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COMBINATORIAL DEPLETION · 8D · RANK-5 · 40% DEPTH

8-Deck Five-Pip Card Depletion at 40% Penetration (4% Audit DEP408)

Removing 15 of 32 Five-Pip Card (Rank-5) cards at 40% penetration of a 8-deck (416-card) shoe leaves 17 Rank-5 cards inside a 250-card stub (DEP408), producing 45.8580% Banker wins, 44.6264% Player wins, 9.5156% Ties, and a 0.6027% Banker house edge under 4%.

Banker EV (4% Vig)
-0.6027%
Player EV (1:1)
-1.2316%
Rank-5 in 250-Card Stub
17/32
Single-Hand Std Dev
0.9350
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 P B P B B P P B B P B
Big Eye Boy = = = = ≠ = = = ≠ ≠ = = = = ≠
Small Road = = ≠ ≠ = = ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (PPBBPPBPBPBBPPBBPB) illustrating derived-road symmetry checks alongside DEP408 (8D Rank-5 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 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 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 (DEP408)
250 / 416 Cards

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

Rank-5 Remaining
17 of 32 Cards

15 5-pip cards (final mandatory Player draw threshold) removed from the 8D pack.

Banker EV (4% Vig)
-0.6027%

Resolved at 45.8580% Banker win rate under 4% settlement.

Player EV (1:1)
-1.2316%

Resolved at 44.6264% Player win rate with 0.9350 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3600% house hold on the 8-to-1 Tie wager in state DEP408.

FINITE-SHOE ENUMERATION · DEP408

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

In combinatorial record DEP408, depleting 15 Rank-5 cards across 40% of a 8D (416-card) pack leaves 17 Five-Pip Card cards among 250 remaining cards, setting Banker win probability to 45.8580% and house edge to 0.6027% (4% Vig).

Because Player draws on (DEP408) two-card 5 and stands on (8D-40%) 6, while Banker 3, 4, (DEP408·8D-40%) and 5 all draw against a Player third-card 5, rank 5 favors Player when depleted. In state DEP408 (8D, 40% depth), each removed Rank-5 card applies a -0.84 bps baseline directional pressure before scaling to the 250-card remainder (17 Rank-5 left), while Winning Banker wagers collect (DEP408-8D) 0.96 units per unit staked (17/32) with 60% of the shoe (DEP408-8D·17/32) still inside the acrylic carrier.

State DEP408 (8D, 40% depth, 17/32 Rank-5 left, 4% Vig)
Wager / MetricState DEP408 Value8D BaselineSettlement Note
DEP408 Banker (4% Vig)45.8580% (-0.6027% EV)45.8597%DEP408 8D 40% (17 Rank-5)
DEP408 Player (1:1)44.6264% (-1.2316% EV)44.6247%DEP408 250-card 8D stub (0.9350 SD)
DEP408 Tie (8:1)9.5156% (-14.3600% EV)9.5156%DEP408 Rank-5 (15 out, 17 in)
TABLEAU & SCOREBOARD SEPARATION · DEP408

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP408 · 8D)

Learners auditing DEP408 (8D at 40% depth, 17/32 Rank-5 in 250 stub cards) can verify that 4% house hold (0.6027% Banker, 1.2316% Player, 14.3600% Tie) operates independently of prior Big Road streaks.

  • DEP408 (8D 40%): 250/416 cards with 17/32 Rank-5 (1A).
  • DEP408 (Rank-5 split): 45.8580% Banker, 44.6264% Player, 9.5156% Tie in 250 8D cards (1B).
  • DEP408 (4% Vig EV): -0.6027% Banker, -1.2316% Player, -14.3600% Tie, 0.9350 SD at 40% (1C).
  • DEP408 (8D roads): red/blue marks log Big Road columns, never 17 Rank-5 stub count (1D).
Table Reality Check

Myth vs. Truth

MythWhen 15 Five-Pip Card cards leave a 8D shoe by 40% depth (DEP408), 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 (17/32 in 250 cards); Banker carries a -0.6027% expectation under 4%.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

Read Every Derived Road at Table Speed

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