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COMBINATORIAL DEPLETION · 1D · RANK-3 · 85% DEPTH

1-Deck Three-Pip (Trey) Depletion at 85% Penetration (EZ Baccarat Audit DEP036)

Removing 3 of 4 Three-Pip (Trey) (Rank-3) cards at 85% penetration of a 1-deck (52-card) shoe leaves 1 Rank-3 cards inside a 8-card stub (DEP036), producing 45.9622% Banker wins, 44.5222% Player wins, 9.5157% Ties, and a 0.8134% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.8134%
Player EV (1:1)
-1.4400%
Rank-3 in 8-Card Stub
1/4
Single-Hand Std Dev
0.9389
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road P P B B P B P B P P B B P B P B P P
Big Eye Boy = = ≠ = = = ≠ ≠ = = ≠ = = = ≠
Small Road ≠ ≠ = = ≠ ≠ ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ = ≠

Reference shoe scoreboard (PPBBPBPBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP036 (1D Rank-3 at 85% 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 (DEP036)
8 / 52 Cards

85% 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 (EZ Bar-7)
-0.8134%

Resolved at 45.9622% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.4400%

Resolved at 44.5222% Player win rate with 0.9389 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3589% house hold on the 8-to-1 Tie wager in state DEP036.

FINITE-SHOE ENUMERATION · DEP036

How Three-Pip (Trey) Depletion at 85% Depth Impacts 1D (EZ Bar-7)

Within single-deck laboratory benchmarks and historical pitch audits, profile DEP036 examines 85% shoe depletion (8 of 52 cards remaining) after 3 Rank-3 cards exit, leaving 1 Three-Pip (Trey) cards and a 0.8134% Banker house hold under EZ Baccarat.

In six-card resolution tree DEP036 (1D at 85% depth, 8 cards left), each removed 3-pip card (dep036-rank-3) modifies the boundary between banker (8c) standing on 5 and drawing (dep036-rank-3·8c) against mid-range player pulls; removing 3 of 4 Rank-3 cards (+0.65 bps weight) leaves Banker at -0.8134% EV under EZ Baccarat.

State DEP036 (1D, 85% depth, 1/4 Rank-3 left, EZ Bar-7)
Wager / MetricState DEP036 Value1D BaselineSettlement Note
DEP036 Banker (EZ Bar-7)45.9622% (-0.8134% EV)45.9595%DEP036 1D 85% (1 Rank-3)
DEP036 Player (1:1)44.5222% (-1.4400% EV)44.5249%DEP036 8-card 1D stub (0.9389 SD)
DEP036 Tie (8:1)9.5157% (-14.3589% EV)9.5156%DEP036 Rank-3 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP036

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP036 · 1D)

Cut-card protocol at 85% depth in DEP036 (1D, 8 stub cards containing 1 Rank-3 cards) ensures the shoe reshuffles long before EZ Baccarat house hold (0.8134% Banker / 1.4400% Player) is overturned.

  • DEP036 (1D 85%): 8/52 cards with 1/4 Rank-3 (3A).
  • DEP036 (Rank-3 split): 45.9622% Banker, 44.5222% Player, 9.5157% Tie in 8 1D cards (3B).
  • DEP036 (EZ Bar-7 EV): -0.8134% Banker, -1.4400% Player, -14.3589% Tie, 0.9389 SD at 85% (3C).
  • DEP036 (1D roads): red/blue marks log Big Road columns, never 1 Rank-3 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Three-Pip (Trey) cards leave a 1D shoe by 85% depth (DEP036), 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 8 cards); Banker carries a -0.8134% expectation under EZ Baccarat.
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