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COMBINATORIAL DEPLETION · 2D · ACE-1 · 75% DEPTH

2-Deck Ace (1-Point Pip) Depletion at 75% Penetration (4% Audit DEP106)

Removing 7 of 8 Ace (1-Point Pip) (Ace-1) cards at 75% penetration of a 2-deck (104-card) shoe leaves 1 Ace-1 cards inside a 26-card stub (DEP106), producing 45.9018% Banker wins, 44.5656% Player wins, 9.5326% Ties, and a 0.4998% Banker house edge under 4%.

Banker EV (4% Vig)
-0.4998%
Player EV (1:1)
-1.3362%
Ace-1 in 26-Card Stub
1/8
Single-Hand Std Dev
0.9373
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 B P P
Big Eye Boy = = ≠ ≠ ≠ = = = = ≠ = = = ≠
Small Road ≠ = = ≠ ≠ = = ≠ ≠ = = ≠
Cockroach Pig = = = = ≠ ≠ ≠ ≠ ≠ = ≠

Reference shoe scoreboard (PPBBPBTBPPBBPBPBPP) illustrating derived-road symmetry checks alongside DEP106 (2D Ace-1 at 75% 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

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

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 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.

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 (DEP106)
26 / 104 Cards

75% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Ace-1 Remaining
1 of 8 Cards

7 Ace cards valued at 1 modulo-10 point removed from the 2D pack.

Banker EV (4% Vig)
-0.4998%

Resolved at 45.9018% Banker win rate under 4% settlement.

Player EV (1:1)
-1.3362%

Resolved at 44.5656% Player win rate with 0.9373 unit standard deviation.

Tie Incidence (8:1)
9.5326%

Produces a 14.2062% house hold on the 8-to-1 Tie wager in state DEP106.

FINITE-SHOE ENUMERATION · DEP106

How Ace (1-Point Pip) Depletion at 75% Depth Impacts 2D (4% Vig)

Within double-deck European salon privé carriers and two-deck shoe pits, profile DEP106 examines 75% shoe depletion (26 of 104 cards remaining) after 7 Ace-1 cards exit, leaving 1 Ace (1-Point Pip) cards and a 0.4998% Banker house hold under 4%.

Removing Aces slightly favors (DEP106) Banker because Banker stands on (2D-75%) 6 against Player third-card Ace (DEP106·2D-75%) while Player must draw on 0–5. In state DEP106 (2D, 75% depth), each removed Ace-1 card applies a +0.44 bps baseline directional pressure before scaling to the 26-card remainder (1 Ace-1 left), while Three-quarters of the shoe (DEP106-2D) has been dealt and winning (1/8) Banker wagers return 0.96 units (DEP106-2D·1/8) net per unit risked.

State DEP106 (2D, 75% depth, 1/8 Ace-1 left, 4% Vig)
Wager / MetricState DEP106 Value2D BaselineSettlement Note
DEP106 Banker (4% Vig)45.9018% (-0.4998% EV)45.8998%DEP106 2D 75% (1 Ace-1)
DEP106 Player (1:1)44.5656% (-1.3362% EV)44.5676%DEP106 26-card 2D stub (0.9373 SD)
DEP106 Tie (8:1)9.5326% (-14.2062% EV)9.5326%DEP106 Ace-1 (7 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP106

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP106 · 2D)

On the electronic scoreboard for DEP106 (2D, 75% depth, 26 cards left), Bead Plate and Big Road circles record Banker (45.9018%) and Player (44.5656%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Ace-1 card counts (1/8).

  • DEP106 (2D 75%): 26/104 cards with 1/8 Ace-1 (3A).
  • DEP106 (Ace-1 split): 45.9018% Banker, 44.5656% Player, 9.5326% Tie in 26 2D cards (3B).
  • DEP106 (4% Vig EV): -0.4998% Banker, -1.3362% Player, -14.2062% Tie, 0.9373 SD at 75% (3C).
  • DEP106 (2D roads): red/blue marks log Big Road columns, never 1 Ace-1 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Ace (1-Point Pip) cards leave a 2D shoe by 75% depth (DEP106), 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 (1/8 in 26 cards); Banker carries a -0.4998% expectation under 4%.
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