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COMBINATORIAL DEPLETION · 8D · RANK-0 · 75% DEPTH

8-Deck 0-Value Tens & Faces Depletion at 75% Penetration (4% Audit DEP367)

Removing 110 of 128 0-Value Tens & Faces (Rank-0) cards at 75% penetration of a 8-deck (416-card) shoe leaves 18 Rank-0 cards inside a 104-card stub (DEP367), producing 45.8629% Banker wins, 44.6213% Player wins, 9.5158% Ties, and a 0.5929% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5929%
Player EV (1:1)
-1.2416%
Rank-0 in 104-Card Stub
18/128
Single-Hand Std Dev
0.9370
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 P B B P B
Big Eye Boy = = = = = = ≠ = = = = = = =
Small Road = = = = = = ≠ ≠ = = = =
Cockroach Pig = = = = = = ≠ ≠ ≠ =

Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP367 (8D Rank-0 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 (DEP367)
104 / 416 Cards

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

Rank-0 Remaining
18 of 128 Cards

110 10, Jack, Queen, and King (zero-point cards) removed from the 8D pack.

Banker EV (4% Vig)
-0.5929%

Resolved at 45.8629% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2416%

Resolved at 44.6213% Player win rate with 0.9370 unit standard deviation.

Tie Incidence (8:1)
9.5158%

Produces a 14.3580% house hold on the 8-to-1 Tie wager in state DEP367.

FINITE-SHOE ENUMERATION · DEP367

How 0-Value Tens & Faces Depletion at 75% Depth Impacts 8D (4% Vig)

When a 8D shoe reaches 75% cut-card depth (104 of 416 cards undealt, state DEP367) with 110 0-Value Tens & Faces cards removed and 18 remaining, Player wins 44.6213% (1.2416% edge) while Banker wins 45.8629% (0.5929% edge under 4%).

Fewer zero-value draws mean (DEP367-Rank-0) third-card pulls change running totals (104c) more frequently instead of leaving (DEP367-Rank-0·104c) totals unchanged. Because 110 of 128 0-Value Tens & Faces cards are absent in DEP367 at 75% 8D penetration (104 cards left), per-card sensitivity (+0.18 bps) interacts directly with three-quarter 75% penetration depth (DEP367) under reduced 4% Banker commission (Rank-0) (0.96:1 payout).

State DEP367 (8D, 75% depth, 18/128 Rank-0 left, 4% Vig)
Wager / MetricState DEP367 Value8D BaselineSettlement Note
DEP367 Banker (4% Vig)45.8629% (-0.5929% EV)45.8597%DEP367 8D 75% (18 Rank-0)
DEP367 Player (1:1)44.6213% (-1.2416% EV)44.6247%DEP367 104-card 8D stub (0.9370 SD)
DEP367 Tie (8:1)9.5158% (-14.3580% EV)9.5156%DEP367 Rank-0 (110 out, 18 in)
TABLEAU & SCOREBOARD SEPARATION · DEP367

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP367 · 8D)

Statistical verification of DEP367 (8D, 75% penetration, 18 0-Value Tens & Faces cards in 104 stub cards) demonstrates why single-rank depletion (110 Rank-0 dealt) shifts edges by basis points around -0.5929% (4% Vig).

  • DEP367 (8D 75%): 104/416 cards with 18/128 Rank-0 (6A).
  • DEP367 (Rank-0 split): 45.8629% Banker, 44.6213% Player, 9.5158% Tie in 104 8D cards (6B).
  • DEP367 (4% Vig EV): -0.5929% Banker, -1.2416% Player, -14.3580% Tie, 0.9370 SD at 75% (6C).
  • DEP367 (8D roads): red/blue marks log Big Road columns, never 18 Rank-0 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 110 0-Value Tens & Faces cards leave a 8D shoe by 75% depth (DEP367), 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-0 stub counts (18/128 in 104 cards); Banker carries a -0.5929% expectation under 4%.
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