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COMBINATORIAL DEPLETION · 8D · RANK-5 · 70% DEPTH

8-Deck Five-Pip Card Depletion at 70% Penetration (5% Audit DEP411)

Removing 26 of 32 Five-Pip Card (Rank-5) cards at 70% penetration of a 8-deck (416-card) shoe leaves 6 Rank-5 cards inside a 125-card stub (DEP411), producing 45.8562% Banker wins, 44.6282% Player wins, 9.5155% Ties, and a 1.0648% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0648%
Player EV (1:1)
-1.2280%
Rank-5 in 125-Card Stub
6/32
Single-Hand Std Dev
0.9380
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 DEP411 (8D Rank-5 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

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 (DEP411)
125 / 416 Cards

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

Rank-5 Remaining
6 of 32 Cards

26 5-pip cards (final mandatory Player draw threshold) removed from the 8D pack.

Banker EV (5% Vig)
-1.0648%

Resolved at 45.8562% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2280%

Resolved at 44.6282% Player win rate with 0.9380 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3603% house hold on the 8-to-1 Tie wager in state DEP411.

FINITE-SHOE ENUMERATION · DEP411

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

At 70% penetration of a 416-card (8D) shoe, state DEP411 isolates 26 dealt Rank-5 cards (6 remaining inside 125 stub cards), yielding 45.8562% Banker wins, 44.6282% Player wins, and 0.9380 per-hand standard deviation under 5%.

In 8D audit DEP411 (125/416 stub at 70% depth), fewer 5s in the (dep411-rank-5) stub reduce banker third-card improvements (125c) from 3 to 8 and (dep411-rank-5·125c) from 4 to 9. Removing 26 Rank-5 cards (-0.84 bps per card) alongside 5% Vig rules sets Tie hold to 14.3603% (9.5155% frequency).

State DEP411 (8D, 70% depth, 6/32 Rank-5 left, 5% Vig)
Wager / MetricState DEP411 Value8D BaselineSettlement Note
DEP411 Banker (5% Vig)45.8562% (-1.0648% EV)45.8597%DEP411 8D 70% (6 Rank-5)
DEP411 Player (1:1)44.6282% (-1.2280% EV)44.6247%DEP411 125-card 8D stub (0.9380 SD)
DEP411 Tie (8:1)9.5155% (-14.3603% EV)9.5156%DEP411 Rank-5 (26 out, 6 in)
TABLEAU & SCOREBOARD SEPARATION · DEP411

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP411 · 8D)

In studio and floor audits of DEP411 (125 cards undealt out of 416 in 8D at 70% depth), a 0.9380 unit standard deviation accompanies the 6-card Rank-5 stub under 5% Vig (45.8562% Banker vs 44.6282% Player).

  • DEP411 (8D 70%): 125/416 cards with 6/32 Rank-5 (2A).
  • DEP411 (Rank-5 split): 45.8562% Banker, 44.6282% Player, 9.5155% Tie in 125 8D cards (2B).
  • DEP411 (5% Vig EV): -1.0648% Banker, -1.2280% Player, -14.3603% Tie, 0.9380 SD at 70% (2C).
  • DEP411 (8D roads): red/blue marks log Big Road columns, never 6 Rank-5 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 26 Five-Pip Card cards leave a 8D shoe by 70% depth (DEP411), 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-5 stub counts (6/32 in 125 cards); Banker carries a -1.0648% 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