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COMBINATORIAL DEPLETION · 1D · RANK-7 · 75% DEPTH

1-Deck Seven-Pip Card Depletion at 75% Penetration (4% Audit DEP070)

Removing 3 of 4 Seven-Pip Card (Rank-7) cards at 75% penetration of a 1-deck (52-card) shoe leaves 1 Rank-7 cards inside a 13-card stub (DEP070), producing 45.9563% Banker wins, 44.5282% Player wins, 9.5155% Ties, and a 0.4102% Banker house edge under 4%.

Banker EV (4% Vig)
-0.4102%
Player EV (1:1)
-1.4280%
Rank-7 in 13-Card Stub
1/4
Single-Hand Std Dev
0.9391
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBBPPPBBPBTBPBPP) illustrating derived-road symmetry checks alongside DEP070 (1D Rank-7 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

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 2 goes down to Row 3, so use Rule 2: look 1 column 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.

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

Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP070)
13 / 52 Cards

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

Rank-7 Remaining
1 of 4 Cards

3 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 1D pack.

Banker EV (4% Vig)
-0.4102%

Resolved at 45.9563% Banker win rate under 4% settlement.

Player EV (1:1)
-1.4280%

Resolved at 44.5282% Player win rate with 0.9391 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3603% house hold on the 8-to-1 Tie wager in state DEP070.

FINITE-SHOE ENUMERATION · DEP070

How Seven-Pip Card Depletion at 75% Depth Impacts 1D (4% Vig)

Quantitative proof DEP070 documents 1D rank depletion at 75% depth: 3 exited Rank-7 cards leave 1 of 4 in the 13-card stub, generating 45.9563% Banker wins (-0.4102% EV under 4% Vig) and 44.5282% Player wins.

Because depleting 7s lowers the (dep070-rank-7) rate of winning three-card banker (13c) 7 hands (the barred push (dep070-rank-7·13c) total on ez baccarat tables), state DEP070 (75% 1D depth, 3 Rank-7 removed, 1 in 13 cards) registers a -0.83 bps rank derivative and 0.4102% Banker house edge (4% Vig).

State DEP070 (1D, 75% depth, 1/4 Rank-7 left, 4% Vig)
Wager / MetricState DEP070 Value1D BaselineSettlement Note
DEP070 Banker (4% Vig)45.9563% (-0.4102% EV)45.9595%DEP070 1D 75% (1 Rank-7)
DEP070 Player (1:1)44.5282% (-1.4280% EV)44.5249%DEP070 13-card 1D stub (0.9391 SD)
DEP070 Tie (8:1)9.5155% (-14.3603% EV)9.5156%DEP070 Rank-7 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP070

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP070 · 1D)

While DEP070 tracks 3 removed Seven-Pip Card cards across 75% of a 52-card (1D) shoe (13 remaining, 0.4102% 4% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP070 (1D 75%): 13/52 cards with 1/4 Rank-7 (5A).
  • DEP070 (Rank-7 split): 45.9563% Banker, 44.5282% Player, 9.5155% Tie in 13 1D cards (5B).
  • DEP070 (4% Vig EV): -0.4102% Banker, -1.4280% Player, -14.3603% Tie, 0.9391 SD at 75% (5C).
  • DEP070 (1D roads): red/blue marks log Big Road columns, never 1 Rank-7 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Seven-Pip Card cards leave a 1D shoe by 75% depth (DEP070), 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-7 stub counts (1/4 in 13 cards); Banker carries a -0.4102% 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