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COMBINATORIAL DEPLETION · 8D · RANK-2 · 40% DEPTH

8-Deck Two-Pip (Deuce) Depletion at 40% Penetration (4% Audit DEP381)

Removing 15 of 32 Two-Pip (Deuce) (Rank-2) cards at 40% penetration of a 8-deck (416-card) shoe leaves 17 Rank-2 cards inside a 250-card stub (DEP381), producing 45.8607% Banker wins, 44.6236% Player wins, 9.5156% Ties, and a 0.5973% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5973%
Player EV (1:1)
-1.2371%
Rank-2 in 250-Card Stub
17/32
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 P B B P P B P B B P P B P
Big Eye Boy = = ≠ = ≠ ≠ = = ≠ = ≠ ≠ = = ≠
Small Road ≠ ≠ ≠ ≠ ≠ ≠ ≠ ≠ ≠ ≠ ≠ ≠ ≠
Cockroach Pig ≠ = = ≠ ≠ = ≠ = = ≠ ≠ =

Reference shoe scoreboard (BBPPBPBBPPBPBBPPBP) illustrating derived-road symmetry checks alongside DEP381 (8D Rank-2 at 40% 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 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #2

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 5 goes down to Row 2, so use Rule 2: look 3 columns back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP381)
250 / 416 Cards

40% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-2 Remaining
17 of 32 Cards

15 2-pip cards across all four suits removed from the 8D pack.

Banker EV (4% Vig)
-0.5973%

Resolved at 45.8607% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2371%

Resolved at 44.6236% Player win rate with 0.9341 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3592% house hold on the 8-to-1 Tie wager in state DEP381.

FINITE-SHOE ENUMERATION · DEP381

How Two-Pip (Deuce) Depletion at 40% Depth Impacts 8D (4% Vig)

When a 8D shoe reaches 40% cut-card depth (250 of 416 cards undealt, state DEP381) with 15 Two-Pip (Deuce) cards removed and 17 remaining, Player wins 44.6236% (1.2371% edge) while Banker wins 45.8607% (0.5973% edge under 4%).

Why does Rank-2 carry a +0.52 bps per-card effect in DEP381? On Banker total 4, (DEP381) Banker draws against Player third-card (8D-40%) 2 through 7; removing 2s (DEP381·8D-40%) trims low-pip Player third-card triggers, and at 40% penetration (17 Two-Pip (Deuce) cards left in 250 8D cards), winning banker wagers collect (dep381-8d) 0.96 units per unit staked (17/32) with 60% of the shoe (dep381-8d·17/32) still inside the acrylic carrier.

State DEP381 (8D, 40% depth, 17/32 Rank-2 left, 4% Vig)
Wager / MetricState DEP381 Value8D BaselineSettlement Note
DEP381 Banker (4% Vig)45.8607% (-0.5973% EV)45.8597%DEP381 8D 40% (17 Rank-2)
DEP381 Player (1:1)44.6236% (-1.2371% EV)44.6247%DEP381 250-card 8D stub (0.9341 SD)
DEP381 Tie (8:1)9.5156% (-14.3592% EV)9.5156%DEP381 Rank-2 (15 out, 17 in)
TABLEAU & SCOREBOARD SEPARATION · DEP381

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP381 · 8D)

While DEP381 tracks 15 removed Two-Pip (Deuce) cards across 40% of a 416-card (8D) shoe (250 remaining, 0.5973% 4% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP381 (8D 40%): 250/416 cards with 17/32 Rank-2 (6A).
  • DEP381 (Rank-2 split): 45.8607% Banker, 44.6236% Player, 9.5156% Tie in 250 8D cards (6B).
  • DEP381 (4% Vig EV): -0.5973% Banker, -1.2371% Player, -14.3592% Tie, 0.9341 SD at 40% (6C).
  • DEP381 (8D roads): red/blue marks log Big Road columns, never 17 Rank-2 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 15 Two-Pip (Deuce) cards leave a 8D shoe by 40% depth (DEP381), 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 (17/32 in 250 cards); Banker carries a -0.5973% 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