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COMBINATORIAL DEPLETION · 8D · RANK-7 · 85% DEPTH

8-Deck Seven-Pip Card Depletion at 85% Penetration (EZ Baccarat Audit DEP432)

Removing 31 of 32 Seven-Pip Card (Rank-7) cards at 85% penetration of a 8-deck (416-card) shoe leaves 1 Rank-7 cards inside a 62-card stub (DEP432), producing 45.8553% Banker wins, 44.6292% Player wins, 9.5155% Ties, and a 1.0273% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-1.0273%
Player EV (1:1)
-1.2261%
Rank-7 in 62-Card Stub
1/32
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 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 DEP432 (8D 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 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 (DEP432)
62 / 416 Cards

85% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-7 Remaining
1 of 32 Cards

31 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 8D pack.

Banker EV (EZ Bar-7)
-1.0273%

Resolved at 45.8553% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.2261%

Resolved at 44.6292% Player win rate with 0.9401 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3606% house hold on the 8-to-1 Tie wager in state DEP432.

FINITE-SHOE ENUMERATION · DEP432

How Seven-Pip Card Depletion at 85% Depth Impacts 8D (EZ Bar-7)

Exact conditional enumeration DEP432 for a 8D shoe at 85% depth (62/416 cards undealt) with 1 remaining Rank-7 cards confirms a 1.0273% Banker edge (EZ Bar-7), 1.2261% Player edge, and 14.3606% Tie edge.

In six-card resolution tree DEP432 (8D at 85% depth, 62 cards left), depleting 7s lowers the (dep432-rank-7) rate of winning three-card banker (62c) 7 hands (the barred push (dep432-rank-7·62c) total on ez baccarat tables); removing 31 of 32 Rank-7 cards (-0.83 bps weight) leaves Banker at -1.0273% EV under EZ Baccarat.

State DEP432 (8D, 85% depth, 1/32 Rank-7 left, EZ Bar-7)
Wager / MetricState DEP432 Value8D BaselineSettlement Note
DEP432 Banker (EZ Bar-7)45.8553% (-1.0273% EV)45.8597%DEP432 8D 85% (1 Rank-7)
DEP432 Player (1:1)44.6292% (-1.2261% EV)44.6247%DEP432 62-card 8D stub (0.9401 SD)
DEP432 Tie (8:1)9.5155% (-14.3606% EV)9.5156%DEP432 Rank-7 (31 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP432

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP432 · 8D)

Whether DEP432 is observed in eight-deck Macau, Las Vegas Strip, and Singapore standard shoes at 85% depth (62/416 cards left, 1 Rank-7 remaining), EZ Bar-7 settlement locks Banker EV at -1.0273% and Player EV at -1.2261% with 9.5155% Ties.

  • DEP432 (8D 85%): 62/416 cards with 1/32 Rank-7 (2A).
  • DEP432 (Rank-7 split): 45.8553% Banker, 44.6292% Player, 9.5155% Tie in 62 8D cards (2B).
  • DEP432 (EZ Bar-7 EV): -1.0273% Banker, -1.2261% Player, -14.3606% Tie, 0.9401 SD at 85% (2C).
  • DEP432 (8D roads): red/blue marks log Big Road columns, never 1 Rank-7 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 31 Seven-Pip Card cards leave a 8D shoe by 85% depth (DEP432), 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 (1/32 in 62 cards); Banker carries a -1.0273% 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