Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 1D Rank-2 Depletion at 85% Depth (EZ Bar-7)
COMBINATORIAL DEPLETION · 1D · RANK-2 · 85% DEPTH

1-Deck Two-Pip (Deuce) Depletion at 85% Penetration (EZ Baccarat Audit DEP027)

Removing 3 of 4 Two-Pip (Deuce) (Rank-2) cards at 85% penetration of a 1-deck (52-card) shoe leaves 1 Rank-2 cards inside a 8-card stub (DEP027), producing 45.9616% Banker wins, 44.5227% Player wins, 9.5157% Ties, and a 0.8145% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-0.8145%
Player EV (1:1)
-1.4389%
Rank-2 in 8-Card Stub
1/4
Single-Hand Std Dev
0.9386
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 DEP027 (1D Rank-2 at 85% 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 (DEP027)
8 / 52 Cards

85% 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 (EZ Bar-7)
-0.8145%

Resolved at 45.9616% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.4389%

Resolved at 44.5227% Player win rate with 0.9386 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3589% house hold on the 8-to-1 Tie wager in state DEP027.

FINITE-SHOE ENUMERATION · DEP027

How Two-Pip (Deuce) Depletion at 85% Depth Impacts 1D (EZ Bar-7)

Shoe-stub analysis DEP027 inspects 8 remaining cards at 85% penetration of a 52-card (1D) pack after 3 Two-Pip (Deuce) cards have cleared, leaving 1 Rank-2 cards and a 0.8145% EZ Baccarat Banker edge.

Depleting 2s shifts the (DEP027-Rank-2) probability of Banker converting a (8c) two-card 4 or 5 into (DEP027-Rank-2·8c) a winning three-card 6 or 7. Because 3 of 4 Two-Pip (Deuce) cards are absent in DEP027 at 85% 1D penetration (8 cards left), per-card sensitivity (+0.52 bps) interacts directly with cut-card boundary 85% penetration (DEP027) depth under EZ Baccarat barred (Rank-2) 3-card Banker 7 rules.

State DEP027 (1D, 85% depth, 1/4 Rank-2 left, EZ Bar-7)
Wager / MetricState DEP027 Value1D BaselineSettlement Note
DEP027 Banker (EZ Bar-7)45.9616% (-0.8145% EV)45.9595%DEP027 1D 85% (1 Rank-2)
DEP027 Player (1:1)44.5227% (-1.4389% EV)44.5249%DEP027 8-card 1D stub (0.9386 SD)
DEP027 Tie (8:1)9.5157% (-14.3589% EV)9.5156%DEP027 Rank-2 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP027

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP027 · 1D)

Synthesizing DEP027 (1D at 85% depth, 1 Two-Pip (Deuce) cards left inside 8 stub cards): EZ Baccarat rules produce a 0.8145% Banker edge, 1.4389% Player edge, 14.3589% Tie edge, and 0.9386 unit volatility.

  • DEP027 (1D 85%): 8/52 cards with 1/4 Rank-2 (7A).
  • DEP027 (Rank-2 split): 45.9616% Banker, 44.5227% Player, 9.5157% Tie in 8 1D cards (7B).
  • DEP027 (EZ Bar-7 EV): -0.8145% Banker, -1.4389% Player, -14.3589% Tie, 0.9386 SD at 85% (7C).
  • DEP027 (1D roads): red/blue marks log Big Road columns, never 1 Rank-2 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Two-Pip (Deuce) cards leave a 1D shoe by 85% depth (DEP027), 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 8 cards); Banker carries a -0.8145% expectation under EZ Baccarat.
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