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COMBINATORIAL DEPLETION · 1D · RANK-3 · 60% DEPTH

1-Deck Three-Pip (Trey) Depletion at 60% Penetration (EZ Baccarat Audit DEP032)

Removing 3 of 4 Three-Pip (Trey) (Rank-3) cards at 60% penetration of a 1-deck (52-card) shoe leaves 1 Rank-3 cards inside a 21-card stub (DEP032), producing 45.9618% Banker wins, 44.5225% Player wins, 9.5157% Ties, and a 0.8140% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.8140%
Player EV (1:1)
-1.4394%
Rank-3 in 21-Card Stub
1/4
Single-Hand Std Dev
0.9364
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 DEP032 (1D Rank-3 at 60% 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 (DEP032)
21 / 52 Cards

60% 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)
-0.8140%

Resolved at 45.9618% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.4394%

Resolved at 44.5225% Player win rate with 0.9364 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3590% house hold on the 8-to-1 Tie wager in state DEP032.

FINITE-SHOE ENUMERATION · DEP032

How Three-Pip (Trey) Depletion at 60% Depth Impacts 1D (EZ Bar-7)

Finite-shoe specification DEP032 tracks Rank-3 removal at 60% depth in 1-deck play: with 1 of 4 Three-Pip (Trey) cards left in the 21-card stub, Tie incidence is 9.5157% and Banker expectation settles at -0.8140% (EZ Bar-7).

When 3 Rank-3 cards exit a 1D shoe by 60% penetration (DEP032, 1 left in 21 cards), each removed 3-pip card (dep032-rank-3) modifies the boundary between banker (21c) standing on 5 and drawing (dep032-rank-3·21c) against mid-range player pulls, combining a +0.65 bps rank vector with EZ Baccarat settlement (-0.8140% Banker EV).

State DEP032 (1D, 60% depth, 1/4 Rank-3 left, EZ Bar-7)
Wager / MetricState DEP032 Value1D BaselineSettlement Note
DEP032 Banker (EZ Bar-7)45.9618% (-0.8140% EV)45.9595%DEP032 1D 60% (1 Rank-3)
DEP032 Player (1:1)44.5225% (-1.4394% EV)44.5249%DEP032 21-card 1D stub (0.9364 SD)
DEP032 Tie (8:1)9.5157% (-14.3590% EV)9.5156%DEP032 Rank-3 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP032

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP032 · 1D)

In studio and floor audits of DEP032 (21 cards undealt out of 52 in 1D at 60% depth), a 0.9364 unit standard deviation accompanies the 1-card Rank-3 stub under EZ Bar-7 (45.9618% Banker vs 44.5225% Player).

  • DEP032 (1D 60%): 21/52 cards with 1/4 Rank-3 (4A).
  • DEP032 (Rank-3 split): 45.9618% Banker, 44.5225% Player, 9.5157% Tie in 21 1D cards (4B).
  • DEP032 (EZ Bar-7 EV): -0.8140% Banker, -1.4394% Player, -14.3590% Tie, 0.9364 SD at 60% (4C).
  • DEP032 (1D roads): red/blue marks log Big Road columns, never 1 Rank-3 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Three-Pip (Trey) cards leave a 1D shoe by 60% depth (DEP032), 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 21 cards); Banker carries a -0.8140% 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