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COMBINATORIAL DEPLETION · 6D · RANK-3 · 25% DEPTH

6-Deck Three-Pip (Trey) Depletion at 25% Penetration (5% Audit DEP299)

Removing 7 of 24 Three-Pip (Trey) (Rank-3) cards at 25% penetration of a 6-deck (312-card) shoe leaves 17 Rank-3 cards inside a 234-card stub (DEP299), producing 45.8655% Banker wins, 44.5895% Player wins, 9.5449% Ties, and a 1.0173% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0173%
Player EV (1:1)
-1.2760%
Rank-3 in 234-Card Stub
17/24
Single-Hand Std Dev
0.9329
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBBBBPPPPBBPPBP) illustrating derived-road symmetry checks alongside DEP299 (6D Rank-3 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

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

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 4 goes down to Row 3, so use Rule 2: look 3 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.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP299)
234 / 312 Cards

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

Rank-3 Remaining
17 of 24 Cards

7 3-pip cards across all four suits removed from the 6D pack.

Banker EV (5% Vig)
-1.0173%

Resolved at 45.8655% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2760%

Resolved at 44.5895% Player win rate with 0.9329 unit standard deviation.

Tie Incidence (8:1)
9.5449%

Produces a 14.0957% house hold on the 8-to-1 Tie wager in state DEP299.

FINITE-SHOE ENUMERATION · DEP299

How Three-Pip (Trey) Depletion at 25% Depth Impacts 6D (5% Vig)

At 25% penetration of a 312-card (6D) shoe, state DEP299 isolates 7 dealt Rank-3 cards (17 remaining inside 234 stub cards), yielding 45.8655% Banker wins, 44.5895% Player wins, and 0.9329 per-hand standard deviation under 5%.

Under the fixed third-card tableau for DEP299, banker total 4 draws (dep299) on player third-card 3, and (6d-25%) banker total 5 stands on (dep299·6d-25%) player third-card 3, creating asymmetric sensitivity. With 17 Rank-3 cards inside 234 remaining 6D cards (25% dealt), single-card slope (+0.65 bps) keeps Banker house edge at 1.0173% and Player at 1.2760%.

State DEP299 (6D, 25% depth, 17/24 Rank-3 left, 5% Vig)
Wager / MetricState DEP299 Value6D BaselineSettlement Note
DEP299 Banker (5% Vig)45.8655% (-1.0173% EV)45.8648%DEP299 6D 25% (17 Rank-3)
DEP299 Player (1:1)44.5895% (-1.2760% EV)44.5903%DEP299 234-card 6D stub (0.9329 SD)
DEP299 Tie (8:1)9.5449% (-14.0957% EV)9.5449%DEP299 Rank-3 (7 out, 17 in)
TABLEAU & SCOREBOARD SEPARATION · DEP299

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP299 · 6D)

Even at 25% penetration in DEP299 where 7 Rank-3 cards have exited a 6D shoe (17 left in 234 cards), derived-road red and blue entries measure structural regularity on the Big Road—not whether Banker (-1.0173% EV, 5% Vig) or Player (-1.2760% EV) is favored next.

  • DEP299 (6D 25%): 234/312 cards with 17/24 Rank-3 (2A).
  • DEP299 (Rank-3 split): 45.8655% Banker, 44.5895% Player, 9.5449% Tie in 234 6D cards (2B).
  • DEP299 (5% Vig EV): -1.0173% Banker, -1.2760% Player, -14.0957% Tie, 0.9329 SD at 25% (2C).
  • DEP299 (6D roads): red/blue marks log Big Road columns, never 17 Rank-3 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Three-Pip (Trey) cards leave a 6D shoe by 25% depth (DEP299), 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 (17/24 in 234 cards); Banker carries a -1.0173% 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