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COMBINATORIAL DEPLETION · 2D · ACE-1 · 25% DEPTH

2-Deck Ace (1-Point Pip) Depletion at 25% Penetration (5% Audit DEP101)

Removing 2 of 8 Ace (1-Point Pip) (Ace-1) cards at 25% penetration of a 2-deck (104-card) shoe leaves 6 Ace-1 cards inside a 78-card stub (DEP101), producing 45.9002% Banker wins, 44.5672% Player wins, 9.5326% Ties, and a 0.9620% Banker house edge under 5%.

Banker EV (5% Vig)
-0.9620%
Player EV (1:1)
-1.3331%
Ace-1 in 78-Card Stub
6/8
Single-Hand Std Dev
0.9323
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPPBBBPPBPTBPBBP) illustrating derived-road symmetry checks alongside DEP101 (2D Ace-1 at 25% 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

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

  1. Column 2 goes down to Row 3, so use Rule 2: look 1 column 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.

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

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 (DEP101)
78 / 104 Cards

25% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Ace-1 Remaining
6 of 8 Cards

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

Banker EV (5% Vig)
-0.9620%

Resolved at 45.9002% Banker win rate under 5% settlement.

Player EV (1:1)
-1.3331%

Resolved at 44.5672% Player win rate with 0.9323 unit standard deviation.

Tie Incidence (8:1)
9.5326%

Produces a 14.2065% house hold on the 8-to-1 Tie wager in state DEP101.

FINITE-SHOE ENUMERATION · DEP101

How Ace (1-Point Pip) Depletion at 25% Depth Impacts 2D (5% Vig)

When a 2D shoe reaches 25% cut-card depth (78 of 104 cards undealt, state DEP101) with 2 Ace (1-Point Pip) cards removed and 6 remaining, Player wins 44.5672% (1.3331% edge) while Banker wins 45.9002% (0.9620% edge under 5%).

When 2 Ace-1 cards exit a 2D shoe by 25% penetration (DEP101, 6 left in 78 cards), when fewer aces remain, (dep101-ace-1) player 7 and 8 third-card (78c) transitions from 6 and 7 (dep101-ace-1·78c) occur less often during six-card resolutions, combining a +0.44 bps rank vector with 5% settlement (-0.9620% Banker EV).

State DEP101 (2D, 25% depth, 6/8 Ace-1 left, 5% Vig)
Wager / MetricState DEP101 Value2D BaselineSettlement Note
DEP101 Banker (5% Vig)45.9002% (-0.9620% EV)45.8998%DEP101 2D 25% (6 Ace-1)
DEP101 Player (1:1)44.5672% (-1.3331% EV)44.5676%DEP101 78-card 2D stub (0.9323 SD)
DEP101 Tie (8:1)9.5326% (-14.2065% EV)9.5326%DEP101 Ace-1 (2 out, 6 in)
TABLEAU & SCOREBOARD SEPARATION · DEP101

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP101 · 2D)

While DEP101 tracks 2 removed Ace (1-Point Pip) cards across 25% of a 104-card (2D) shoe (78 remaining, 0.9620% 5% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP101 (2D 25%): 78/104 cards with 6/8 Ace-1 (6A).
  • DEP101 (Ace-1 split): 45.9002% Banker, 44.5672% Player, 9.5326% Tie in 78 2D cards (6B).
  • DEP101 (5% Vig EV): -0.9620% Banker, -1.3331% Player, -14.2065% Tie, 0.9323 SD at 25% (6C).
  • DEP101 (2D roads): red/blue marks log Big Road columns, never 6 Ace-1 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 2 Ace (1-Point Pip) cards leave a 2D shoe by 25% depth (DEP101), 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 (6/8 in 78 cards); Banker carries a -0.9620% expectation under 5%.
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