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COMBINATORIAL DEPLETION · 4D · RANK-3 · 80% DEPTH

4-Deck Three-Pip (Trey) Depletion at 80% Penetration (Super 6 Audit DEP215)

Removing 15 of 16 Three-Pip (Trey) (Rank-3) cards at 80% penetration of a 4-deck (208-card) shoe leaves 1 Rank-3 cards inside a 42-card stub (DEP215), producing 45.8764% Banker wins, 44.5817% Player wins, 9.5419% Ties, and a 1.3982% Banker house edge under Super 6.

Banker EV (Super 6)
-1.3982%
Player EV (1:1)
-1.2948%
Rank-3 in 42-Card Stub
1/16
Single-Hand Std Dev
0.9384
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 DEP215 (4D Rank-3 at 80% 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 (DEP215)
42 / 208 Cards

80% penetration depth in 4D (four-deck Asian VIP salons and compact automatic shuffler shoes).

Rank-3 Remaining
1 of 16 Cards

15 3-pip cards across all four suits removed from the 4D pack.

Banker EV (Super 6)
-1.3982%

Resolved at 45.8764% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.2948%

Resolved at 44.5817% Player win rate with 0.9384 unit standard deviation.

Tie Incidence (8:1)
9.5419%

Produces a 14.1229% house hold on the 8-to-1 Tie wager in state DEP215.

FINITE-SHOE ENUMERATION · DEP215

How Three-Pip (Trey) Depletion at 80% Depth Impacts 4D (Super 6)

At 80% penetration of a 208-card (4D) shoe, state DEP215 isolates 15 dealt Rank-3 cards (1 remaining inside 42 stub cards), yielding 45.8764% Banker wins, 44.5817% Player wins, and 0.9384 per-hand standard deviation under Super 6.

Comparing initial 208-card 4D weights against stub DEP215 (42 cards, 80% depth, 1 Rank-3 left) illustrates how banker total 4 draws (dep215) on player third-card 3, and (4d-80%) banker total 5 stands on (dep215·4d-80%) player third-card 3, creating asymmetric sensitivity (+0.65 bps slope, 1.3982% Super 6 edge).

State DEP215 (4D, 80% depth, 1/16 Rank-3 left, Super 6)
Wager / MetricState DEP215 Value4D BaselineSettlement Note
DEP215 Banker (Super 6)45.8764% (-1.3982% EV)45.8732%DEP215 4D 80% (1 Rank-3)
DEP215 Player (1:1)44.5817% (-1.2948% EV)44.5850%DEP215 42-card 4D stub (0.9384 SD)
DEP215 Tie (8:1)9.5419% (-14.1229% EV)9.5418%DEP215 Rank-3 (15 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP215

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP215 · 4D)

While DEP215 tracks 15 removed Three-Pip (Trey) cards across 80% of a 208-card (4D) shoe (42 remaining, 1.3982% Super 6 edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP215 (4D 80%): 42/208 cards with 1/16 Rank-3 (2A).
  • DEP215 (Rank-3 split): 45.8764% Banker, 44.5817% Player, 9.5419% Tie in 42 4D cards (2B).
  • DEP215 (Super 6 EV): -1.3982% Banker, -1.2948% Player, -14.1229% Tie, 0.9384 SD at 80% (2C).
  • DEP215 (4D roads): red/blue marks log Big Road columns, never 1 Rank-3 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 15 Three-Pip (Trey) cards leave a 4D shoe by 80% depth (DEP215), 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 (1/16 in 42 cards); Banker carries a -1.3982% 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