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COMBINATORIAL DEPLETION · 2D · RANK-0 · 10% DEPTH

2-Deck 0-Value Tens & Faces Depletion at 10% Penetration (5% Audit DEP091)

Removing 4 of 32 0-Value Tens & Faces (Rank-0) cards at 10% penetration of a 2-deck (104-card) shoe leaves 28 Rank-0 cards inside a 94-card stub (DEP091), producing 45.9001% Banker wins, 44.5673% Player wins, 9.5326% Ties, and a 0.9622% Banker house edge under 5%.

Banker EV (5% Vig)
-0.9622%
Player EV (1:1)
-1.3328%
Rank-0 in 94-Card Stub
28/32
Single-Hand Std Dev
0.9305
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 DEP091 (2D Rank-0 at 10% 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 (DEP091)
94 / 104 Cards

10% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Rank-0 Remaining
28 of 32 Cards

4 10, Jack, Queen, and King (zero-point cards) removed from the 2D pack.

Banker EV (5% Vig)
-0.9622%

Resolved at 45.9001% Banker win rate under 5% settlement.

Player EV (1:1)
-1.3328%

Resolved at 44.5673% Player win rate with 0.9305 unit standard deviation.

Tie Incidence (8:1)
9.5326%

Produces a 14.2064% house hold on the 8-to-1 Tie wager in state DEP091.

FINITE-SHOE ENUMERATION · DEP091

How 0-Value Tens & Faces Depletion at 10% Depth Impacts 2D (5% Vig)

Card-removal benchmark DEP091 measures 0-Value Tens & Faces (Rank-0) scarcity at 10% depth in a 2-deck shoe: 4 removed ranks leave 28 in the 94-card remainder, shifting Banker win share to 45.9001% (0.9622% edge, 5% Vig).

Tableau audit DEP091 confirms that depleting zero-point cards reduces (dep091) modulo-10 standoffs and alters two-card (2d-10%) natural combinations paired with 8s (dep091·2d-10%) and 9s. Inside the 94-card 2D stub (10% depth, 28/32 Rank-0 remaining, +0.18 bps slope), standard deviation is 0.9305 under 5% Vig.

State DEP091 (2D, 10% depth, 28/32 Rank-0 left, 5% Vig)
Wager / MetricState DEP091 Value2D BaselineSettlement Note
DEP091 Banker (5% Vig)45.9001% (-0.9622% EV)45.8998%DEP091 2D 10% (28 Rank-0)
DEP091 Player (1:1)44.5673% (-1.3328% EV)44.5676%DEP091 94-card 2D stub (0.9305 SD)
DEP091 Tie (8:1)9.5326% (-14.2064% EV)9.5326%DEP091 Rank-0 (4 out, 28 in)
TABLEAU & SCOREBOARD SEPARATION · DEP091

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP091 · 2D)

On the electronic scoreboard for DEP091 (2D, 10% depth, 94 cards left), Bead Plate and Big Road circles record Banker (45.9001%) and Player (44.5673%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Rank-0 card counts (28/32).

  • DEP091 (2D 10%): 94/104 cards with 28/32 Rank-0 (5A).
  • DEP091 (Rank-0 split): 45.9001% Banker, 44.5673% Player, 9.5326% Tie in 94 2D cards (5B).
  • DEP091 (5% Vig EV): -0.9622% Banker, -1.3328% Player, -14.2064% Tie, 0.9305 SD at 10% (5C).
  • DEP091 (2D roads): red/blue marks log Big Road columns, never 28 Rank-0 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 4 0-Value Tens & Faces cards leave a 2D shoe by 10% depth (DEP091), 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 Rank-0 stub counts (28/32 in 94 cards); Banker carries a -0.9622% 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