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COMBINATORIAL DEPLETION · 1D · ACE-1 · 85% DEPTH

1-Deck Ace (1-Point Pip) Depletion at 85% Penetration (EZ Baccarat Audit DEP018)

Removing 3 of 4 Ace (1-Point Pip) (Ace-1) cards at 85% penetration of a 1-deck (52-card) shoe leaves 1 Ace-1 cards inside a 8-card stub (DEP018), producing 45.9613% Banker wins, 44.5231% Player wins, 9.5156% Ties, and a 0.8152% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.8152%
Player EV (1:1)
-1.4382%
Ace-1 in 8-Card Stub
1/4
Single-Hand Std Dev
0.9383
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 B P
Big Eye Boy = = = = = = ≠ = = = = ≠ ≠ = =
Small Road = = = = = = ≠ ≠ = = = ≠ ≠
Cockroach Pig = = = = = = ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (PPBBPPBBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP018 (1D Ace-1 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 (DEP018)
8 / 52 Cards

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

Ace-1 Remaining
1 of 4 Cards

3 Ace cards valued at 1 modulo-10 point removed from the 1D pack.

Banker EV (EZ Bar-7)
-0.8152%

Resolved at 45.9613% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.4382%

Resolved at 44.5231% Player win rate with 0.9383 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3592% house hold on the 8-to-1 Tie wager in state DEP018.

FINITE-SHOE ENUMERATION · DEP018

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

Finite-shoe specification DEP018 tracks Ace-1 removal at 85% depth in 1-deck play: with 1 of 4 Ace (1-Point Pip) cards left in the 8-card stub, Tie incidence is 9.5156% and Banker expectation settles at -0.8152% (EZ Bar-7).

For DEP018 (1-deck shoe, 85% dealt), removing aces slightly favors (dep018) banker because banker stands on (1d-85%) 6 against player third-card ace (dep018·1d-85%) while player must draw on 0–5. Holding 1 of 4 Ace-1 cards in a 8-card stub with +0.44 bps rank slope yields 45.9613% Banker, 44.5231% Player, and 9.5156% Tie.

State DEP018 (1D, 85% depth, 1/4 Ace-1 left, EZ Bar-7)
Wager / MetricState DEP018 Value1D BaselineSettlement Note
DEP018 Banker (EZ Bar-7)45.9613% (-0.8152% EV)45.9595%DEP018 1D 85% (1 Ace-1)
DEP018 Player (1:1)44.5231% (-1.4382% EV)44.5249%DEP018 8-card 1D stub (0.9383 SD)
DEP018 Tie (8:1)9.5156% (-14.3592% EV)9.5156%DEP018 Ace-1 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP018

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP018 · 1D)

For DEP018 (8 remaining cards in a 52-card 1D shoe at 85% depth), tracking all 3 exited Ace-1 cards moves Banker win rate to 45.9613% (-0.8152% EV, EZ Bar-7) and Player to 44.5231% (-1.4382% EV).

  • DEP018 (1D 85%): 8/52 cards with 1/4 Ace-1 (4A).
  • DEP018 (Ace-1 split): 45.9613% Banker, 44.5231% Player, 9.5156% Tie in 8 1D cards (4B).
  • DEP018 (EZ Bar-7 EV): -0.8152% Banker, -1.4382% Player, -14.3592% Tie, 0.9383 SD at 85% (4C).
  • DEP018 (1D roads): red/blue marks log Big Road columns, never 1 Ace-1 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Ace (1-Point Pip) cards leave a 1D shoe by 85% depth (DEP018), 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 Ace-1 stub counts (1/4 in 8 cards); Banker carries a -0.8152% 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