Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 8D Rank-4 Depletion at 50% Depth (Super 6)
COMBINATORIAL DEPLETION · 8D · RANK-4 · 50% DEPTH

8-Deck Four-Pip Card Depletion at 50% Penetration (Super 6 Audit DEP400)

Removing 18 of 32 Four-Pip Card (Rank-4) cards at 50% penetration of a 8-deck (416-card) shoe leaves 14 Rank-4 cards inside a 208-card stub (DEP400), producing 45.8627% Banker wins, 44.6216% Player wins, 9.5157% Ties, and a 1.4519% Banker house edge under Super 6.

Banker EV (Super 6)
-1.4519%
Player EV (1:1)
-1.2411%
Rank-4 in 208-Card Stub
14/32
Single-Hand Std Dev
0.9357
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 B P P B B P B P B
Big Eye Boy = = = = = = ≠ ≠ ≠ ≠ = = = =
Small Road = = = = = = ≠ = = = = =
Cockroach Pig = = = = = = ≠ = = ≠

Reference shoe scoreboard (PPBBPPBBPPBBPBTBPB) illustrating derived-road symmetry checks alongside DEP400 (8D Rank-4 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 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP400)
208 / 416 Cards

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

Rank-4 Remaining
14 of 32 Cards

18 4-pip cards (strongest pro-Banker removal sensitivity) removed from the 8D pack.

Banker EV (Super 6)
-1.4519%

Resolved at 45.8627% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.2411%

Resolved at 44.6216% Player win rate with 0.9357 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3591% house hold on the 8-to-1 Tie wager in state DEP400.

FINITE-SHOE ENUMERATION · DEP400

How Four-Pip Card Depletion at 50% Depth Impacts 8D (Super 6)

Within eight-deck Macau, Las Vegas Strip, and Singapore standard shoes, profile DEP400 examines 50% shoe depletion (208 of 416 cards remaining) after 18 Rank-4 cards exit, leaving 14 Four-Pip Card cards and a 1.4519% Banker house hold under Super 6.

In 8D audit DEP400 (208/416 stub at 50% depth), removing 4s produces the (dep400-rank-4) single largest per-card shift toward (208c) banker (and away from player) (dep400-rank-4·208c) of any rank in the shoe. Removing 18 Rank-4 cards (+1.19 bps per card) alongside Super 6 rules sets Tie hold to 14.3591% (9.5157% frequency).

State DEP400 (8D, 50% depth, 14/32 Rank-4 left, Super 6)
Wager / MetricState DEP400 Value8D BaselineSettlement Note
DEP400 Banker (Super 6)45.8627% (-1.4519% EV)45.8597%DEP400 8D 50% (14 Rank-4)
DEP400 Player (1:1)44.6216% (-1.2411% EV)44.6247%DEP400 208-card 8D stub (0.9357 SD)
DEP400 Tie (8:1)9.5157% (-14.3591% EV)9.5156%DEP400 Rank-4 (18 out, 14 in)
TABLEAU & SCOREBOARD SEPARATION · DEP400

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP400 · 8D)

Cut-card protocol at 50% depth in DEP400 (8D, 208 stub cards containing 14 Rank-4 cards) ensures the shoe reshuffles long before Super 6 house hold (1.4519% Banker / 1.2411% Player) is overturned.

  • DEP400 (8D 50%): 208/416 cards with 14/32 Rank-4 (3A).
  • DEP400 (Rank-4 split): 45.8627% Banker, 44.6216% Player, 9.5157% Tie in 208 8D cards (3B).
  • DEP400 (Super 6 EV): -1.4519% Banker, -1.2411% Player, -14.3591% Tie, 0.9357 SD at 50% (3C).
  • DEP400 (8D roads): red/blue marks log Big Road columns, never 14 Rank-4 stub count (3D).
Table Reality Check

Myth vs. Truth

MythWhen 18 Four-Pip Card cards leave a 8D shoe by 50% depth (DEP400), 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-4 stub counts (14/32 in 208 cards); Banker carries a -1.4519% 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