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

8-Deck Eight-Pip Card Depletion at 10% Penetration (5% Audit DEP433)

Removing 4 of 32 Eight-Pip Card (Rank-8) cards at 10% penetration of a 8-deck (416-card) shoe leaves 28 Rank-8 cards inside a 374-card stub (DEP433), producing 45.8595% Banker wins, 44.6249% Player wins, 9.5156% Ties, and a 1.0584% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0584%
Player EV (1:1)
-1.2346%
Rank-8 in 374-Card Stub
28/32
Single-Hand Std Dev
0.9329
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 DEP433 (8D Rank-8 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

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 (DEP433)
374 / 416 Cards

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

Rank-8 Remaining
28 of 32 Cards

4 8-pip cards (Natural 8 generator and Banker 3 block) removed from the 8D pack.

Banker EV (5% Vig)
-1.0584%

Resolved at 45.8595% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2346%

Resolved at 44.6249% Player win rate with 0.9329 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3597% house hold on the 8-to-1 Tie wager in state DEP433.

FINITE-SHOE ENUMERATION · DEP433

How Eight-Pip Card Depletion at 10% Depth Impacts 8D (5% Vig)

Shoe-stub analysis DEP433 inspects 374 remaining cards at 10% penetration of a 416-card (8D) pack after 4 Eight-Pip Card cards have cleared, leaving 28 Rank-8 cards and a 1.0584% 5% Banker edge.

On Banker total 3, (DEP433) Banker draws against every Player (8D-10%) third card except 8; removing (DEP433·8D-10%) 8s eliminates Banker 3's sole standing exception. In state DEP433 (8D, 10% depth), each removed Rank-8 card applies a -0.50 bps baseline directional pressure before scaling to the 374-card remainder (28 Rank-8 left), while Winning Banker tickets pay (DEP433-8D) 0.95 units per unit staked (28/32) while 90% of the initial (DEP433-8D·28/32) shoe remains undealt.

State DEP433 (8D, 10% depth, 28/32 Rank-8 left, 5% Vig)
Wager / MetricState DEP433 Value8D BaselineSettlement Note
DEP433 Banker (5% Vig)45.8595% (-1.0584% EV)45.8597%DEP433 8D 10% (28 Rank-8)
DEP433 Player (1:1)44.6249% (-1.2346% EV)44.6247%DEP433 374-card 8D stub (0.9329 SD)
DEP433 Tie (8:1)9.5156% (-14.3597% EV)9.5156%DEP433 Rank-8 (4 out, 28 in)
TABLEAU & SCOREBOARD SEPARATION · DEP433

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP433 · 8D)

In DEP433, the 374-card 8D stub (10% penetration, 4 of 32 Rank-8 dealt) yields 45.8595% Banker, 44.6249% Player, and 9.5156% Tie outcomes with 0.9329 dispersion under 5% Vig.

  • DEP433 (8D 10%): 374/416 cards with 28/32 Rank-8 (7A).
  • DEP433 (Rank-8 split): 45.8595% Banker, 44.6249% Player, 9.5156% Tie in 374 8D cards (7B).
  • DEP433 (5% Vig EV): -1.0584% Banker, -1.2346% Player, -14.3597% Tie, 0.9329 SD at 10% (7C).
  • DEP433 (8D roads): red/blue marks log Big Road columns, never 28 Rank-8 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 4 Eight-Pip Card cards leave a 8D shoe by 10% depth (DEP433), 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 (28/32 in 374 cards); Banker carries a -1.0584% 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