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COMBINATORIAL DEPLETION · 2D · RANK-0 · 25% DEPTH

2-Deck 0-Value Tens & Faces Depletion at 25% Penetration (5% Audit DEP092)

Removing 9 of 32 0-Value Tens & Faces (Rank-0) cards at 25% penetration of a 2-deck (104-card) shoe leaves 23 Rank-0 cards inside a 78-card stub (DEP092), producing 45.9006% Banker wins, 44.5668% Player wins, 9.5326% Ties, and a 0.9612% Banker house edge under 5%.

Banker EV (5% Vig)
-0.9612%
Player EV (1:1)
-1.3338%
Rank-0 in 78-Card Stub
23/32
Single-Hand Std Dev
0.9320
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPPPPBBBBPPBBPB) illustrating derived-road symmetry checks alongside DEP092 (2D Rank-0 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

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 (DEP092)
78 / 104 Cards

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

Rank-0 Remaining
23 of 32 Cards

9 10, Jack, Queen, and King (zero-point cards) removed from the 2D pack.

Banker EV (5% Vig)
-0.9612%

Resolved at 45.9006% Banker win rate under 5% settlement.

Player EV (1:1)
-1.3338%

Resolved at 44.5668% Player win rate with 0.9320 unit standard deviation.

Tie Incidence (8:1)
9.5326%

Produces a 14.2062% house hold on the 8-to-1 Tie wager in state DEP092.

FINITE-SHOE ENUMERATION · DEP092

How 0-Value Tens & Faces Depletion at 25% Depth Impacts 2D (5% Vig)

Within double-deck European salon privé carriers and two-deck shoe pits, profile DEP092 examines 25% shoe depletion (78 of 104 cards remaining) after 9 Rank-0 cards exit, leaving 23 0-Value Tens & Faces cards and a 0.9612% Banker house hold under 5%.

Because fewer zero-value draws mean (dep092-rank-0) third-card pulls change running totals (78c) more frequently instead of leaving (dep092-rank-0·78c) totals unchanged, state DEP092 (25% 2D depth, 9 Rank-0 removed, 23 in 78 cards) registers a +0.18 bps rank derivative and 0.9612% Banker house edge (5% Vig).

State DEP092 (2D, 25% depth, 23/32 Rank-0 left, 5% Vig)
Wager / MetricState DEP092 Value2D BaselineSettlement Note
DEP092 Banker (5% Vig)45.9006% (-0.9612% EV)45.8998%DEP092 2D 25% (23 Rank-0)
DEP092 Player (1:1)44.5668% (-1.3338% EV)44.5676%DEP092 78-card 2D stub (0.9320 SD)
DEP092 Tie (8:1)9.5326% (-14.2062% EV)9.5326%DEP092 Rank-0 (9 out, 23 in)
TABLEAU & SCOREBOARD SEPARATION · DEP092

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP092 · 2D)

In studio and floor audits of DEP092 (78 cards undealt out of 104 in 2D at 25% depth), a 0.9320 unit standard deviation accompanies the 23-card Rank-0 stub under 5% Vig (45.9006% Banker vs 44.5668% Player).

  • DEP092 (2D 25%): 78/104 cards with 23/32 Rank-0 (3A).
  • DEP092 (Rank-0 split): 45.9006% Banker, 44.5668% Player, 9.5326% Tie in 78 2D cards (3B).
  • DEP092 (5% Vig EV): -0.9612% Banker, -1.3338% Player, -14.2062% Tie, 0.9320 SD at 25% (3C).
  • DEP092 (2D roads): red/blue marks log Big Road columns, never 23 Rank-0 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 9 0-Value Tens & Faces cards leave a 2D shoe by 25% depth (DEP092), 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 (23/32 in 78 cards); Banker carries a -0.9612% 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