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COMBINATORIAL DEPLETION · 8D · RANK-2 · 10% DEPTH

8-Deck Two-Pip (Deuce) Depletion at 10% Penetration (5% Audit DEP379)

Removing 4 of 32 Two-Pip (Deuce) (Rank-2) cards at 10% penetration of a 8-deck (416-card) shoe leaves 28 Rank-2 cards inside a 374-card stub (DEP379), producing 45.8599% Banker wins, 44.6245% Player wins, 9.5156% Ties, and a 1.0575% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0575%
Player EV (1:1)
-1.2355%
Rank-2 in 374-Card Stub
28/32
Single-Hand Std Dev
0.9311
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBBBBPPPPBBPPBP) illustrating derived-road symmetry checks alongside DEP379 (8D Rank-2 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

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 3 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Cockroach Pig Mark #2

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 4 goes down to Row 3, so use Rule 2: look 3 columns back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP379)
374 / 416 Cards

10% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-2 Remaining
28 of 32 Cards

4 2-pip cards across all four suits removed from the 8D pack.

Banker EV (5% Vig)
-1.0575%

Resolved at 45.8599% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2355%

Resolved at 44.6245% Player win rate with 0.9311 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3595% house hold on the 8-to-1 Tie wager in state DEP379.

FINITE-SHOE ENUMERATION · DEP379

How Two-Pip (Deuce) Depletion at 10% Depth Impacts 8D (5% Vig)

Audit DEP379 evaluates a 8-deck (416-card) shoe at 10% penetration where 4 of 32 Two-Pip (Deuce) cards have exited, leaving 28 Rank-2 cards inside the 374-card stub with Banker EV at -1.0575% under 5%.

Under the fixed third-card tableau for DEP379, on banker total 4, (dep379) banker draws against player third-card (8d-10%) 2 through 7; removing 2s (dep379·8d-10%) trims low-pip player third-card triggers. With 28 Rank-2 cards inside 374 remaining 8D cards (10% dealt), single-card slope (+0.52 bps) keeps Banker house edge at 1.0575% and Player at 1.2355%.

State DEP379 (8D, 10% depth, 28/32 Rank-2 left, 5% Vig)
Wager / MetricState DEP379 Value8D BaselineSettlement Note
DEP379 Banker (5% Vig)45.8599% (-1.0575% EV)45.8597%DEP379 8D 10% (28 Rank-2)
DEP379 Player (1:1)44.6245% (-1.2355% EV)44.6247%DEP379 374-card 8D stub (0.9311 SD)
DEP379 Tie (8:1)9.5156% (-14.3595% EV)9.5156%DEP379 Rank-2 (4 out, 28 in)
TABLEAU & SCOREBOARD SEPARATION · DEP379

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP379 · 8D)

Whether DEP379 is observed in eight-deck Macau, Las Vegas Strip, and Singapore standard shoes at 10% depth (374/416 cards left, 28 Rank-2 remaining), 5% Vig settlement locks Banker EV at -1.0575% and Player EV at -1.2355% with 9.5156% Ties.

  • DEP379 (8D 10%): 374/416 cards with 28/32 Rank-2 (3A).
  • DEP379 (Rank-2 split): 45.8599% Banker, 44.6245% Player, 9.5156% Tie in 374 8D cards (3B).
  • DEP379 (5% Vig EV): -1.0575% Banker, -1.2355% Player, -14.3595% Tie, 0.9311 SD at 10% (3C).
  • DEP379 (8D roads): red/blue marks log Big Road columns, never 28 Rank-2 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 4 Two-Pip (Deuce) cards leave a 8D shoe by 10% depth (DEP379), 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 (28/32 in 374 cards); Banker carries a -1.0575% expectation under 5%.
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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