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COMBINATORIAL DEPLETION · 1D · RANK-4 · 50% DEPTH

1-Deck Four-Pip Card Depletion at 50% Penetration (Super 6 Audit DEP040)

Removing 2 of 4 Four-Pip Card (Rank-4) cards at 50% penetration of a 1-deck (52-card) shoe leaves 2 Rank-4 cards inside a 26-card stub (DEP040), producing 45.9622% Banker wins, 44.5222% Player wins, 9.5156% Ties, and a 1.2530% Banker house edge under Super 6.

Banker EV (Super 6)
-1.2530%
Player EV (1:1)
-1.4400%
Rank-4 in 26-Card Stub
2/4
Single-Hand Std Dev
0.9357
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 P B P B B P P B B P B
Big Eye Boy = = = = ≠ = = = ≠ ≠ = = = = ≠
Small Road = = ≠ ≠ = = ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (PPBBPPBPBPBBPPBBPB) illustrating derived-road symmetry checks alongside DEP040 (1D Rank-4 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 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP040)
26 / 52 Cards

50% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-4 Remaining
2 of 4 Cards

2 4-pip cards (strongest pro-Banker removal sensitivity) removed from the 1D pack.

Banker EV (Super 6)
-1.2530%

Resolved at 45.9622% Banker win rate under Super 6 settlement.

Player EV (1:1)
-1.4400%

Resolved at 44.5222% Player win rate with 0.9357 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3592% house hold on the 8-to-1 Tie wager in state DEP040.

FINITE-SHOE ENUMERATION · DEP040

How Four-Pip Card Depletion at 50% Depth Impacts 1D (Super 6)

Exact conditional enumeration DEP040 for a 1D shoe at 50% depth (26/52 cards undealt) with 2 remaining Rank-4 cards confirms a 1.2530% Banker edge (Super 6), 1.4400% Player edge, and 14.3592% Tie edge.

In 1D audit DEP040 (26/52 stub at 50% depth), removing 4s produces the (dep040-rank-4) single largest per-card shift toward (26c) banker (and away from player) (dep040-rank-4·26c) of any rank in the shoe. Removing 2 Rank-4 cards (+1.19 bps per card) alongside Super 6 rules sets Tie hold to 14.3592% (9.5156% frequency).

State DEP040 (1D, 50% depth, 2/4 Rank-4 left, Super 6)
Wager / MetricState DEP040 Value1D BaselineSettlement Note
DEP040 Banker (Super 6)45.9622% (-1.2530% EV)45.9595%DEP040 1D 50% (2 Rank-4)
DEP040 Player (1:1)44.5222% (-1.4400% EV)44.5249%DEP040 26-card 1D stub (0.9357 SD)
DEP040 Tie (8:1)9.5156% (-14.3592% EV)9.5156%DEP040 Rank-4 (2 out, 2 in)
TABLEAU & SCOREBOARD SEPARATION · DEP040

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP040 · 1D)

While DEP040 tracks 2 removed Four-Pip Card cards across 50% of a 52-card (1D) shoe (26 remaining, 1.2530% Super 6 edge), Big Eye Boy (lookback 1), Small Road (lookback 2), and Cockroach Pig (lookback 3) evaluate only Big Road column shapes.

  • DEP040 (1D 50%): 26/52 cards with 2/4 Rank-4 (2A).
  • DEP040 (Rank-4 split): 45.9622% Banker, 44.5222% Player, 9.5156% Tie in 26 1D cards (2B).
  • DEP040 (Super 6 EV): -1.2530% Banker, -1.4400% Player, -14.3592% Tie, 0.9357 SD at 50% (2C).
  • DEP040 (1D roads): red/blue marks log Big Road columns, never 2 Rank-4 stub count (2D).
Table Reality Check

Myth vs. Truth

MythWhen 2 Four-Pip Card cards leave a 1D shoe by 50% depth (DEP040), 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-4 stub counts (2/4 in 26 cards); Banker carries a -1.2530% 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