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COMBINATORIAL DEPLETION · 8D · RANK-4 · 70% DEPTH

8-Deck Four-Pip Card Depletion at 70% Penetration (5% Audit DEP402)

Removing 26 of 32 Four-Pip Card (Rank-4) cards at 70% penetration of a 8-deck (416-card) shoe leaves 6 Rank-4 cards inside a 125-card stub (DEP402), producing 45.8646% Banker wins, 44.6197% Player wins, 9.5157% Ties, and a 1.0483% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0483%
Player EV (1:1)
-1.2449%
Rank-4 in 125-Card Stub
6/32
Single-Hand Std Dev
0.9377
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (PPBBPPBBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP402 (8D Rank-4 at 70% 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 (DEP402)
125 / 416 Cards

70% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-4 Remaining
6 of 32 Cards

26 4-pip cards (strongest pro-Banker removal sensitivity) removed from the 8D pack.

Banker EV (5% Vig)
-1.0483%

Resolved at 45.8646% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2449%

Resolved at 44.6197% Player win rate with 0.9377 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3589% house hold on the 8-to-1 Tie wager in state DEP402.

FINITE-SHOE ENUMERATION · DEP402

How Four-Pip Card Depletion at 70% Depth Impacts 8D (5% Vig)

Depletion matrix entry DEP402 pairs 8D (416 cards) at 70% penetration with 26 removed Four-Pip Card cards (6 left in 125 cards), fixing per-hand volatility at 0.9377 and Banker house hold at 1.0483% (5% Vig).

Tracking DEP402 across 125 remaining 8D cards (70% depth) shows that removing 4s produces the (dep402-rank-4) single largest per-card shift toward (125c) banker (and away from player) (dep402-rank-4·125c) of any rank in the shoe. With 26 Rank-4 cards gone (+1.19 bps unit sensitivity), Banker expectation is -1.0483% (5% Vig) vs -1.2449% on Player.

State DEP402 (8D, 70% depth, 6/32 Rank-4 left, 5% Vig)
Wager / MetricState DEP402 Value8D BaselineSettlement Note
DEP402 Banker (5% Vig)45.8646% (-1.0483% EV)45.8597%DEP402 8D 70% (6 Rank-4)
DEP402 Player (1:1)44.6197% (-1.2449% EV)44.6247%DEP402 125-card 8D stub (0.9377 SD)
DEP402 Tie (8:1)9.5157% (-14.3589% EV)9.5156%DEP402 Rank-4 (26 out, 6 in)
TABLEAU & SCOREBOARD SEPARATION · DEP402

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP402 · 8D)

Whether DEP402 is observed in eight-deck Macau, Las Vegas Strip, and Singapore standard shoes at 70% depth (125/416 cards left, 6 Rank-4 remaining), 5% Vig settlement locks Banker EV at -1.0483% and Player EV at -1.2449% with 9.5157% Ties.

  • DEP402 (8D 70%): 125/416 cards with 6/32 Rank-4 (6A).
  • DEP402 (Rank-4 split): 45.8646% Banker, 44.6197% Player, 9.5157% Tie in 125 8D cards (6B).
  • DEP402 (5% Vig EV): -1.0483% Banker, -1.2449% Player, -14.3589% Tie, 0.9377 SD at 70% (6C).
  • DEP402 (8D roads): red/blue marks log Big Road columns, never 6 Rank-4 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 26 Four-Pip Card cards leave a 8D shoe by 70% depth (DEP402), 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-4 stub counts (6/32 in 125 cards); Banker carries a -1.0483% expectation under 5%.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

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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