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COMBINATORIAL DEPLETION · 1D · RANK-8 · 75% DEPTH

1-Deck Eight-Pip Card Depletion at 75% Penetration (4% Audit DEP079)

Removing 3 of 4 Eight-Pip Card (Rank-8) cards at 75% penetration of a 1-deck (52-card) shoe leaves 1 Rank-8 cards inside a 13-card stub (DEP079), producing 45.9575% Banker wins, 44.5269% Player wins, 9.5155% Ties, and a 0.4077% Banker house edge under 4%.

Banker EV (4% Vig)
-0.4077%
Player EV (1:1)
-1.4306%
Rank-8 in 13-Card Stub
1/4
Single-Hand Std Dev
0.9394
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 P B B P B
Big Eye Boy = = = = = = ≠ = = = = = = =
Small Road = = = = = = ≠ ≠ = = = =
Cockroach Pig = = = = = = ≠ ≠ ≠ =

Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP079 (1D Rank-8 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 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 (DEP079)
13 / 52 Cards

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

Rank-8 Remaining
1 of 4 Cards

3 8-pip cards (Natural 8 generator and Banker 3 block) removed from the 1D pack.

Banker EV (4% Vig)
-0.4077%

Resolved at 45.9575% Banker win rate under 4% settlement.

Player EV (1:1)
-1.4306%

Resolved at 44.5269% Player win rate with 0.9394 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3603% house hold on the 8-to-1 Tie wager in state DEP079.

FINITE-SHOE ENUMERATION · DEP079

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

Across 14,658,134,400 initial 1D permutations, depletion node DEP079 narrows to a 13-card stub (75% depth) holding 1 of 4 Rank-8 cards, where Banker resolves at 45.9575% (-0.4077% EV) and Player at 44.5269% (-1.4306% EV).

When 3 Rank-8 cards exit a 1D shoe by 75% penetration (DEP079, 1 left in 13 cards), depleting 8-pip cards also (dep079-rank-8) lowers two-card natural 8 lockouts (13c) when paired with zero-point tens (dep079-rank-8·13c) and court cards, combining a -0.50 bps rank vector with 4% settlement (-0.4077% Banker EV).

State DEP079 (1D, 75% depth, 1/4 Rank-8 left, 4% Vig)
Wager / MetricState DEP079 Value1D BaselineSettlement Note
DEP079 Banker (4% Vig)45.9575% (-0.4077% EV)45.9595%DEP079 1D 75% (1 Rank-8)
DEP079 Player (1:1)44.5269% (-1.4306% EV)44.5249%DEP079 13-card 1D stub (0.9394 SD)
DEP079 Tie (8:1)9.5155% (-14.3603% EV)9.5156%DEP079 Rank-8 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP079

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP079 · 1D)

Even at 75% penetration in DEP079 where 3 Rank-8 cards have exited a 1D shoe (1 left in 13 cards), derived-road red and blue entries measure structural regularity on the Big Road—not whether Banker (-0.4077% EV, 4% Vig) or Player (-1.4306% EV) is favored next.

  • DEP079 (1D 75%): 13/52 cards with 1/4 Rank-8 (1A).
  • DEP079 (Rank-8 split): 45.9575% Banker, 44.5269% Player, 9.5155% Tie in 13 1D cards (1B).
  • DEP079 (4% Vig EV): -0.4077% Banker, -1.4306% Player, -14.3603% Tie, 0.9394 SD at 75% (1C).
  • DEP079 (1D roads): red/blue marks log Big Road columns, never 1 Rank-8 stub count (1D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Eight-Pip Card cards leave a 1D shoe by 75% depth (DEP079), 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-8 stub counts (1/4 in 13 cards); Banker carries a -0.4077% expectation under 4%.
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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
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