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COMBINATORIAL DEPLETION · 1D · RANK-7 · 10% DEPTH

1-Deck Seven-Pip Card Depletion at 10% Penetration (5% Audit DEP064)

Removing 1 of 4 Seven-Pip Card (Rank-7) cards at 10% penetration of a 1-deck (52-card) shoe leaves 3 Rank-7 cards inside a 47-card stub (DEP064), producing 45.9588% Banker wins, 44.5256% Player wins, 9.5156% Ties, and a 0.8648% Banker house edge under 5%.

Banker EV (5% Vig)
-0.8648%
Player EV (1:1)
-1.4331%
Rank-7 in 47-Card Stub
3/4
Single-Hand Std Dev
0.9326
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPPBBPPBBPBTBPB) illustrating derived-road symmetry checks alongside DEP064 (1D Rank-7 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

Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

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

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.

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 (DEP064)
47 / 52 Cards

10% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-7 Remaining
3 of 4 Cards

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

Banker EV (5% Vig)
-0.8648%

Resolved at 45.9588% Banker win rate under 5% settlement.

Player EV (1:1)
-1.4331%

Resolved at 44.5256% Player win rate with 0.9326 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3598% house hold on the 8-to-1 Tie wager in state DEP064.

FINITE-SHOE ENUMERATION · DEP064

How Seven-Pip Card Depletion at 10% Depth Impacts 1D (5% Vig)

Within single-deck laboratory benchmarks and historical pitch audits, profile DEP064 examines 10% shoe depletion (47 of 52 cards remaining) after 1 Rank-7 cards exit, leaving 3 Seven-Pip Card cards and a 0.8648% Banker house hold under 5%.

Tracking DEP064 across 47 remaining 1D cards (10% depth) shows that depleting 7s lowers the (dep064-rank-7) rate of winning three-card banker (47c) 7 hands (the barred push (dep064-rank-7·47c) total on ez baccarat tables). With 1 Rank-7 cards gone (-0.83 bps unit sensitivity), Banker expectation is -0.8648% (5% Vig) vs -1.4331% on Player.

State DEP064 (1D, 10% depth, 3/4 Rank-7 left, 5% Vig)
Wager / MetricState DEP064 Value1D BaselineSettlement Note
DEP064 Banker (5% Vig)45.9588% (-0.8648% EV)45.9595%DEP064 1D 10% (3 Rank-7)
DEP064 Player (1:1)44.5256% (-1.4331% EV)44.5249%DEP064 47-card 1D stub (0.9326 SD)
DEP064 Tie (8:1)9.5156% (-14.3598% EV)9.5156%DEP064 Rank-7 (1 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP064

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP064 · 1D)

Even at 10% penetration in DEP064 where 1 Rank-7 cards have exited a 1D shoe (3 left in 47 cards), derived-road red and blue entries measure structural regularity on the Big Road—not whether Banker (-0.8648% EV, 5% Vig) or Player (-1.4331% EV) is favored next.

  • DEP064 (1D 10%): 47/52 cards with 3/4 Rank-7 (3A).
  • DEP064 (Rank-7 split): 45.9588% Banker, 44.5256% Player, 9.5156% Tie in 47 1D cards (3B).
  • DEP064 (5% Vig EV): -0.8648% Banker, -1.4331% Player, -14.3598% Tie, 0.9326 SD at 10% (3C).
  • DEP064 (1D roads): red/blue marks log Big Road columns, never 3 Rank-7 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 1 Seven-Pip Card cards leave a 1D shoe by 10% depth (DEP064), 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 (3/4 in 47 cards); Banker carries a -0.8648% expectation under 5%.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

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  • 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