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COMBINATORIAL DEPLETION · 6D · RANK-5 · 75% DEPTH

6-Deck Five-Pip Card Depletion at 75% Penetration (4% Audit DEP322)

Removing 21 of 24 Five-Pip Card (Rank-5) cards at 75% penetration of a 6-deck (312-card) shoe leaves 3 Rank-5 cards inside a 78-card stub (DEP322), producing 45.8610% Banker wins, 44.5942% Player wins, 9.5448% Ties, and a 0.5677% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5677%
Player EV (1:1)
-1.2668%
Rank-5 in 78-Card Stub
3/24
Single-Hand Std Dev
0.9385
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPPBBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP322 (6D Rank-5 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 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 (DEP322)
78 / 312 Cards

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

Rank-5 Remaining
3 of 24 Cards

21 5-pip cards (final mandatory Player draw threshold) removed from the 6D pack.

Banker EV (4% Vig)
-0.5677%

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

Player EV (1:1)
-1.2668%

Resolved at 44.5942% Player win rate with 0.9385 unit standard deviation.

Tie Incidence (8:1)
9.5448%

Produces a 14.0967% house hold on the 8-to-1 Tie wager in state DEP322.

FINITE-SHOE ENUMERATION · DEP322

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

Quantitative proof DEP322 documents 6D rank depletion at 75% depth: 21 exited Rank-5 cards leave 3 of 24 in the 78-card stub, generating 45.8610% Banker wins (-0.5677% EV under 4% Vig) and 44.5942% Player wins.

Because Player draws on (DEP322) two-card 5 and stands on (6D-75%) 6, while Banker 3, 4, (DEP322·6D-75%) and 5 all draw against a Player third-card 5, rank 5 favors Player when depleted. In state DEP322 (6D, 75% depth), each removed Rank-5 card applies a -0.84 bps baseline directional pressure before scaling to the 78-card remainder (3 Rank-5 left), while Three-quarters of the shoe (DEP322-6D) has been dealt and winning (3/24) Banker wagers return 0.96 units (DEP322-6D·3/24) net per unit risked.

State DEP322 (6D, 75% depth, 3/24 Rank-5 left, 4% Vig)
Wager / MetricState DEP322 Value6D BaselineSettlement Note
DEP322 Banker (4% Vig)45.8610% (-0.5677% EV)45.8648%DEP322 6D 75% (3 Rank-5)
DEP322 Player (1:1)44.5942% (-1.2668% EV)44.5903%DEP322 78-card 6D stub (0.9385 SD)
DEP322 Tie (8:1)9.5448% (-14.0967% EV)9.5449%DEP322 Rank-5 (21 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP322

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP322 · 6D)

Synthesizing DEP322 (6D at 75% depth, 3 Five-Pip Card cards left inside 78 stub cards): 4% rules produce a 0.5677% Banker edge, 1.2668% Player edge, 14.0967% Tie edge, and 0.9385 unit volatility.

  • DEP322 (6D 75%): 78/312 cards with 3/24 Rank-5 (5A).
  • DEP322 (Rank-5 split): 45.8610% Banker, 44.5942% Player, 9.5448% Tie in 78 6D cards (5B).
  • DEP322 (4% Vig EV): -0.5677% Banker, -1.2668% Player, -14.0967% Tie, 0.9385 SD at 75% (5C).
  • DEP322 (6D roads): red/blue marks log Big Road columns, never 3 Rank-5 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 21 Five-Pip Card cards leave a 6D shoe by 75% depth (DEP322), 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-5 stub counts (3/24 in 78 cards); Banker carries a -0.5677% 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