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

8-Deck Eight-Pip Card Depletion at 75% Penetration (4% Audit DEP439)

Removing 28 of 32 Eight-Pip Card (Rank-8) cards at 75% penetration of a 8-deck (416-card) shoe leaves 4 Rank-8 cards inside a 104-card stub (DEP439), producing 45.8574% Banker wins, 44.6271% Player wins, 9.5155% Ties, and a 0.6039% Banker house edge under 4%.

Banker EV (4% Vig)
-0.6039%
Player EV (1:1)
-1.2304%
Rank-8 in 104-Card Stub
4/32
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 B P B P P B B P P B P
Big Eye Boy = = = = ≠ = = = ≠ ≠ = = = = ≠
Small Road = = ≠ ≠ = = ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP439 (8D 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 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP439)
104 / 416 Cards

75% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-8 Remaining
4 of 32 Cards

28 8-pip cards (Natural 8 generator and Banker 3 block) removed from the 8D pack.

Banker EV (4% Vig)
-0.6039%

Resolved at 45.8574% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2304%

Resolved at 44.6271% Player win rate with 0.9394 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3604% house hold on the 8-to-1 Tie wager in state DEP439.

FINITE-SHOE ENUMERATION · DEP439

How Eight-Pip Card Depletion at 75% Depth Impacts 8D (4% Vig)

At 75% penetration of a 416-card (8D) shoe, state DEP439 isolates 28 dealt Rank-8 cards (4 remaining inside 104 stub cards), yielding 45.8574% Banker wins, 44.6271% Player wins, and 0.9394 per-hand standard deviation under 4%.

When 28 Rank-8 cards exit a 8D shoe by 75% penetration (DEP439, 4 left in 104 cards), depleting 8-pip cards also (dep439-rank-8) lowers two-card natural 8 lockouts (104c) when paired with zero-point tens (dep439-rank-8·104c) and court cards, combining a -0.50 bps rank vector with 4% settlement (-0.6039% Banker EV).

State DEP439 (8D, 75% depth, 4/32 Rank-8 left, 4% Vig)
Wager / MetricState DEP439 Value8D BaselineSettlement Note
DEP439 Banker (4% Vig)45.8574% (-0.6039% EV)45.8597%DEP439 8D 75% (4 Rank-8)
DEP439 Player (1:1)44.6271% (-1.2304% EV)44.6247%DEP439 104-card 8D stub (0.9394 SD)
DEP439 Tie (8:1)9.5155% (-14.3604% EV)9.5156%DEP439 Rank-8 (28 out, 4 in)
TABLEAU & SCOREBOARD SEPARATION · DEP439

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP439 · 8D)

Across 100-hand session horizons at state DEP439 (8D 75% depth, 4/32 Rank-8 in 104 cards), single-hand dispersion (0.9394 SD) dominates the 0.6039% (4% Vig) Banker and 1.2304% Player expectation gap.

  • DEP439 (8D 75%): 104/416 cards with 4/32 Rank-8 (2A).
  • DEP439 (Rank-8 split): 45.8574% Banker, 44.6271% Player, 9.5155% Tie in 104 8D cards (2B).
  • DEP439 (4% Vig EV): -0.6039% Banker, -1.2304% Player, -14.3604% Tie, 0.9394 SD at 75% (2C).
  • DEP439 (8D roads): red/blue marks log Big Road columns, never 4 Rank-8 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 28 Eight-Pip Card cards leave a 8D shoe by 75% depth (DEP439), 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 (4/32 in 104 cards); Banker carries a -0.6039% 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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