Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 8D Rank-7 Depletion at 50% Depth (Super 6)
COMBINATORIAL DEPLETION · 8D · RANK-7 · 50% DEPTH

8-Deck Seven-Pip Card Depletion at 50% Penetration (Super 6 Audit DEP427)

Removing 18 of 32 Seven-Pip Card (Rank-7) cards at 50% penetration of a 8-deck (416-card) shoe leaves 14 Rank-7 cards inside a 208-card stub (DEP427), producing 45.8576% Banker wins, 44.6269% Player wins, 9.5155% Ties, and a 1.4623% Banker house edge under Super 6.

Banker EV (Super 6)
-1.4623%
Player EV (1:1)
-1.2307%
Rank-7 in 208-Card Stub
14/32
Single-Hand Std Dev
0.9366
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 DEP427 (8D Rank-7 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

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 (DEP427)
208 / 416 Cards

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

Rank-7 Remaining
14 of 32 Cards

18 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 8D pack.

Banker EV (Super 6)
-1.4623%

Resolved at 45.8576% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.2307%

Resolved at 44.6269% Player win rate with 0.9366 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3601% house hold on the 8-to-1 Tie wager in state DEP427.

FINITE-SHOE ENUMERATION · DEP427

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

Card-removal benchmark DEP427 measures Seven-Pip Card (Rank-7) scarcity at 50% depth in a 8-deck shoe: 18 removed ranks leave 14 in the 208-card remainder, shifting Banker win share to 45.8576% (1.4623% edge, Super 6).

Combinatorial weighting in DEP427 (208 cards left from 416 at 50% depth) is governed by two rules: player stands pat on (dep427) two-card 7, and a player (8d-50%) third-card 7 is the highest (dep427·8d-50%) card that forces banker 4, 5, and 6 to draw, and banker wins on totals (dep427-8d) 1–5 and 7–9 pay 1:1 (14/32) while any winning 2-card or (dep427-8d·14/32) 3-card banker 6 pays 50 cents on the dollar (-0.83 bps per Rank-7 removed).

State DEP427 (8D, 50% depth, 14/32 Rank-7 left, Super 6)
Wager / MetricState DEP427 Value8D BaselineSettlement Note
DEP427 Banker (Super 6)45.8576% (-1.4623% EV)45.8597%DEP427 8D 50% (14 Rank-7)
DEP427 Player (1:1)44.6269% (-1.2307% EV)44.6247%DEP427 208-card 8D stub (0.9366 SD)
DEP427 Tie (8:1)9.5155% (-14.3601% EV)9.5156%DEP427 Rank-7 (18 out, 14 in)
TABLEAU & SCOREBOARD SEPARATION · DEP427

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP427 · 8D)

For DEP427 (208 remaining cards in a 416-card 8D shoe at 50% depth), tracking all 18 exited Rank-7 cards moves Banker win rate to 45.8576% (-1.4623% EV, Super 6) and Player to 44.6269% (-1.2307% EV).

  • DEP427 (8D 50%): 208/416 cards with 14/32 Rank-7 (5A).
  • DEP427 (Rank-7 split): 45.8576% Banker, 44.6269% Player, 9.5155% Tie in 208 8D cards (5B).
  • DEP427 (Super 6 EV): -1.4623% Banker, -1.2307% Player, -14.3601% Tie, 0.9366 SD at 50% (5C).
  • DEP427 (8D roads): red/blue marks log Big Road columns, never 14 Rank-7 stub count (5D).
Table Reality Check

Myth vs. Truth

MythWhen 18 Seven-Pip Card cards leave a 8D shoe by 50% depth (DEP427), 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-7 stub counts (14/32 in 208 cards); Banker carries a -1.4623% 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