Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 1D Rank-8 Depletion at 80% Depth (Super 6)
COMBINATORIAL DEPLETION · 1D · RANK-8 · 80% DEPTH

1-Deck Eight-Pip Card Depletion at 80% Penetration (Super 6 Audit DEP080)

Removing 3 of 4 Eight-Pip Card (Rank-8) cards at 80% penetration of a 1-deck (52-card) shoe leaves 1 Rank-8 cards inside a 10-card stub (DEP080), producing 45.9575% Banker wins, 44.5270% Player wins, 9.5155% Ties, and a 1.2625% Banker house edge under Super 6.

Banker EV (Super 6)
-1.2625%
Player EV (1:1)
-1.4305%
Rank-8 in 10-Card Stub
1/4
Single-Hand Std Dev
0.9399
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 DEP080 (1D Rank-8 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 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 (DEP080)
10 / 52 Cards

80% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-8 Remaining
1 of 4 Cards

3 8-pip cards (Natural 8 generator and Banker 3 block) removed from the 1D pack.

Banker EV (Super 6)
-1.2625%

Resolved at 45.9575% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.4305%

Resolved at 44.5270% Player win rate with 0.9399 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3603% house hold on the 8-to-1 Tie wager in state DEP080.

FINITE-SHOE ENUMERATION · DEP080

How Eight-Pip Card Depletion at 80% Depth Impacts 1D (Super 6)

Depletion matrix entry DEP080 pairs 1D (52 cards) at 80% penetration with 3 removed Eight-Pip Card cards (1 left in 10 cards), fixing per-hand volatility at 0.9399 and Banker house hold at 1.2625% (Super 6).

Tableau audit DEP080 confirms that on banker total 3, (dep080) banker draws against every player (1d-80%) third card except 8; removing (dep080·1d-80%) 8s eliminates banker 3's sole standing exception. Inside the 10-card 1D stub (80% depth, 1/4 Rank-8 remaining, -0.50 bps slope), standard deviation is 0.9399 under Super 6.

State DEP080 (1D, 80% depth, 1/4 Rank-8 left, Super 6)
Wager / MetricState DEP080 Value1D BaselineSettlement Note
DEP080 Banker (Super 6)45.9575% (-1.2625% EV)45.9595%DEP080 1D 80% (1 Rank-8)
DEP080 Player (1:1)44.5270% (-1.4305% EV)44.5249%DEP080 10-card 1D stub (0.9399 SD)
DEP080 Tie (8:1)9.5155% (-14.3603% EV)9.5156%DEP080 Rank-8 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP080

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP080 · 1D)

Comparing DEP080 (80% 1D depth, 3 Rank-8 removed, 1 remaining in 10 cards) against fresh-shoe baselines shows how finite-stub variance (0.9399 SD) coexists with a 1.2625% Super 6 Banker house edge.

  • DEP080 (1D 80%): 10/52 cards with 1/4 Rank-8 (6A).
  • DEP080 (Rank-8 split): 45.9575% Banker, 44.5270% Player, 9.5155% Tie in 10 1D cards (6B).
  • DEP080 (Super 6 EV): -1.2625% Banker, -1.4305% Player, -14.3603% Tie, 0.9399 SD at 80% (6C).
  • DEP080 (1D roads): red/blue marks log Big Road columns, never 1 Rank-8 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Eight-Pip Card cards leave a 1D shoe by 80% depth (DEP080), 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-8 stub counts (1/4 in 10 cards); Banker carries a -1.2625% 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