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COMBINATORIAL DEPLETION · 8D · RANK-8 · 40% DEPTH

8-Deck Eight-Pip Card Depletion at 40% Penetration (4% Audit DEP435)

Removing 15 of 32 Eight-Pip Card (Rank-8) cards at 40% penetration of a 8-deck (416-card) shoe leaves 17 Rank-8 cards inside a 250-card stub (DEP435), producing 45.8587% Banker wins, 44.6257% Player wins, 9.5156% Ties, and a 0.6014% Banker house edge under 4%.

Banker EV (4% Vig)
-0.6014%
Player EV (1:1)
-1.2330%
Rank-8 in 250-Card Stub
17/32
Single-Hand Std Dev
0.9359
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference shoe scoreboard (BBPPBPBPBBPPBPBPBB) illustrating derived-road symmetry checks alongside DEP435 (8D Rank-8 at 40% 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 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #2

Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP435)
250 / 416 Cards

40% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-8 Remaining
17 of 32 Cards

15 8-pip cards (Natural 8 generator and Banker 3 block) removed from the 8D pack.

Banker EV (4% Vig)
-0.6014%

Resolved at 45.8587% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2330%

Resolved at 44.6257% Player win rate with 0.9359 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3600% house hold on the 8-to-1 Tie wager in state DEP435.

FINITE-SHOE ENUMERATION · DEP435

How Eight-Pip Card Depletion at 40% Depth Impacts 8D (4% Vig)

Audit DEP435 evaluates a 8-deck (416-card) shoe at 40% penetration where 15 of 32 Eight-Pip Card cards have exited, leaving 17 Rank-8 cards inside the 250-card stub with Banker EV at -0.6014% under 4%.

Tracking DEP435 across 250 remaining 8D cards (40% depth) shows that depleting 8-pip cards also (dep435-rank-8) lowers two-card natural 8 lockouts (250c) when paired with zero-point tens (dep435-rank-8·250c) and court cards. With 15 Rank-8 cards gone (-0.50 bps unit sensitivity), Banker expectation is -0.6014% (4% Vig) vs -1.2330% on Player.

State DEP435 (8D, 40% depth, 17/32 Rank-8 left, 4% Vig)
Wager / MetricState DEP435 Value8D BaselineSettlement Note
DEP435 Banker (4% Vig)45.8587% (-0.6014% EV)45.8597%DEP435 8D 40% (17 Rank-8)
DEP435 Player (1:1)44.6257% (-1.2330% EV)44.6247%DEP435 250-card 8D stub (0.9359 SD)
DEP435 Tie (8:1)9.5156% (-14.3600% EV)9.5156%DEP435 Rank-8 (15 out, 17 in)
TABLEAU & SCOREBOARD SEPARATION · DEP435

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP435 · 8D)

While DEP435 tracks 15 removed Eight-Pip Card cards across 40% of a 416-card (8D) shoe (250 remaining, 0.6014% 4% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP435 (8D 40%): 250/416 cards with 17/32 Rank-8 (3A).
  • DEP435 (Rank-8 split): 45.8587% Banker, 44.6257% Player, 9.5156% Tie in 250 8D cards (3B).
  • DEP435 (4% Vig EV): -0.6014% Banker, -1.2330% Player, -14.3600% Tie, 0.9359 SD at 40% (3C).
  • DEP435 (8D roads): red/blue marks log Big Road columns, never 17 Rank-8 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 15 Eight-Pip Card cards leave a 8D shoe by 40% depth (DEP435), 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 (17/32 in 250 cards); Banker carries a -0.6014% expectation under 4%.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

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Every reference guide, glossary definition, and road calculator on Baccarat Smart is open for everyone. When you want all 6 modules and 36 lessons (about 5.5 hours of lessons) organized in structured step-by-step order with 74 hands-on boards, 94 quiz checks along the way, and Cloud Shoe Log sync across web, iPhone, and Android, start Module 1 (10 lessons, about 64 minutes of lessons) free or unlock full membership for $25 a month.

  • 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