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COMBINATORIAL DEPLETION · 8D · RANK-7 · 80% DEPTH

8-Deck Seven-Pip Card Depletion at 80% Penetration (Super 6 Audit DEP431)

Removing 29 of 32 Seven-Pip Card (Rank-7) cards at 80% penetration of a 8-deck (416-card) shoe leaves 3 Rank-7 cards inside a 83-card stub (DEP431), producing 45.8557% Banker wins, 44.6288% Player wins, 9.5155% Ties, and a 1.4661% Banker house edge under Super 6.

Banker EV (Super 6)
-1.4661%
Player EV (1:1)
-1.2269%
Rank-7 in 83-Card Stub
3/32
Single-Hand Std Dev
0.9396
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 P B B P P B B P B
Big Eye Boy = = = = = = ≠ = = = = = = =
Small Road = = = = = = ≠ ≠ = = = =
Cockroach Pig = = = = = = ≠ ≠ ≠ =

Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP431 (8D Rank-7 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 (DEP431)
83 / 416 Cards

80% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-7 Remaining
3 of 32 Cards

29 7-pip cards (Player stand total and Dragon 7 boundary) removed from the 8D pack.

Banker EV (Super 6)
-1.4661%

Resolved at 45.8557% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.2269%

Resolved at 44.6288% Player win rate with 0.9396 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3605% house hold on the 8-to-1 Tie wager in state DEP431.

FINITE-SHOE ENUMERATION · DEP431

How Seven-Pip Card Depletion at 80% Depth Impacts 8D (Super 6)

Removing 29 of 32 Rank-7 cards by the 80% mark of a 8-deck shoe (DEP431, 83 cards left) leaves 3 Seven-Pip Card cards and adjusts conditional probabilities to 45.8557% Banker, 44.6288% Player, and 9.5155% Tie under Super 6.

Comparing initial 416-card 8D weights against stub DEP431 (83 cards, 80% depth, 3 Rank-7 left) illustrates how player stands pat on (dep431) two-card 7, and a player (8d-80%) third-card 7 is the highest (dep431·8d-80%) card that forces banker 4, 5, and 6 to draw (-0.83 bps slope, 1.4661% Super 6 edge).

State DEP431 (8D, 80% depth, 3/32 Rank-7 left, Super 6)
Wager / MetricState DEP431 Value8D BaselineSettlement Note
DEP431 Banker (Super 6)45.8557% (-1.4661% EV)45.8597%DEP431 8D 80% (3 Rank-7)
DEP431 Player (1:1)44.6288% (-1.2269% EV)44.6247%DEP431 83-card 8D stub (0.9396 SD)
DEP431 Tie (8:1)9.5155% (-14.3605% EV)9.5156%DEP431 Rank-7 (29 out, 3 in)
TABLEAU & SCOREBOARD SEPARATION · DEP431

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP431 · 8D)

Scoreboard literacy in DEP431 separates two independent concepts: 8D card-removal math (3 Rank-7 left in 83 cards at 80% depth, 0.9396 volatility) and derived-road comparison rules (Rule 1 column-depth checks and Rule 2 two-cell lookbacks).

  • DEP431 (8D 80%): 83/416 cards with 3/32 Rank-7 (4A).
  • DEP431 (Rank-7 split): 45.8557% Banker, 44.6288% Player, 9.5155% Tie in 83 8D cards (4B).
  • DEP431 (Super 6 EV): -1.4661% Banker, -1.2269% Player, -14.3605% Tie, 0.9396 SD at 80% (4C).
  • DEP431 (8D roads): red/blue marks log Big Road columns, never 3 Rank-7 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 29 Seven-Pip Card cards leave a 8D shoe by 80% depth (DEP431), 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 (3/32 in 83 cards); Banker carries a -1.4661% expectation under Super 6.
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  • 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