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COMBINATORIAL DEPLETION · 8D · RANK-2 · 75% DEPTH

8-Deck Two-Pip (Deuce) Depletion at 75% Penetration (4% Audit DEP385)

Removing 28 of 32 Two-Pip (Deuce) (Rank-2) cards at 75% penetration of a 8-deck (416-card) shoe leaves 4 Rank-2 cards inside a 104-card stub (DEP385), producing 45.8621% Banker wins, 44.6222% Player wins, 9.5157% Ties, and a 0.5947% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5947%
Player EV (1:1)
-1.2398%
Rank-2 in 104-Card Stub
4/32
Single-Hand Std Dev
0.9376
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 B B P B P
Big Eye Boy = = = = = = ≠ = = = ≠ ≠ ≠ =
Small Road = = = = ≠ ≠ = = ≠ ≠ = ≠
Cockroach Pig = = ≠ ≠ ≠ = ≠ ≠ = =

Reference shoe scoreboard (BBPPBBPPBPTBPBBPBP) illustrating derived-road symmetry checks alongside DEP385 (8D Rank-2 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 (DEP385)
104 / 416 Cards

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

Rank-2 Remaining
4 of 32 Cards

28 2-pip cards across all four suits removed from the 8D pack.

Banker EV (4% Vig)
-0.5947%

Resolved at 45.8621% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2398%

Resolved at 44.6222% Player win rate with 0.9376 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3588% house hold on the 8-to-1 Tie wager in state DEP385.

FINITE-SHOE ENUMERATION · DEP385

How Two-Pip (Deuce) Depletion at 75% Depth Impacts 8D (4% Vig)

Card-removal benchmark DEP385 measures Two-Pip (Deuce) (Rank-2) scarcity at 75% depth in a 8-deck shoe: 28 removed ranks leave 4 in the 104-card remainder, shifting Banker win share to 45.8621% (0.5947% edge, 4% Vig).

Combinatorial weighting in DEP385 (104 cards left from 416 at 75% depth) is governed by two rules: on banker total 4, (dep385) banker draws against player third-card (8d-75%) 2 through 7; removing 2s (dep385·8d-75%) trims low-pip player third-card triggers, and three-quarters of the shoe (dep385-8d) has been dealt and winning (4/32) banker wagers return 0.96 units (dep385-8d·4/32) net per unit risked (+0.52 bps per Rank-2 removed).

State DEP385 (8D, 75% depth, 4/32 Rank-2 left, 4% Vig)
Wager / MetricState DEP385 Value8D BaselineSettlement Note
DEP385 Banker (4% Vig)45.8621% (-0.5947% EV)45.8597%DEP385 8D 75% (4 Rank-2)
DEP385 Player (1:1)44.6222% (-1.2398% EV)44.6247%DEP385 104-card 8D stub (0.9376 SD)
DEP385 Tie (8:1)9.5157% (-14.3588% EV)9.5156%DEP385 Rank-2 (28 out, 4 in)
TABLEAU & SCOREBOARD SEPARATION · DEP385

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP385 · 8D)

Across 100-hand session horizons at state DEP385 (8D 75% depth, 4/32 Rank-2 in 104 cards), single-hand dispersion (0.9376 SD) dominates the 0.5947% (4% Vig) Banker and 1.2398% Player expectation gap.

  • DEP385 (8D 75%): 104/416 cards with 4/32 Rank-2 (5A).
  • DEP385 (Rank-2 split): 45.8621% Banker, 44.6222% Player, 9.5157% Tie in 104 8D cards (5B).
  • DEP385 (4% Vig EV): -0.5947% Banker, -1.2398% Player, -14.3588% Tie, 0.9376 SD at 75% (5C).
  • DEP385 (8D roads): red/blue marks log Big Road columns, never 4 Rank-2 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 28 Two-Pip (Deuce) cards leave a 8D shoe by 75% depth (DEP385), 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-2 stub counts (4/32 in 104 cards); Banker carries a -0.5947% 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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