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COMBINATORIAL DEPLETION · 2D · ACE-1 · 50% DEPTH

2-Deck Ace (1-Point Pip) Depletion at 50% Penetration (Super 6 Audit DEP103)

Removing 5 of 8 Ace (1-Point Pip) (Ace-1) cards at 50% penetration of a 2-deck (104-card) shoe leaves 3 Ace-1 cards inside a 52-card stub (DEP103), producing 45.9010% Banker wins, 44.5663% Player wins, 9.5326% Ties, and a 1.3583% Banker house edge under Super 6.

Banker EV (Super 6)
-1.3583%
Player EV (1:1)
-1.3347%
Ace-1 in 52-Card Stub
3/8
Single-Hand Std Dev
0.9348
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP103 (2D Ace-1 at 50% 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 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP103)
52 / 104 Cards

50% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Ace-1 Remaining
3 of 8 Cards

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

Banker EV (Super 6)
-1.3583%

Resolved at 45.9010% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.3347%

Resolved at 44.5663% Player win rate with 0.9348 unit standard deviation.

Tie Incidence (8:1)
9.5326%

Produces a 14.2063% house hold on the 8-to-1 Tie wager in state DEP103.

FINITE-SHOE ENUMERATION · DEP103

How Ace (1-Point Pip) Depletion at 50% Depth Impacts 2D (Super 6)

At 50% penetration of a 104-card (2D) shoe, state DEP103 isolates 5 dealt Ace-1 cards (3 remaining inside 52 stub cards), yielding 45.9010% Banker wins, 44.5663% Player wins, and 0.9348 per-hand standard deviation under Super 6.

Because when fewer aces remain, (dep103-ace-1) player 7 and 8 third-card (52c) transitions from 6 and 7 (dep103-ace-1·52c) occur less often during six-card resolutions, state DEP103 (50% 2D depth, 5 Ace-1 removed, 3 in 52 cards) registers a +0.44 bps rank derivative and 1.3583% Banker house edge (Super 6).

State DEP103 (2D, 50% depth, 3/8 Ace-1 left, Super 6)
Wager / MetricState DEP103 Value2D BaselineSettlement Note
DEP103 Banker (Super 6)45.9010% (-1.3583% EV)45.8998%DEP103 2D 50% (3 Ace-1)
DEP103 Player (1:1)44.5663% (-1.3347% EV)44.5676%DEP103 52-card 2D stub (0.9348 SD)
DEP103 Tie (8:1)9.5326% (-14.2063% EV)9.5326%DEP103 Ace-1 (5 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP103

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP103 · 2D)

Synthesizing DEP103 (2D at 50% depth, 3 Ace (1-Point Pip) cards left inside 52 stub cards): Super 6 rules produce a 1.3583% Banker edge, 1.3347% Player edge, 14.2063% Tie edge, and 0.9348 unit volatility.

  • DEP103 (2D 50%): 52/104 cards with 3/8 Ace-1 (2A).
  • DEP103 (Ace-1 split): 45.9010% Banker, 44.5663% Player, 9.5326% Tie in 52 2D cards (2B).
  • DEP103 (Super 6 EV): -1.3583% Banker, -1.3347% Player, -14.2063% Tie, 0.9348 SD at 50% (2C).
  • DEP103 (2D roads): red/blue marks log Big Road columns, never 3 Ace-1 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 5 Ace (1-Point Pip) cards leave a 2D shoe by 50% depth (DEP103), 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 (3/8 in 52 cards); Banker carries a -1.3583% 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