Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 6D Rank-2 Depletion at 75% Depth (4% Vig)
COMBINATORIAL DEPLETION · 6D · RANK-2 · 75% DEPTH

6-Deck Two-Pip (Deuce) Depletion at 75% Penetration (4% Audit DEP295)

Removing 21 of 24 Two-Pip (Deuce) (Rank-2) cards at 75% penetration of a 6-deck (312-card) shoe leaves 3 Rank-2 cards inside a 78-card stub (DEP295), producing 45.8672% Banker wins, 44.5878% Player wins, 9.5450% Ties, and a 0.5554% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5554%
Player EV (1:1)
-1.2793%
Rank-2 in 78-Card Stub
3/24
Single-Hand Std Dev
0.9376
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 B P B P P B B P P B P
Big Eye Boy = = = = ≠ = = = ≠ ≠ = = = = ≠
Small Road = = ≠ ≠ = = ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP295 (6D Rank-2 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 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 (DEP295)
78 / 312 Cards

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

Rank-2 Remaining
3 of 24 Cards

21 2-pip cards across all four suits removed from the 6D pack.

Banker EV (4% Vig)
-0.5554%

Resolved at 45.8672% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2793%

Resolved at 44.5878% Player win rate with 0.9376 unit standard deviation.

Tie Incidence (8:1)
9.5450%

Produces a 14.0951% house hold on the 8-to-1 Tie wager in state DEP295.

FINITE-SHOE ENUMERATION · DEP295

How Two-Pip (Deuce) Depletion at 75% Depth Impacts 6D (4% Vig)

Audit DEP295 evaluates a 6-deck (312-card) shoe at 75% penetration where 21 of 24 Two-Pip (Deuce) cards have exited, leaving 3 Rank-2 cards inside the 78-card stub with Banker EV at -0.5554% under 4%.

Comparing initial 312-card 6D weights against stub DEP295 (78 cards, 75% depth, 3 Rank-2 left) illustrates how on banker total 4, (dep295) banker draws against player third-card (6d-75%) 2 through 7; removing 2s (dep295·6d-75%) trims low-pip player third-card triggers (+0.52 bps slope, 0.5554% 4% Vig edge).

State DEP295 (6D, 75% depth, 3/24 Rank-2 left, 4% Vig)
Wager / MetricState DEP295 Value6D BaselineSettlement Note
DEP295 Banker (4% Vig)45.8672% (-0.5554% EV)45.8648%DEP295 6D 75% (3 Rank-2)
DEP295 Player (1:1)44.5878% (-1.2793% EV)44.5903%DEP295 78-card 6D stub (0.9376 SD)
DEP295 Tie (8:1)9.5450% (-14.0951% EV)9.5449%DEP295 Rank-2 (21 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP295

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP295 · 6D)

Across 100-hand session horizons at state DEP295 (6D 75% depth, 3/24 Rank-2 in 78 cards), single-hand dispersion (0.9376 SD) dominates the 0.5554% (4% Vig) Banker and 1.2793% Player expectation gap.

  • DEP295 (6D 75%): 78/312 cards with 3/24 Rank-2 (3A).
  • DEP295 (Rank-2 split): 45.8672% Banker, 44.5878% Player, 9.5450% Tie in 78 6D cards (3B).
  • DEP295 (4% Vig EV): -0.5554% Banker, -1.2793% Player, -14.0951% Tie, 0.9376 SD at 75% (3C).
  • DEP295 (6D roads): red/blue marks log Big Road columns, never 3 Rank-2 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 21 Two-Pip (Deuce) cards leave a 6D shoe by 75% depth (DEP295), 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-2 stub counts (3/24 in 78 cards); Banker carries a -0.5554% 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