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COMBINATORIAL DEPLETION · 1D · ACE-1 · 60% DEPTH

1-Deck Ace (1-Point Pip) Depletion at 60% Penetration (EZ Baccarat Audit DEP014)

Removing 3 of 4 Ace (1-Point Pip) (Ace-1) cards at 60% penetration of a 1-deck (52-card) shoe leaves 1 Ace-1 cards inside a 21-card stub (DEP014), producing 45.9611% Banker wins, 44.5233% Player wins, 9.5156% Ties, and a 0.8156% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.8156%
Player EV (1:1)
-1.4378%
Ace-1 in 21-Card Stub
1/4
Single-Hand Std Dev
0.9358
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPBPPBBPBPPBBPB) illustrating derived-road symmetry checks alongside DEP014 (1D Ace-1 at 60% 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 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #2

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 5 goes down to Row 2, so use Rule 2: look 3 columns back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP014)
21 / 52 Cards

60% 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)
-0.8156%

Resolved at 45.9611% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.4378%

Resolved at 44.5233% Player win rate with 0.9358 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3593% house hold on the 8-to-1 Tie wager in state DEP014.

FINITE-SHOE ENUMERATION · DEP014

How Ace (1-Point Pip) Depletion at 60% Depth Impacts 1D (EZ Bar-7)

Quantitative proof DEP014 documents 1D rank depletion at 60% depth: 3 exited Ace-1 cards leave 1 of 4 in the 21-card stub, generating 45.9611% Banker wins (-0.8156% EV under EZ Bar-7) and 44.5233% Player wins.

In six-card resolution tree DEP014 (1D at 60% depth, 21 cards left), when fewer aces remain, (dep014-ace-1) player 7 and 8 third-card (21c) transitions from 6 and 7 (dep014-ace-1·21c) occur less often during six-card resolutions; removing 3 of 4 Ace-1 cards (+0.44 bps weight) leaves Banker at -0.8156% EV under EZ Baccarat.

State DEP014 (1D, 60% depth, 1/4 Ace-1 left, EZ Bar-7)
Wager / MetricState DEP014 Value1D BaselineSettlement Note
DEP014 Banker (EZ Bar-7)45.9611% (-0.8156% EV)45.9595%DEP014 1D 60% (1 Ace-1)
DEP014 Player (1:1)44.5233% (-1.4378% EV)44.5249%DEP014 21-card 1D stub (0.9358 SD)
DEP014 Tie (8:1)9.5156% (-14.3593% EV)9.5156%DEP014 Ace-1 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP014

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP014 · 1D)

Across 100-hand session horizons at state DEP014 (1D 60% depth, 1/4 Ace-1 in 21 cards), single-hand dispersion (0.9358 SD) dominates the 0.8156% (EZ Bar-7) Banker and 1.4378% Player expectation gap.

  • DEP014 (1D 60%): 21/52 cards with 1/4 Ace-1 (5A).
  • DEP014 (Ace-1 split): 45.9611% Banker, 44.5233% Player, 9.5156% Tie in 21 1D cards (5B).
  • DEP014 (EZ Bar-7 EV): -0.8156% Banker, -1.4378% Player, -14.3593% Tie, 0.9358 SD at 60% (5C).
  • DEP014 (1D roads): red/blue marks log Big Road columns, never 1 Ace-1 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Ace (1-Point Pip) cards leave a 1D shoe by 60% depth (DEP014), 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 21 cards); Banker carries a -0.8156% 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