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COMBINATORIAL DEPLETION · 2D · ACE-1 · 80% DEPTH

2-Deck Ace (1-Point Pip) Depletion at 80% Penetration (Super 6 Audit DEP107)

Removing 7 of 8 Ace (1-Point Pip) (Ace-1) cards at 80% penetration of a 2-deck (104-card) shoe leaves 1 Ace-1 cards inside a 21-card stub (DEP107), producing 45.9019% Banker wins, 44.5655% Player wins, 9.5326% Ties, and a 1.3566% Banker house edge under Super 6.

Banker EV (Super 6)
-1.3566%
Player EV (1:1)
-1.3364%
Ace-1 in 21-Card Stub
1/8
Single-Hand Std Dev
0.9378
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBBBBPPPPBBPPBP) illustrating derived-road symmetry checks alongside DEP107 (2D Ace-1 at 80% 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 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 3 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Cockroach Pig Mark #2

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 4 goes down to Row 3, so use Rule 2: look 3 columns back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP107)
21 / 104 Cards

80% 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 (Super 6)
-1.3566%

Resolved at 45.9019% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.3364%

Resolved at 44.5655% Player win rate with 0.9378 unit standard deviation.

Tie Incidence (8:1)
9.5326%

Produces a 14.2062% house hold on the 8-to-1 Tie wager in state DEP107.

FINITE-SHOE ENUMERATION · DEP107

How Ace (1-Point Pip) Depletion at 80% Depth Impacts 2D (Super 6)

Across 112,869,612,134,400 initial 2D permutations, depletion node DEP107 narrows to a 21-card stub (80% depth) holding 1 of 8 Ace-1 cards, where Banker resolves at 45.9019% (-1.3566% EV) and Player at 44.5655% (-1.3364% EV).

When fewer Aces remain, (DEP107-Ace-1) Player 7 and 8 third-card (21c) transitions from 6 and 7 (DEP107-Ace-1·21c) occur less often during six-card resolutions. Because 7 of 8 Ace (1-Point Pip) cards are absent in DEP107 at 80% 2D penetration (21 cards left), per-card sensitivity (+0.44 bps) interacts directly with deep-shoe 80% penetration depth (DEP107) under Super 6 no-commission rules (Ace-1) (winning Banker 6 pays 1:2) (DEP107·Ace-1).

State DEP107 (2D, 80% depth, 1/8 Ace-1 left, Super 6)
Wager / MetricState DEP107 Value2D BaselineSettlement Note
DEP107 Banker (Super 6)45.9019% (-1.3566% EV)45.8998%DEP107 2D 80% (1 Ace-1)
DEP107 Player (1:1)44.5655% (-1.3364% EV)44.5676%DEP107 21-card 2D stub (0.9378 SD)
DEP107 Tie (8:1)9.5326% (-14.2062% EV)9.5326%DEP107 Ace-1 (7 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP107

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP107 · 2D)

In studio and floor audits of DEP107 (21 cards undealt out of 104 in 2D at 80% depth), a 0.9378 unit standard deviation accompanies the 1-card Ace-1 stub under Super 6 (45.9019% Banker vs 44.5655% Player).

  • DEP107 (2D 80%): 21/104 cards with 1/8 Ace-1 (1A).
  • DEP107 (Ace-1 split): 45.9019% Banker, 44.5655% Player, 9.5326% Tie in 21 2D cards (1B).
  • DEP107 (Super 6 EV): -1.3566% Banker, -1.3364% Player, -14.2062% Tie, 0.9378 SD at 80% (1C).
  • DEP107 (2D roads): red/blue marks log Big Road columns, never 1 Ace-1 stub count (1D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Ace (1-Point Pip) cards leave a 2D shoe by 80% depth (DEP107), 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 21 cards); Banker carries a -1.3566% expectation under Super 6.
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