tie (8:1)9.5448% (-14.0967% EV)9.5449%DEP349 Rank-8 (21 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP349

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP349 · 6D)

In DEP349, the 78-card 6D stub (75% penetration, 21 of 24 Rank-8 dealt) yields 45.8625% Banker, 44.5927% Player, and 9.5448% Tie outcomes with 0.9394 dispersion under 4% Vig.

  • DEP349 (6D 75%): 78/312 cards with 3/24 Rank-8 (7A).
  • DEP349 (Rank-8 split): 45.8625% Banker, 44.5927% Player, 9.5448% Tie in 78 6D cards (7B).
  • DEP349 (4% Vig EV): -0.5646% Banker, -1.2699% Player, -14.0967% Tie, 0.9394 SD at 75% (7C).
  • DEP349 (6D roads): red/blue marks log Big Road columns, never 3 Rank-8 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 21 Eight-Pip Card cards leave a 6D shoe by 75% depth (DEP349), 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-8 stub counts (3/24 in 78 cards); Banker carries a -0.5646% 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