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COMBINATORIAL DEPLETION · 1D · RANK-2 · 75% DEPTH

1-Deck Two-Pip (Deuce) Depletion at 75% Penetration (4% Audit DEP025)

Removing 3 of 4 Two-Pip (Deuce) (Rank-2) cards at 75% penetration of a 1-deck (52-card) shoe leaves 1 Rank-2 cards inside a 13-card stub (DEP025), producing 45.9615% Banker wins, 44.5228% Player wins, 9.5157% Ties, and a 0.3997% Banker house edge under 4%.

Banker EV (4% Vig)
-0.3997%
Player EV (1:1)
-1.4387%
Rank-2 in 13-Card Stub
1/4
Single-Hand Std Dev
0.9376
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 P B B P B P B B P
Big Eye Boy = = ≠ = = ≠ ≠ = = ≠ = = ≠ ≠
Small Road ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠
Cockroach Pig ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ ≠ ≠

Reference shoe scoreboard (BBPPBPTBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP025 (1D Rank-2 at 75% 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 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

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 (DEP025)
13 / 52 Cards

75% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-2 Remaining
1 of 4 Cards

3 2-pip cards across all four suits removed from the 1D pack.

Banker EV (4% Vig)
-0.3997%

Resolved at 45.9615% Banker win rate under 4% settlement.

Player EV (1:1)
-1.4387%

Resolved at 44.5228% Player win rate with 0.9376 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3589% house hold on the 8-to-1 Tie wager in state DEP025.

FINITE-SHOE ENUMERATION · DEP025

How Two-Pip (Deuce) Depletion at 75% Depth Impacts 1D (4% Vig)

Removing 3 of 4 Rank-2 cards by the 75% mark of a 1-deck shoe (DEP025, 13 cards left) leaves 1 Two-Pip (Deuce) cards and adjusts conditional probabilities to 45.9615% Banker, 44.5228% Player, and 9.5157% Tie under 4%.

In six-card resolution tree DEP025 (1D at 75% depth, 13 cards left), depleting 2s shifts the (dep025-rank-2) probability of banker converting a (13c) two-card 4 or 5 into (dep025-rank-2·13c) a winning three-card 6 or 7; removing 3 of 4 Rank-2 cards (+0.52 bps weight) leaves Banker at -0.3997% EV under 4%.

State DEP025 (1D, 75% depth, 1/4 Rank-2 left, 4% Vig)
Wager / MetricState DEP025 Value1D BaselineSettlement Note
DEP025 Banker (4% Vig)45.9615% (-0.3997% EV)45.9595%DEP025 1D 75% (1 Rank-2)
DEP025 Player (1:1)44.5228% (-1.4387% EV)44.5249%DEP025 13-card 1D stub (0.9376 SD)
DEP025 Tie (8:1)9.5157% (-14.3589% EV)9.5156%DEP025 Rank-2 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP025

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP025 · 1D)

While DEP025 tracks 3 removed Two-Pip (Deuce) cards across 75% of a 52-card (1D) shoe (13 remaining, 0.3997% 4% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP025 (1D 75%): 13/52 cards with 1/4 Rank-2 (4A).
  • DEP025 (Rank-2 split): 45.9615% Banker, 44.5228% Player, 9.5157% Tie in 13 1D cards (4B).
  • DEP025 (4% Vig EV): -0.3997% Banker, -1.4387% Player, -14.3589% Tie, 0.9376 SD at 75% (4C).
  • DEP025 (1D roads): red/blue marks log Big Road columns, never 1 Rank-2 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Two-Pip (Deuce) cards leave a 1D shoe by 75% depth (DEP025), 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-2 stub counts (1/4 in 13 cards); Banker carries a -0.3997% expectation under 4%.
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