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COMBINATORIAL DEPLETION · 4D · RANK-2 · 25% DEPTH

4-Deck Two-Pip (Deuce) Depletion at 25% Penetration (5% Audit DEP200)

Removing 5 of 16 Two-Pip (Deuce) (Rank-2) cards at 25% penetration of a 4-deck (208-card) shoe leaves 11 Rank-2 cards inside a 156-card stub (DEP200), producing 45.8738% Banker wins, 44.5843% Player wins, 9.5418% Ties, and a 1.0042% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0042%
Player EV (1:1)
-1.2895%
Rank-2 in 156-Card Stub
11/16
Single-Hand Std Dev
0.9326
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 P B P B B P P B B P B
Big Eye Boy = = = = ≠ = = = ≠ ≠ = = = = ≠
Small Road = = ≠ ≠ = = ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (PPBBPPBPBPBBPPBBPB) illustrating derived-road symmetry checks alongside DEP200 (4D Rank-2 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

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 (DEP200)
156 / 208 Cards

25% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).

Rank-2 Remaining
11 of 16 Cards

5 2-pip cards across all four suits removed from the 4D pack.

Banker EV (5% Vig)
-1.0042%

Resolved at 45.8738% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2895%

Resolved at 44.5843% Player win rate with 0.9326 unit standard deviation.

Tie Incidence (8:1)
9.5418%

Produces a 14.1236% house hold on the 8-to-1 Tie wager in state DEP200.

FINITE-SHOE ENUMERATION · DEP200

How Two-Pip (Deuce) Depletion at 25% Depth Impacts 4D (5% Vig)

Finite-shoe specification DEP200 tracks Rank-2 removal at 25% depth in 4-deck play: with 11 of 16 Two-Pip (Deuce) cards left in the 156-card stub, Tie incidence is 9.5418% and Banker expectation settles at -1.0042% (5% Vig).

Combinatorial weighting in DEP200 (156 cards left from 208 at 25% depth) is governed by two rules: on banker total 4, (dep200) banker draws against player third-card (4d-25%) 2 through 7; removing 2s (dep200·4d-25%) trims low-pip player third-card triggers, and one-quarter of the shoe (dep200-4d) has exited the carrier and (11/16) winning banker wagers pay 0.95 (dep200-4d·11/16) to 1 after 5% house tax (+0.52 bps per Rank-2 removed).

State DEP200 (4D, 25% depth, 11/16 Rank-2 left, 5% Vig)
Wager / MetricState DEP200 Value4D BaselineSettlement Note
DEP200 Banker (5% Vig)45.8738% (-1.0042% EV)45.8732%DEP200 4D 25% (11 Rank-2)
DEP200 Player (1:1)44.5843% (-1.2895% EV)44.5850%DEP200 156-card 4D stub (0.9326 SD)
DEP200 Tie (8:1)9.5418% (-14.1236% EV)9.5418%DEP200 Rank-2 (5 out, 11 in)
TABLEAU & SCOREBOARD SEPARATION · DEP200

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP200 · 4D)

While DEP200 tracks 5 removed Two-Pip (Deuce) cards across 25% of a 208-card (4D) shoe (156 remaining, 1.0042% 5% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP200 (4D 25%): 156/208 cards with 11/16 Rank-2 (4A).
  • DEP200 (Rank-2 split): 45.8738% Banker, 44.5843% Player, 9.5418% Tie in 156 4D cards (4B).
  • DEP200 (5% Vig EV): -1.0042% Banker, -1.2895% Player, -14.1236% Tie, 0.9326 SD at 25% (4C).
  • DEP200 (4D roads): red/blue marks log Big Road columns, never 11 Rank-2 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 5 Two-Pip (Deuce) cards leave a 4D shoe by 25% depth (DEP200), 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 (11/16 in 156 cards); Banker carries a -1.0042% 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