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COMBINATORIAL DEPLETION · 2D · RANK-6 · 25% DEPTH

2-Deck Six-Pip Card Depletion at 25% Penetration (5% Audit DEP146)

Removing 2 of 8 Six-Pip Card (Rank-6) cards at 25% penetration of a 2-deck (104-card) shoe leaves 6 Rank-6 cards inside a 78-card stub (DEP146), producing 45.8987% Banker wins, 44.5687% Player wins, 9.5326% Ties, and a 0.9649% Banker house edge under 5%.

Banker EV (5% Vig)
-0.9649%
Player EV (1:1)
-1.3300%
Rank-6 in 78-Card Stub
6/8
Single-Hand Std Dev
0.9338
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 DEP146 (2D Rank-6 at 25% 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 (DEP146)
78 / 104 Cards

25% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Rank-6 Remaining
6 of 8 Cards

2 6-pip cards (standing threshold and Banker 6 trigger) removed from the 2D pack.

Banker EV (5% Vig)
-0.9649%

Resolved at 45.8987% Banker win rate under 5% settlement.

Player EV (1:1)
-1.3300%

Resolved at 44.5687% Player win rate with 0.9338 unit standard deviation.

Tie Incidence (8:1)
9.5326%

Produces a 14.2068% house hold on the 8-to-1 Tie wager in state DEP146.

FINITE-SHOE ENUMERATION · DEP146

How Six-Pip Card Depletion at 25% Depth Impacts 2D (5% Vig)

Under 5% settlement (5% Vig), combinatorial state DEP146 models a 2D carrier with 78 cards left (25% dealt) and 6/8 Six-Pip Card cards remaining, producing a 0.9649% Banker edge versus 1.3300% on Player.

Mechanical draw trees in DEP146 reflect how removing 6-pip cards produces (dep146-rank-6) the strongest per-card shift toward (78c) the player side and reduces (dep146-rank-6·78c) barred banker 6 incidence. At 25% 2D depth (6 Rank-6 left of 8 in 78 cards, -1.13 bps slope), one-quarter of the shoe (dep146-2d) has exited the carrier and (6/8) winning banker wagers pay 0.95 (dep146-2d·6/8) to 1 after 5% house tax.

State DEP146 (2D, 25% depth, 6/8 Rank-6 left, 5% Vig)
Wager / MetricState DEP146 Value2D BaselineSettlement Note
DEP146 Banker (5% Vig)45.8987% (-0.9649% EV)45.8998%DEP146 2D 25% (6 Rank-6)
DEP146 Player (1:1)44.5687% (-1.3300% EV)44.5676%DEP146 78-card 2D stub (0.9338 SD)
DEP146 Tie (8:1)9.5326% (-14.2068% EV)9.5326%DEP146 Rank-6 (2 out, 6 in)
TABLEAU & SCOREBOARD SEPARATION · DEP146

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP146 · 2D)

While DEP146 tracks 2 removed Six-Pip Card cards across 25% of a 104-card (2D) shoe (78 remaining, 0.9649% 5% Vig edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP146 (2D 25%): 78/104 cards with 6/8 Rank-6 (7A).
  • DEP146 (Rank-6 split): 45.8987% Banker, 44.5687% Player, 9.5326% Tie in 78 2D cards (7B).
  • DEP146 (5% Vig EV): -0.9649% Banker, -1.3300% Player, -14.2068% Tie, 0.9338 SD at 25% (7C).
  • DEP146 (2D roads): red/blue marks log Big Road columns, never 6 Rank-6 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 2 Six-Pip Card cards leave a 2D shoe by 25% depth (DEP146), 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 (6/8 in 78 cards); Banker carries a -0.9649% expectation under 5%.
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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