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COMBINATORIAL DEPLETION · 8D · RANK-6 · 50% DEPTH

8-Deck Six-Pip Card Depletion at 50% Penetration (Super 6 Audit DEP418)

Removing 18 of 32 Six-Pip Card (Rank-6) cards at 50% penetration of a 8-deck (416-card) shoe leaves 14 Rank-6 cards inside a 208-card stub (DEP418), producing 45.8568% Banker wins, 44.6276% Player wins, 9.5155% Ties, and a 1.4638% Banker house edge under Super 6.

Banker EV (Super 6)
-1.4638%
Player EV (1:1)
-1.2292%
Rank-6 in 208-Card Stub
14/32
Single-Hand Std Dev
0.9363
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 DEP418 (8D Rank-6 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

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 (DEP418)
208 / 416 Cards

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

Rank-6 Remaining
14 of 32 Cards

18 6-pip cards (standing threshold and Banker 6 trigger) removed from the 8D pack.

Banker EV (Super 6)
-1.4638%

Resolved at 45.8568% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.2292%

Resolved at 44.6276% Player win rate with 0.9363 unit standard deviation.

Tie Incidence (8:1)
9.5155%

Produces a 14.3601% house hold on the 8-to-1 Tie wager in state DEP418.

FINITE-SHOE ENUMERATION · DEP418

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

Exact conditional enumeration DEP418 for a 8D shoe at 50% depth (208/416 cards undealt) with 14 remaining Rank-6 cards confirms a 1.4638% Banker edge (Super 6), 1.2292% Player edge, and 14.3601% Tie edge.

Tableau audit DEP418 confirms that banker 6 only draws (dep418) when player pulls a third-card (8d-50%) 6 or 7; depleting 6s (dep418·8d-50%) directly alters both banker 6 draws and super 6 settlement frequency. Inside the 208-card 8D stub (50% depth, 14/32 Rank-6 remaining, -1.13 bps slope), standard deviation is 0.9363 under Super 6.

State DEP418 (8D, 50% depth, 14/32 Rank-6 left, Super 6)
Wager / MetricState DEP418 Value8D BaselineSettlement Note
DEP418 Banker (Super 6)45.8568% (-1.4638% EV)45.8597%DEP418 8D 50% (14 Rank-6)
DEP418 Player (1:1)44.6276% (-1.2292% EV)44.6247%DEP418 208-card 8D stub (0.9363 SD)
DEP418 Tie (8:1)9.5155% (-14.3601% EV)9.5156%DEP418 Rank-6 (18 out, 14 in)
TABLEAU & SCOREBOARD SEPARATION · DEP418

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP418 · 8D)

In DEP418, the 208-card 8D stub (50% penetration, 18 of 32 Rank-6 dealt) yields 45.8568% Banker, 44.6276% Player, and 9.5155% Tie outcomes with 0.9363 dispersion under Super 6.

  • DEP418 (8D 50%): 208/416 cards with 14/32 Rank-6 (2A).
  • DEP418 (Rank-6 split): 45.8568% Banker, 44.6276% Player, 9.5155% Tie in 208 8D cards (2B).
  • DEP418 (Super 6 EV): -1.4638% Banker, -1.2292% Player, -14.3601% Tie, 0.9363 SD at 50% (2C).
  • DEP418 (8D roads): red/blue marks log Big Road columns, never 14 Rank-6 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 18 Six-Pip Card cards leave a 8D shoe by 50% depth (DEP418), 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-6 stub counts (14/32 in 208 cards); Banker carries a -1.4638% 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