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COMBINATORIAL DEPLETION · 6D · RANK-7 · 75% DEPTH

6-Deck Seven-Pip Card Depletion at 75% Penetration (4% Audit DEP340)

Removing 21 of 24 Seven-Pip Card (Rank-7) cards at 75% penetration of a 6-deck (312-card) shoe leaves 3 Rank-7 cards inside a 78-card stub (DEP340), producing 45.8610% Banker wins, 44.5942% Player wins, 9.5448% Ties, and a 0.5676% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5676%
Player EV (1:1)
-1.2669%
Rank-7 in 78-Card Stub
3/24
Single-Hand Std Dev
0.9391
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPBPBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP340 (6D Rank-7 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

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 (DEP340)
78 / 312 Cards

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

Rank-7 Remaining
3 of 24 Cards

21 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 6D pack.

Banker EV (4% Vig)
-0.5676%

Resolved at 45.8610% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2669%

Resolved at 44.5942% Player win rate with 0.9391 unit standard deviation.

Tie Incidence (8:1)
9.5448%

Produces a 14.0967% house hold on the 8-to-1 Tie wager in state DEP340.

FINITE-SHOE ENUMERATION · DEP340

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

Finite-shoe specification DEP340 tracks Rank-7 removal at 75% depth in 6-deck play: with 3 of 24 Seven-Pip Card cards left in the 78-card stub, Tie incidence is 9.5448% and Banker expectation settles at -0.5676% (4% Vig).

Tableau audit DEP340 confirms that player stands pat on (dep340) two-card 7, and a player (6d-75%) third-card 7 is the highest (dep340·6d-75%) card that forces banker 4, 5, and 6 to draw. Inside the 78-card 6D stub (75% depth, 3/24 Rank-7 remaining, -0.83 bps slope), standard deviation is 0.9391 under 4% Vig.

State DEP340 (6D, 75% depth, 3/24 Rank-7 left, 4% Vig)
Wager / MetricState DEP340 Value6D BaselineSettlement Note
DEP340 Banker (4% Vig)45.8610% (-0.5676% EV)45.8648%DEP340 6D 75% (3 Rank-7)
DEP340 Player (1:1)44.5942% (-1.2669% EV)44.5903%DEP340 78-card 6D stub (0.9391 SD)
DEP340 Tie (8:1)9.5448% (-14.0967% EV)9.5449%DEP340 Rank-7 (21 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP340

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP340 · 6D)

Across 100-hand session horizons at state DEP340 (6D 75% depth, 3/24 Rank-7 in 78 cards), single-hand dispersion (0.9391 SD) dominates the 0.5676% (4% Vig) Banker and 1.2669% Player expectation gap.

  • DEP340 (6D 75%): 78/312 cards with 3/24 Rank-7 (4A).
  • DEP340 (Rank-7 split): 45.8610% Banker, 44.5942% Player, 9.5448% Tie in 78 6D cards (4B).
  • DEP340 (4% Vig EV): -0.5676% Banker, -1.2669% Player, -14.0967% Tie, 0.9391 SD at 75% (4C).
  • DEP340 (6D roads): red/blue marks log Big Road columns, never 3 Rank-7 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 21 Seven-Pip Card cards leave a 6D shoe by 75% depth (DEP340), 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-7 stub counts (3/24 in 78 cards); Banker carries a -0.5676% 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