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COMBINATORIAL DEPLETION · 6D · RANK-3 · 70% DEPTH

6-Deck Three-Pip (Trey) Depletion at 70% Penetration (5% Audit DEP303)

Removing 19 of 24 Three-Pip (Trey) (Rank-3) cards at 70% penetration of a 6-deck (312-card) shoe leaves 5 Rank-3 cards inside a 94-card stub (DEP303), producing 45.8674% Banker wins, 44.5876% Player wins, 9.5450% Ties, and a 1.0136% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0136%
Player EV (1:1)
-1.2798%
Rank-3 in 94-Card Stub
5/24
Single-Hand Std Dev
0.9374
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 DEP303 (6D Rank-3 at 70% 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 (DEP303)
94 / 312 Cards

70% penetration depth in 6D (six-deck Mini-Baccarat and Midi-Baccarat North American floors).

Rank-3 Remaining
5 of 24 Cards

19 3-pip cards across all four suits removed from the 6D pack.

Banker EV (5% Vig)
-1.0136%

Resolved at 45.8674% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2798%

Resolved at 44.5876% Player win rate with 0.9374 unit standard deviation.

Tie Incidence (8:1)
9.5450%

Produces a 14.0952% house hold on the 8-to-1 Tie wager in state DEP303.

FINITE-SHOE ENUMERATION · DEP303

How Three-Pip (Trey) Depletion at 70% Depth Impacts 6D (5% Vig)

Across 89,520,558,110,592,000 initial 6D permutations, depletion node DEP303 narrows to a 94-card stub (70% depth) holding 5 of 24 Rank-3 cards, where Banker resolves at 45.8674% (-1.0136% EV) and Player at 44.5876% (-1.2798% EV).

For DEP303 (6-deck shoe, 70% dealt), banker total 4 draws (dep303) on player third-card 3, and (6d-70%) banker total 5 stands on (dep303·6d-70%) player third-card 3, creating asymmetric sensitivity. Holding 5 of 24 Rank-3 cards in a 94-card stub with +0.65 bps rank slope yields 45.8674% Banker, 44.5876% Player, and 9.5450% Tie.

State DEP303 (6D, 70% depth, 5/24 Rank-3 left, 5% Vig)
Wager / MetricState DEP303 Value6D BaselineSettlement Note
DEP303 Banker (5% Vig)45.8674% (-1.0136% EV)45.8648%DEP303 6D 70% (5 Rank-3)
DEP303 Player (1:1)44.5876% (-1.2798% EV)44.5903%DEP303 94-card 6D stub (0.9374 SD)
DEP303 Tie (8:1)9.5450% (-14.0952% EV)9.5449%DEP303 Rank-3 (19 out, 5 in)
TABLEAU & SCOREBOARD SEPARATION · DEP303

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP303 · 6D)

Whether DEP303 is observed in six-deck Mini-Baccarat and Midi-Baccarat North American floors at 70% depth (94/312 cards left, 5 Rank-3 remaining), 5% Vig settlement locks Banker EV at -1.0136% and Player EV at -1.2798% with 9.5450% Ties.

  • DEP303 (6D 70%): 94/312 cards with 5/24 Rank-3 (1A).
  • DEP303 (Rank-3 split): 45.8674% Banker, 44.5876% Player, 9.5450% Tie in 94 6D cards (1B).
  • DEP303 (5% Vig EV): -1.0136% Banker, -1.2798% Player, -14.0952% Tie, 0.9374 SD at 70% (1C).
  • DEP303 (6D roads): red/blue marks log Big Road columns, never 5 Rank-3 stub count (1D).
Table Reality Check

Myth vs. Truth

MythWhen 19 Three-Pip (Trey) cards leave a 6D shoe by 70% depth (DEP303), 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-3 stub counts (5/24 in 94 cards); Banker carries a -1.0136% 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