Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 8D Rank-9 Depletion at 85% Depth (EZ Bar-7)
COMBINATORIAL DEPLETION · 8D · RANK-9 · 85% DEPTH

8-Deck Nine-Pip Card Depletion at 85% Penetration (EZ Baccarat Audit DEP450)

Removing 31 of 32 Nine-Pip Card (Rank-9) cards at 85% penetration of a 8-deck (416-card) shoe leaves 1 Rank-9 cards inside a 62-card stub (DEP450), producing 45.8585% Banker wins, 44.6260% Player wins, 9.5155% Ties, and a 1.0209% Banker house edge under EZ Baccarat.

Banker EV (EZ Bar-7)
-1.0209%
Player EV (1:1)
-1.2325%
Rank-9 in 62-Card Stub
1/32
Single-Hand Std Dev
0.9407
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 B P
Big Eye Boy = = = = = = ≠ = = = = ≠ ≠ = =
Small Road = = = = = = ≠ ≠ = = = ≠ ≠
Cockroach Pig = = = = = = ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (PPBBPPBBPPBBPBPBBP) illustrating derived-road symmetry checks alongside DEP450 (8D Rank-9 at 85% 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 (DEP450)
62 / 416 Cards

85% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-9 Remaining
1 of 32 Cards

31 9-pip cards (top Natural 9 generator) removed from the 8D pack.

Banker EV (EZ Bar-7)
-1.0209%

Resolved at 45.8585% Banker win rate under EZ Baccarat settlement.

Player EV (1:1)
-1.2325%

Resolved at 44.6260% Player win rate with 0.9407 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3601% house hold on the 8-to-1 Tie wager in state DEP450.

FINITE-SHOE ENUMERATION · DEP450

How Nine-Pip Card Depletion at 85% Depth Impacts 8D (EZ Bar-7)

In combinatorial record DEP450, depleting 31 Rank-9 cards across 85% of a 8D (416-card) pack leaves 1 Nine-Pip Card cards among 62 remaining cards, setting Banker win probability to 45.8585% and house edge to 1.0209% (EZ Bar-7).

When 31 Rank-9 cards exit a 8D shoe by 85% penetration (DEP450, 1 left in 62 cards), when 9s are depleted (dep450-rank-9) late in the shoe, more (62c) hands bypass four-card natural resolution (dep450-rank-9·62c) and enter the five- and six-card tableau, combining a -0.23 bps rank vector with EZ Baccarat settlement (-1.0209% Banker EV).

State DEP450 (8D, 85% depth, 1/32 Rank-9 left, EZ Bar-7)
Wager / MetricState DEP450 Value8D BaselineSettlement Note
DEP450 Banker (EZ Bar-7)45.8585% (-1.0209% EV)45.8597%DEP450 8D 85% (1 Rank-9)
DEP450 Player (1:1)44.6260% (-1.2325% EV)44.6247%DEP450 62-card 8D stub (0.9407 SD)
DEP450 Tie (8:1)9.5155% (-14.3601% EV)9.5156%DEP450 Rank-9 (31 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP450

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP450 · 8D)

While DEP450 tracks 31 removed Nine-Pip Card cards across 85% of a 416-card (8D) shoe (62 remaining, 1.0209% EZ Bar-7 edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP450 (8D 85%): 62/416 cards with 1/32 Rank-9 (1A).
  • DEP450 (Rank-9 split): 45.8585% Banker, 44.6260% Player, 9.5155% Tie in 62 8D cards (1B).
  • DEP450 (EZ Bar-7 EV): -1.0209% Banker, -1.2325% Player, -14.3601% Tie, 0.9407 SD at 85% (1C).
  • DEP450 (8D roads): red/blue marks log Big Road columns, never 1 Rank-9 stub count (1D).
Table Reality Check

Myth vs. Truth

MythWhen 31 Nine-Pip Card cards leave a 8D shoe by 85% depth (DEP450), 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 (1/32 in 62 cards); Banker carries a -1.0209% expectation under EZ Baccarat.
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