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COMBINATORIAL DEPLETION · 8D · RANK-3 · 80% DEPTH

8-Deck Three-Pip (Trey) Depletion at 80% Penetration (Super 6 Audit DEP395)

Removing 29 of 32 Three-Pip (Trey) (Rank-3) cards at 80% penetration of a 8-deck (416-card) shoe leaves 3 Rank-3 cards inside a 83-card stub (DEP395), producing 45.8628% Banker wins, 44.6215% Player wins, 9.5157% Ties, and a 1.4516% Banker house edge under Super 6.

Banker EV (Super 6)
-1.4516%
Player EV (1:1)
-1.2414%
Rank-3 in 83-Card Stub
3/32
Single-Hand Std Dev
0.9384
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 DEP395 (8D Rank-3 at 80% 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 (DEP395)
83 / 416 Cards

80% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-3 Remaining
3 of 32 Cards

29 3-pip cards across all four suits removed from the 8D pack.

Banker EV (Super 6)
-1.4516%

Resolved at 45.8628% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.2414%

Resolved at 44.6215% Player win rate with 0.9384 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3587% house hold on the 8-to-1 Tie wager in state DEP395.

FINITE-SHOE ENUMERATION · DEP395

How Three-Pip (Trey) Depletion at 80% Depth Impacts 8D (Super 6)

When a 8D shoe reaches 80% cut-card depth (83 of 416 cards undealt, state DEP395) with 29 Three-Pip (Trey) cards removed and 3 remaining, Player wins 44.6215% (1.2414% edge) while Banker wins 45.8628% (1.4516% edge under Super 6).

Comparing initial 416-card 8D weights against stub DEP395 (83 cards, 80% depth, 3 Rank-3 left) illustrates how banker total 4 draws (dep395) on player third-card 3, and (8d-80%) banker total 5 stands on (dep395·8d-80%) player third-card 3, creating asymmetric sensitivity (+0.65 bps slope, 1.4516% Super 6 edge).

State DEP395 (8D, 80% depth, 3/32 Rank-3 left, Super 6)
Wager / MetricState DEP395 Value8D BaselineSettlement Note
DEP395 Banker (Super 6)45.8628% (-1.4516% EV)45.8597%DEP395 8D 80% (3 Rank-3)
DEP395 Player (1:1)44.6215% (-1.2414% EV)44.6247%DEP395 83-card 8D stub (0.9384 SD)
DEP395 Tie (8:1)9.5157% (-14.3587% EV)9.5156%DEP395 Rank-3 (29 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP395

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP395 · 8D)

On the electronic scoreboard for DEP395 (8D, 80% depth, 83 cards left), Bead Plate and Big Road circles record Banker (45.8628%) and Player (44.6215%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Rank-3 card counts (3/32).

  • DEP395 (8D 80%): 83/416 cards with 3/32 Rank-3 (6A).
  • DEP395 (Rank-3 split): 45.8628% Banker, 44.6215% Player, 9.5157% Tie in 83 8D cards (6B).
  • DEP395 (Super 6 EV): -1.4516% Banker, -1.2414% Player, -14.3587% Tie, 0.9384 SD at 80% (6C).
  • DEP395 (8D roads): red/blue marks log Big Road columns, never 3 Rank-3 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 29 Three-Pip (Trey) cards leave a 8D shoe by 80% depth (DEP395), 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-3 stub counts (3/32 in 83 cards); Banker carries a -1.4516% expectation under Super 6.
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