Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 6D Rank-9 Depletion at 80% Depth (Super 6)
COMBINATORIAL DEPLETION · 6D · RANK-9 · 80% DEPTH

6-Deck Nine-Pip Card Depletion at 80% Penetration (Super 6 Audit DEP359)

Removing 22 of 24 Nine-Pip Card (Rank-9) cards at 80% penetration of a 6-deck (312-card) shoe leaves 2 Rank-9 cards inside a 62-card stub (DEP359), producing 45.8637% Banker wins, 44.5915% Player wins, 9.5449% Ties, and a 1.4208% Banker house edge under Super 6.

Banker EV (Super 6)
-1.4208%
Player EV (1:1)
-1.2722%
Rank-9 in 62-Card Stub
2/24
Single-Hand Std Dev
0.9402
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 DEP359 (6D Rank-9 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

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 (DEP359)
62 / 312 Cards

80% penetration depth in 6D (six-deck Mini-Baccarat and Midi-Baccarat North American floors).

Rank-9 Remaining
2 of 24 Cards

22 9-pip cards (top Natural 9 generator) removed from the 6D pack.

Banker EV (Super 6)
-1.4208%

Resolved at 45.8637% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.2722%

Resolved at 44.5915% Player win rate with 0.9402 unit standard deviation.

Tie Incidence (8:1)
9.5449%

Produces a 14.0963% house hold on the 8-to-1 Tie wager in state DEP359.

FINITE-SHOE ENUMERATION · DEP359

How Nine-Pip Card Depletion at 80% Depth Impacts 6D (Super 6)

Across 89,520,558,110,592,000 initial 6D permutations, depletion node DEP359 narrows to a 62-card stub (80% depth) holding 2 of 24 Rank-9 cards, where Banker resolves at 45.8637% (-1.4208% EV) and Player at 44.5915% (-1.2722% EV).

Why does Rank-9 carry a -0.23 bps per-card effect in DEP359? Rank 9 paired with (DEP359) any ten or face card (6D-80%) creates an unbeatable two-card Natural (DEP359·6D-80%) 9 that halts all third-card drawing on both sides, and at 80% penetration (2 Nine-Pip Card cards left in 62 6D cards), only 20% of the (dep359-6d) initial shoe remains undealt while (2/24) winning banker 6 hands forfeit (dep359-6d·2/24) half their payout.

State DEP359 (6D, 80% depth, 2/24 Rank-9 left, Super 6)
Wager / MetricState DEP359 Value6D BaselineSettlement Note
DEP359 Banker (Super 6)45.8637% (-1.4208% EV)45.8648%DEP359 6D 80% (2 Rank-9)
DEP359 Player (1:1)44.5915% (-1.2722% EV)44.5903%DEP359 62-card 6D stub (0.9402 SD)
DEP359 Tie (8:1)9.5449% (-14.0963% EV)9.5449%DEP359 Rank-9 (22 out, 2 in)
TABLEAU & SCOREBOARD SEPARATION · DEP359

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP359 · 6D)

Even at 80% penetration in DEP359 where 22 Rank-9 cards have exited a 6D shoe (2 left in 62 cards), derived-road red and blue entries measure structural regularity on the Big Road—not whether Banker (-1.4208% EV, Super 6) or Player (-1.2722% EV) is favored next.

  • DEP359 (6D 80%): 62/312 cards with 2/24 Rank-9 (1A).
  • DEP359 (Rank-9 split): 45.8637% Banker, 44.5915% Player, 9.5449% Tie in 62 6D cards (1B).
  • DEP359 (Super 6 EV): -1.4208% Banker, -1.2722% Player, -14.0963% Tie, 0.9402 SD at 80% (1C).
  • DEP359 (6D roads): red/blue marks log Big Road columns, never 2 Rank-9 stub count (1D).
Table Reality Check

Myth vs. Truth

MythWhen 22 Nine-Pip Card cards leave a 6D shoe by 80% depth (DEP359), 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-9 stub counts (2/24 in 62 cards); Banker carries a -1.4208% 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