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COMBINATORIAL DEPLETION · 6D · RANK-7 · 25% DEPTH

6-Deck Seven-Pip Card Depletion at 25% Penetration (5% Audit DEP335)

Removing 7 of 24 Seven-Pip Card (Rank-7) cards at 25% penetration of a 6-deck (312-card) shoe leaves 17 Rank-7 cards inside a 234-card stub (DEP335), producing 45.8639% Banker wins, 44.5913% Player wins, 9.5449% Ties, and a 1.0206% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0206%
Player EV (1:1)
-1.2726%
Rank-7 in 234-Card Stub
17/24
Single-Hand Std Dev
0.9341
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 P B B P P B B P B
Big Eye Boy = = = = = = ≠ = = = = = = =
Small Road = = = = = = ≠ ≠ = = = =
Cockroach Pig = = = = = = ≠ ≠ ≠ =

Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP335 (6D Rank-7 at 25% 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 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 (DEP335)
234 / 312 Cards

25% penetration depth in 6D (six-deck Mini-Baccarat and Midi-Baccarat North American floors).

Rank-7 Remaining
17 of 24 Cards

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

Banker EV (5% Vig)
-1.0206%

Resolved at 45.8639% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2726%

Resolved at 44.5913% Player win rate with 0.9341 unit standard deviation.

Tie Incidence (8:1)
9.5449%

Produces a 14.0961% house hold on the 8-to-1 Tie wager in state DEP335.

FINITE-SHOE ENUMERATION · DEP335

How Seven-Pip Card Depletion at 25% Depth Impacts 6D (5% Vig)

Shoe-stub analysis DEP335 inspects 234 remaining cards at 25% penetration of a 312-card (6D) pack after 7 Seven-Pip Card cards have cleared, leaving 17 Rank-7 cards and a 1.0206% 5% Banker edge.

Under the fixed third-card tableau for DEP335, player stands pat on (dep335) two-card 7, and a player (6d-25%) third-card 7 is the highest (dep335·6d-25%) card that forces banker 4, 5, and 6 to draw. With 17 Rank-7 cards inside 234 remaining 6D cards (25% dealt), single-card slope (-0.83 bps) keeps Banker house edge at 1.0206% and Player at 1.2726%.

State DEP335 (6D, 25% depth, 17/24 Rank-7 left, 5% Vig)
Wager / MetricState DEP335 Value6D BaselineSettlement Note
DEP335 Banker (5% Vig)45.8639% (-1.0206% EV)45.8648%DEP335 6D 25% (17 Rank-7)
DEP335 Player (1:1)44.5913% (-1.2726% EV)44.5903%DEP335 234-card 6D stub (0.9341 SD)
DEP335 Tie (8:1)9.5449% (-14.0961% EV)9.5449%DEP335 Rank-7 (7 out, 17 in)
TABLEAU & SCOREBOARD SEPARATION · DEP335

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP335 · 6D)

While DEP335 tracks 7 removed Seven-Pip Card cards across 25% of a 312-card (6D) shoe (234 remaining, 1.0206% 5% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP335 (6D 25%): 234/312 cards with 17/24 Rank-7 (7A).
  • DEP335 (Rank-7 split): 45.8639% Banker, 44.5913% Player, 9.5449% Tie in 234 6D cards (7B).
  • DEP335 (5% Vig EV): -1.0206% Banker, -1.2726% Player, -14.0961% Tie, 0.9341 SD at 25% (7C).
  • DEP335 (6D roads): red/blue marks log Big Road columns, never 17 Rank-7 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Seven-Pip Card cards leave a 6D shoe by 25% depth (DEP335), 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 (17/24 in 234 cards); Banker carries a -1.0206% expectation under 5%.
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