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COMBINATORIAL DEPLETION · 6D · RANK-0 · 75% DEPTH

6-Deck 0-Value Tens & Faces Depletion at 75% Penetration (4% Audit DEP277)

Removing 83 of 96 0-Value Tens & Faces (Rank-0) cards at 75% penetration of a 6-deck (312-card) shoe leaves 13 Rank-0 cards inside a 78-card stub (DEP277), producing 45.8680% Banker wins, 44.5869% Player wins, 9.5451% Ties, and a 0.5536% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5536%
Player EV (1:1)
-1.2812%
Rank-0 in 78-Card Stub
13/96
Single-Hand Std Dev
0.9370
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 DEP277 (6D Rank-0 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

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 (DEP277)
78 / 312 Cards

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

Rank-0 Remaining
13 of 96 Cards

83 10, Jack, Queen, and King (zero-point cards) removed from the 6D pack.

Banker EV (4% Vig)
-0.5536%

Resolved at 45.8680% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2812%

Resolved at 44.5869% Player win rate with 0.9370 unit standard deviation.

Tie Incidence (8:1)
9.5451%

Produces a 14.0943% house hold on the 8-to-1 Tie wager in state DEP277.

FINITE-SHOE ENUMERATION · DEP277

How 0-Value Tens & Faces Depletion at 75% Depth Impacts 6D (4% Vig)

Removing 83 of 96 Rank-0 cards by the 75% mark of a 6-deck shoe (DEP277, 78 cards left) leaves 13 0-Value Tens & Faces cards and adjusts conditional probabilities to 45.8680% Banker, 44.5869% Player, and 9.5451% Tie under 4%.

Under the fixed third-card tableau for DEP277, depleting zero-point cards reduces (dep277) modulo-10 standoffs and alters two-card (6d-75%) natural combinations paired with 8s (dep277·6d-75%) and 9s. With 13 Rank-0 cards inside 78 remaining 6D cards (75% dealt), single-card slope (+0.18 bps) keeps Banker house edge at 0.5536% and Player at 1.2812%.

State DEP277 (6D, 75% depth, 13/96 Rank-0 left, 4% Vig)
Wager / MetricState DEP277 Value6D BaselineSettlement Note
DEP277 Banker (4% Vig)45.8680% (-0.5536% EV)45.8648%DEP277 6D 75% (13 Rank-0)
DEP277 Player (1:1)44.5869% (-1.2812% EV)44.5903%DEP277 78-card 6D stub (0.9370 SD)
DEP277 Tie (8:1)9.5451% (-14.0943% EV)9.5449%DEP277 Rank-0 (83 out, 13 in)
TABLEAU & SCOREBOARD SEPARATION · DEP277

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP277 · 6D)

Synthesizing DEP277 (6D at 75% depth, 13 0-Value Tens & Faces cards left inside 78 stub cards): 4% rules produce a 0.5536% Banker edge, 1.2812% Player edge, 14.0943% Tie edge, and 0.9370 unit volatility.

  • DEP277 (6D 75%): 78/312 cards with 13/96 Rank-0 (4A).
  • DEP277 (Rank-0 split): 45.8680% Banker, 44.5869% Player, 9.5451% Tie in 78 6D cards (4B).
  • DEP277 (4% Vig EV): -0.5536% Banker, -1.2812% Player, -14.0943% Tie, 0.9370 SD at 75% (4C).
  • DEP277 (6D roads): red/blue marks log Big Road columns, never 13 Rank-0 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 83 0-Value Tens & Faces cards leave a 6D shoe by 75% depth (DEP277), 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-0 stub counts (13/96 in 78 cards); Banker carries a -0.5536% 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