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COMBINATORIAL DEPLETION · 1D · RANK-3 · 80% DEPTH

1-Deck Three-Pip (Trey) Depletion at 80% Penetration (Super 6 Audit DEP035)

Removing 3 of 4 Three-Pip (Trey) (Rank-3) cards at 80% penetration of a 1-deck (52-card) shoe leaves 1 Rank-3 cards inside a 10-card stub (DEP035), producing 45.9621% Banker wins, 44.5222% Player wins, 9.5157% Ties, and a 1.2531% Banker house edge under Super 6.

Banker EV (Super 6)
-1.2531%
Player EV (1:1)
-1.4399%
Rank-3 in 10-Card Stub
1/4
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 P B P B B P P B P B P B B
Big Eye Boy = = ≠ = = = ≠ ≠ = = ≠ = = = ≠
Small Road ≠ ≠ = = ≠ ≠ ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ = ≠

Reference shoe scoreboard (BBPPBPBPBBPPBPBPBB) illustrating derived-road symmetry checks alongside DEP035 (1D 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 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

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 (DEP035)
10 / 52 Cards

80% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-3 Remaining
1 of 4 Cards

3 3-pip cards across all four suits removed from the 1D pack.

Banker EV (Super 6)
-1.2531%

Resolved at 45.9621% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.4399%

Resolved at 44.5222% Player win rate with 0.9384 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3589% house hold on the 8-to-1 Tie wager in state DEP035.

FINITE-SHOE ENUMERATION · DEP035

How Three-Pip (Trey) Depletion at 80% Depth Impacts 1D (Super 6)

Card-removal benchmark DEP035 measures Three-Pip (Trey) (Rank-3) scarcity at 80% depth in a 1-deck shoe: 3 removed ranks leave 1 in the 10-card remainder, shifting Banker win share to 45.9621% (1.2531% edge, Super 6).

Comparing initial 52-card 1D weights against stub DEP035 (10 cards, 80% depth, 1 Rank-3 left) illustrates how banker total 4 draws (dep035) on player third-card 3, and (1d-80%) banker total 5 stands on (dep035·1d-80%) player third-card 3, creating asymmetric sensitivity (+0.65 bps slope, 1.2531% Super 6 edge).

State DEP035 (1D, 80% depth, 1/4 Rank-3 left, Super 6)
Wager / MetricState DEP035 Value1D BaselineSettlement Note
DEP035 Banker (Super 6)45.9621% (-1.2531% EV)45.9595%DEP035 1D 80% (1 Rank-3)
DEP035 Player (1:1)44.5222% (-1.4399% EV)44.5249%DEP035 10-card 1D stub (0.9384 SD)
DEP035 Tie (8:1)9.5157% (-14.3589% EV)9.5156%DEP035 Rank-3 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP035

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP035 · 1D)

Comparing DEP035 (80% 1D depth, 3 Rank-3 removed, 1 remaining in 10 cards) against fresh-shoe baselines shows how finite-stub variance (0.9384 SD) coexists with a 1.2531% Super 6 Banker house edge.

  • DEP035 (1D 80%): 10/52 cards with 1/4 Rank-3 (5A).
  • DEP035 (Rank-3 split): 45.9621% Banker, 44.5222% Player, 9.5157% Tie in 10 1D cards (5B).
  • DEP035 (Super 6 EV): -1.2531% Banker, -1.4399% Player, -14.3589% Tie, 0.9384 SD at 80% (5C).
  • DEP035 (1D roads): red/blue marks log Big Road columns, never 1 Rank-3 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Three-Pip (Trey) cards leave a 1D shoe by 80% depth (DEP035), 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 (1/4 in 10 cards); Banker carries a -1.2531% 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