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COMBINATORIAL DEPLETION · 1D · RANK-6 · 85% DEPTH

1-Deck Six-Pip Card Depletion at 85% Penetration (EZ Baccarat Audit DEP063)

Removing 3 of 4 Six-Pip Card (Rank-6) cards at 85% penetration of a 1-deck (52-card) shoe leaves 1 Rank-6 cards inside a 8-card stub (DEP063), producing 45.9549% Banker wins, 44.5296% Player wins, 9.5155% Ties, and a 0.8281% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.8281%
Player EV (1:1)
-1.4253%
Rank-6 in 8-Card Stub
1/4
Single-Hand Std Dev
0.9398
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 P B B P B
Big Eye Boy = = = = = = ≠ = = = = = = =
Small Road = = = = = = ≠ ≠ = = = =
Cockroach Pig = = = = = = ≠ ≠ ≠ =

Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP063 (1D Rank-6 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 (DEP063)
8 / 52 Cards

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

Rank-6 Remaining
1 of 4 Cards

3 6-pip cards (standing threshold and Banker 6 trigger) removed from the 1D pack.

Banker EV (EZ Bar-7)
-0.8281%

Resolved at 45.9549% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.4253%

Resolved at 44.5296% Player win rate with 0.9398 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3603% house hold on the 8-to-1 Tie wager in state DEP063.

FINITE-SHOE ENUMERATION · DEP063

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

Card-removal benchmark DEP063 measures Six-Pip Card (Rank-6) scarcity at 85% depth in a 1-deck shoe: 3 removed ranks leave 1 in the 8-card remainder, shifting Banker win share to 45.9549% (0.8281% edge, EZ Bar-7).

Why does Rank-6 carry a -1.13 bps per-card effect in DEP063? Banker 6 only draws (DEP063) when Player pulls a third-card (1D-85%) 6 or 7; depleting 6s (DEP063·1D-85%) directly alters both Banker 6 draws and Super 6 settlement frequency, and at 85% penetration (1 Six-Pip Card cards left in 8 1D cards), at 85% cut-card penetration, (dep063-1d) only 15% of the pack (1/4) remains and winning 3-card banker (dep063-1d·1/4) 7 hands push.

State DEP063 (1D, 85% depth, 1/4 Rank-6 left, EZ Bar-7)
Wager / MetricState DEP063 Value1D BaselineSettlement Note
DEP063 Banker (EZ Bar-7)45.9549% (-0.8281% EV)45.9595%DEP063 1D 85% (1 Rank-6)
DEP063 Player (1:1)44.5296% (-1.4253% EV)44.5249%DEP063 8-card 1D stub (0.9398 SD)
DEP063 Tie (8:1)9.5155% (-14.3603% EV)9.5156%DEP063 Rank-6 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP063

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP063 · 1D)

For DEP063 (8 remaining cards in a 52-card 1D shoe at 85% depth), tracking all 3 exited Rank-6 cards moves Banker win rate to 45.9549% (-0.8281% EV, EZ Bar-7) and Player to 44.5296% (-1.4253% EV).

  • DEP063 (1D 85%): 8/52 cards with 1/4 Rank-6 (5A).
  • DEP063 (Rank-6 split): 45.9549% Banker, 44.5296% Player, 9.5155% Tie in 8 1D cards (5B).
  • DEP063 (EZ Bar-7 EV): -0.8281% Banker, -1.4253% Player, -14.3603% Tie, 0.9398 SD at 85% (5C).
  • DEP063 (1D roads): red/blue marks log Big Road columns, never 1 Rank-6 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Six-Pip Card cards leave a 1D shoe by 85% depth (DEP063), 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-6 stub counts (1/4 in 8 cards); Banker carries a -0.8281% 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