Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 8D Rank-3 Depletion at 50% Depth (Super 6)
COMBINATORIAL DEPLETION · 8D · RANK-3 · 50% DEPTH

8-Deck Three-Pip (Trey) Depletion at 50% Penetration (Super 6 Audit DEP391)

Removing 18 of 32 Three-Pip (Trey) (Rank-3) cards at 50% penetration of a 8-deck (416-card) shoe leaves 14 Rank-3 cards inside a 208-card stub (DEP391), producing 45.8614% Banker wins, 44.6230% Player wins, 9.5157% Ties, and a 1.4546% Banker house edge under Super 6.

Banker EV (Super 6)
-1.4546%
Player EV (1:1)
-1.2384%
Rank-3 in 208-Card Stub
14/32
Single-Hand Std Dev
0.9354
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 B P B P P B B P P B P
Big Eye Boy = = = = ≠ = = = ≠ ≠ = = = = ≠
Small Road = = ≠ ≠ = = ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP391 (8D Rank-3 at 50% 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 (DEP391)
208 / 416 Cards

50% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-3 Remaining
14 of 32 Cards

18 3-pip cards across all four suits removed from the 8D pack.

Banker EV (Super 6)
-1.4546%

Resolved at 45.8614% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.2384%

Resolved at 44.6230% Player win rate with 0.9354 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3591% house hold on the 8-to-1 Tie wager in state DEP391.

FINITE-SHOE ENUMERATION · DEP391

How Three-Pip (Trey) Depletion at 50% Depth Impacts 8D (Super 6)

Shoe-stub analysis DEP391 inspects 208 remaining cards at 50% penetration of a 416-card (8D) pack after 18 Three-Pip (Trey) cards have cleared, leaving 14 Rank-3 cards and a 1.4546% Super 6 Banker edge.

Banker total 4 draws (DEP391) on Player third-card 3, and (8D-50%) Banker total 5 stands on (DEP391·8D-50%) Player third-card 3, creating asymmetric sensitivity. In state DEP391 (8D, 50% depth), each removed Rank-3 card applies a +0.65 bps baseline directional pressure before scaling to the 208-card remainder (14 Rank-3 left), while Banker wins on totals (DEP391-8D) 1–5 and 7–9 pay 1:1 (14/32) while any winning 2-card or (DEP391-8D·14/32) 3-card Banker 6 pays 50 cents on the dollar.

State DEP391 (8D, 50% depth, 14/32 Rank-3 left, Super 6)
Wager / MetricState DEP391 Value8D BaselineSettlement Note
DEP391 Banker (Super 6)45.8614% (-1.4546% EV)45.8597%DEP391 8D 50% (14 Rank-3)
DEP391 Player (1:1)44.6230% (-1.2384% EV)44.6247%DEP391 208-card 8D stub (0.9354 SD)
DEP391 Tie (8:1)9.5157% (-14.3591% EV)9.5156%DEP391 Rank-3 (18 out, 14 in)
TABLEAU & SCOREBOARD SEPARATION · DEP391

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP391 · 8D)

Cut-card protocol at 50% depth in DEP391 (8D, 208 stub cards containing 14 Rank-3 cards) ensures the shoe reshuffles long before Super 6 house hold (1.4546% Banker / 1.2384% Player) is overturned.

  • DEP391 (8D 50%): 208/416 cards with 14/32 Rank-3 (7A).
  • DEP391 (Rank-3 split): 45.8614% Banker, 44.6230% Player, 9.5157% Tie in 208 8D cards (7B).
  • DEP391 (Super 6 EV): -1.4546% Banker, -1.2384% Player, -14.3591% Tie, 0.9354 SD at 50% (7C).
  • DEP391 (8D roads): red/blue marks log Big Road columns, never 14 Rank-3 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 18 Three-Pip (Trey) cards leave a 8D shoe by 50% depth (DEP391), 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 (14/32 in 208 cards); Banker carries a -1.4546% 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