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COMBINATORIAL DEPLETION · 1D · RANK-6 · 75% DEPTH

1-Deck Six-Pip Card Depletion at 75% Penetration (4% Audit DEP061)

Removing 3 of 4 Six-Pip Card (Rank-6) cards at 75% penetration of a 1-deck (52-card) shoe leaves 1 Rank-6 cards inside a 13-card stub (DEP061), producing 45.9551% Banker wins, 44.5294% Player wins, 9.5155% Ties, and a 0.4125% Banker house edge under 4%.

Banker EV (4% Vig)
-0.4125%
Player EV (1:1)
-1.4257%
Rank-6 in 13-Card Stub
1/4
Single-Hand Std Dev
0.9388
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBPBBPPBPBBPPBP) illustrating derived-road symmetry checks alongside DEP061 (1D Rank-6 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

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 5 goes down to Row 2, so use Rule 2: look 3 columns back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP061)
13 / 52 Cards

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

Rank-6 Remaining
1 of 4 Cards

3 6-pip cards (standing threshold and Banker 6 trigger) removed from the 1D pack.

Banker EV (4% Vig)
-0.4125%

Resolved at 45.9551% Banker win rate under 4% settlement.

Player EV (1:1)
-1.4257%

Resolved at 44.5294% Player win rate with 0.9388 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3603% house hold on the 8-to-1 Tie wager in state DEP061.

FINITE-SHOE ENUMERATION · DEP061

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

At 75% penetration of a 52-card (1D) shoe, state DEP061 isolates 3 dealt Rank-6 cards (1 remaining inside 13 stub cards), yielding 45.9551% Banker wins, 44.5294% Player wins, and 0.9388 per-hand standard deviation under 4%.

Under the fixed third-card tableau for DEP061, banker 6 only draws (dep061) when player pulls a third-card (1d-75%) 6 or 7; depleting 6s (dep061·1d-75%) directly alters both banker 6 draws and super 6 settlement frequency. With 1 Rank-6 cards inside 13 remaining 1D cards (75% dealt), single-card slope (-1.13 bps) keeps Banker house edge at 0.4125% and Player at 1.4257%.

State DEP061 (1D, 75% depth, 1/4 Rank-6 left, 4% Vig)
Wager / MetricState DEP061 Value1D BaselineSettlement Note
DEP061 Banker (4% Vig)45.9551% (-0.4125% EV)45.9595%DEP061 1D 75% (1 Rank-6)
DEP061 Player (1:1)44.5294% (-1.4257% EV)44.5249%DEP061 13-card 1D stub (0.9388 SD)
DEP061 Tie (8:1)9.5155% (-14.3603% EV)9.5156%DEP061 Rank-6 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP061

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP061 · 1D)

On the electronic scoreboard for DEP061 (1D, 75% depth, 13 cards left), Bead Plate and Big Road circles record Banker (45.9551%) and Player (44.5294%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Rank-6 card counts (1/4).

  • DEP061 (1D 75%): 13/52 cards with 1/4 Rank-6 (2A).
  • DEP061 (Rank-6 split): 45.9551% Banker, 44.5294% Player, 9.5155% Tie in 13 1D cards (2B).
  • DEP061 (4% Vig EV): -0.4125% Banker, -1.4257% Player, -14.3603% Tie, 0.9388 SD at 75% (2C).
  • DEP061 (1D roads): red/blue marks log Big Road columns, never 1 Rank-6 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Six-Pip Card cards leave a 1D shoe by 75% depth (DEP061), 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-6 stub counts (1/4 in 13 cards); Banker carries a -0.4125% expectation under 4%.
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Read Every Derived Road at Table Speed

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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