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COMBINATORIAL DEPLETION · 1D · RANK-7 · 85% DEPTH

1-Deck Seven-Pip Card Depletion at 85% Penetration (EZ Baccarat Audit DEP072)

Removing 3 of 4 Seven-Pip Card (Rank-7) cards at 85% penetration of a 1-deck (52-card) shoe leaves 1 Rank-7 cards inside a 8-card stub (DEP072), producing 45.9561% Banker wins, 44.5284% Player wins, 9.5155% Ties, and a 0.8257% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.8257%
Player EV (1:1)
-1.4277%
Rank-7 in 8-Card Stub
1/4
Single-Hand Std Dev
0.9401
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 DEP072 (1D Rank-7 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 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 (DEP072)
8 / 52 Cards

85% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-7 Remaining
1 of 4 Cards

3 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 1D pack.

Banker EV (EZ Bar-7)
-0.8257%

Resolved at 45.9561% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.4277%

Resolved at 44.5284% Player win rate with 0.9401 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3603% house hold on the 8-to-1 Tie wager in state DEP072.

FINITE-SHOE ENUMERATION · DEP072

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

In combinatorial record DEP072, depleting 3 Rank-7 cards across 85% of a 1D (52-card) pack leaves 1 Seven-Pip Card cards among 8 remaining cards, setting Banker win probability to 45.9561% and house edge to 0.8257% (EZ Bar-7).

Under the fixed third-card tableau for DEP072, player stands pat on (dep072) two-card 7, and a player (1d-85%) third-card 7 is the highest (dep072·1d-85%) card that forces banker 4, 5, and 6 to draw. With 1 Rank-7 cards inside 8 remaining 1D cards (85% dealt), single-card slope (-0.83 bps) keeps Banker house edge at 0.8257% and Player at 1.4277%.

State DEP072 (1D, 85% depth, 1/4 Rank-7 left, EZ Bar-7)
Wager / MetricState DEP072 Value1D BaselineSettlement Note
DEP072 Banker (EZ Bar-7)45.9561% (-0.8257% EV)45.9595%DEP072 1D 85% (1 Rank-7)
DEP072 Player (1:1)44.5284% (-1.4277% EV)44.5249%DEP072 8-card 1D stub (0.9401 SD)
DEP072 Tie (8:1)9.5155% (-14.3603% EV)9.5156%DEP072 Rank-7 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP072

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP072 · 1D)

Statistical verification of DEP072 (1D, 85% penetration, 1 Seven-Pip Card cards in 8 stub cards) demonstrates why single-rank depletion (3 Rank-7 dealt) shifts edges by basis points around -0.8257% (EZ Bar-7).

  • DEP072 (1D 85%): 8/52 cards with 1/4 Rank-7 (1A).
  • DEP072 (Rank-7 split): 45.9561% Banker, 44.5284% Player, 9.5155% Tie in 8 1D cards (1B).
  • DEP072 (EZ Bar-7 EV): -0.8257% Banker, -1.4277% Player, -14.3603% Tie, 0.9401 SD at 85% (1C).
  • DEP072 (1D roads): red/blue marks log Big Road columns, never 1 Rank-7 stub count (1D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Seven-Pip Card cards leave a 1D shoe by 85% depth (DEP072), 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-7 stub counts (1/4 in 8 cards); Banker carries a -0.8257% expectation under EZ Baccarat.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

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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