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COMBINATORIAL DEPLETION · 1D · RANK-8 · 85% DEPTH

1-Deck Eight-Pip Card Depletion at 85% Penetration (EZ Baccarat Audit DEP081)

Removing 3 of 4 Eight-Pip Card (Rank-8) cards at 85% penetration of a 1-deck (52-card) shoe leaves 1 Rank-8 cards inside a 8-card stub (DEP081), producing 45.9575% Banker wins, 44.5270% Player wins, 9.5155% Ties, and a 0.8230% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.8230%
Player EV (1:1)
-1.4304%
Rank-8 in 8-Card Stub
1/4
Single-Hand Std Dev
0.9404
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBBPPBPTBPBBPBP) illustrating derived-road symmetry checks alongside DEP081 (1D Rank-8 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 (DEP081)
8 / 52 Cards

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

Rank-8 Remaining
1 of 4 Cards

3 8-pip cards (Natural 8 generator and Banker 3 block) removed from the 1D pack.

Banker EV (EZ Bar-7)
-0.8230%

Resolved at 45.9575% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.4304%

Resolved at 44.5270% Player win rate with 0.9404 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3603% house hold on the 8-to-1 Tie wager in state DEP081.

FINITE-SHOE ENUMERATION · DEP081

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

Removing 3 of 4 Rank-8 cards by the 85% mark of a 1-deck shoe (DEP081, 8 cards left) leaves 1 Eight-Pip Card cards and adjusts conditional probabilities to 45.9575% Banker, 44.5270% Player, and 9.5155% Tie under EZ Baccarat.

Because depleting 8-pip cards also (dep081-rank-8) lowers two-card natural 8 lockouts (8c) when paired with zero-point tens (dep081-rank-8·8c) and court cards, state DEP081 (85% 1D depth, 3 Rank-8 removed, 1 in 8 cards) registers a -0.50 bps rank derivative and 0.8230% Banker house edge (EZ Bar-7).

State DEP081 (1D, 85% depth, 1/4 Rank-8 left, EZ Bar-7)
Wager / MetricState DEP081 Value1D BaselineSettlement Note
DEP081 Banker (EZ Bar-7)45.9575% (-0.8230% EV)45.9595%DEP081 1D 85% (1 Rank-8)
DEP081 Player (1:1)44.5270% (-1.4304% EV)44.5249%DEP081 8-card 1D stub (0.9404 SD)
DEP081 Tie (8:1)9.5155% (-14.3603% EV)9.5156%DEP081 Rank-8 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP081

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP081 · 1D)

Cut-card protocol at 85% depth in DEP081 (1D, 8 stub cards containing 1 Rank-8 cards) ensures the shoe reshuffles long before EZ Baccarat house hold (0.8230% Banker / 1.4304% Player) is overturned.

  • DEP081 (1D 85%): 8/52 cards with 1/4 Rank-8 (4A).
  • DEP081 (Rank-8 split): 45.9575% Banker, 44.5270% Player, 9.5155% Tie in 8 1D cards (4B).
  • DEP081 (EZ Bar-7 EV): -0.8230% Banker, -1.4304% Player, -14.3603% Tie, 0.9404 SD at 85% (4C).
  • DEP081 (1D roads): red/blue marks log Big Road columns, never 1 Rank-8 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Eight-Pip Card cards leave a 1D shoe by 85% depth (DEP081), 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-8 stub counts (1/4 in 8 cards); Banker carries a -0.8230% 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