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COMBINATORIAL DEPLETION · 2D · RANK-2 · 50% DEPTH

2-Deck Two-Pip (Deuce) Depletion at 50% Penetration (Super 6 Audit DEP112)

Removing 5 of 8 Two-Pip (Deuce) (Rank-2) cards at 50% penetration of a 2-deck (104-card) shoe leaves 3 Rank-2 cards inside a 52-card stub (DEP112), producing 45.9013% Banker wins, 44.5661% Player wins, 9.5327% Ties, and a 1.3578% Banker house edge under Super 6.

Banker EV (Super 6)
-1.3578%
Player EV (1:1)
-1.3352%
Rank-2 in 52-Card Stub
3/8
Single-Hand Std Dev
0.9351
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
Big Eye Boy = = = = = = ≠ ≠ ≠ ≠ = = = =
Small Road = = = = = = ≠ = = = = =
Cockroach Pig = = = = = = ≠ = = ≠

Reference shoe scoreboard (PPBBPPBBPPBBPBTBPB) illustrating derived-road symmetry checks alongside DEP112 (2D Rank-2 at 50% 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 (DEP112)
52 / 104 Cards

50% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Rank-2 Remaining
3 of 8 Cards

5 2-pip cards across all four suits removed from the 2D pack.

Banker EV (Super 6)
-1.3578%

Resolved at 45.9013% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.3352%

Resolved at 44.5661% Player win rate with 0.9351 unit standard deviation.

Tie Incidence (8:1)
9.5327%

Produces a 14.2061% house hold on the 8-to-1 Tie wager in state DEP112.

FINITE-SHOE ENUMERATION · DEP112

How Two-Pip (Deuce) Depletion at 50% Depth Impacts 2D (Super 6)

Quantitative proof DEP112 documents 2D rank depletion at 50% depth: 5 exited Rank-2 cards leave 3 of 8 in the 52-card stub, generating 45.9013% Banker wins (-1.3578% EV under Super 6) and 44.5661% Player wins.

For DEP112 (2-deck shoe, 50% dealt), on banker total 4, (dep112) banker draws against player third-card (2d-50%) 2 through 7; removing 2s (dep112·2d-50%) trims low-pip player third-card triggers. Holding 3 of 8 Rank-2 cards in a 52-card stub with +0.52 bps rank slope yields 45.9013% Banker, 44.5661% Player, and 9.5327% Tie.

State DEP112 (2D, 50% depth, 3/8 Rank-2 left, Super 6)
Wager / MetricState DEP112 Value2D BaselineSettlement Note
DEP112 Banker (Super 6)45.9013% (-1.3578% EV)45.8998%DEP112 2D 50% (3 Rank-2)
DEP112 Player (1:1)44.5661% (-1.3352% EV)44.5676%DEP112 52-card 2D stub (0.9351 SD)
DEP112 Tie (8:1)9.5327% (-14.2061% EV)9.5326%DEP112 Rank-2 (5 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP112

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP112 · 2D)

Scoreboard literacy in DEP112 separates two independent concepts: 2D card-removal math (3 Rank-2 left in 52 cards at 50% depth, 0.9351 volatility) and derived-road comparison rules (Rule 1 column-depth checks and Rule 2 two-cell lookbacks).

  • DEP112 (2D 50%): 52/104 cards with 3/8 Rank-2 (5A).
  • DEP112 (Rank-2 split): 45.9013% Banker, 44.5661% Player, 9.5327% Tie in 52 2D cards (5B).
  • DEP112 (Super 6 EV): -1.3578% Banker, -1.3352% Player, -14.2061% Tie, 0.9351 SD at 50% (5C).
  • DEP112 (2D roads): red/blue marks log Big Road columns, never 3 Rank-2 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 5 Two-Pip (Deuce) cards leave a 2D shoe by 50% depth (DEP112), 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 (3/8 in 52 cards); Banker carries a -1.3578% expectation under Super 6.
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