Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 1D Rank-2 Depletion at 70% Depth (5% Vig)
COMBINATORIAL DEPLETION · 1D · RANK-2 · 70% DEPTH

1-Deck Two-Pip (Deuce) Depletion at 70% Penetration (5% Audit DEP024)

Removing 3 of 4 Two-Pip (Deuce) (Rank-2) cards at 70% penetration of a 1-deck (52-card) shoe leaves 1 Rank-2 cards inside a 16-card stub (DEP024), producing 45.9615% Banker wins, 44.5228% Player wins, 9.5157% Ties, and a 0.8594% Banker house edge under 5%.

Banker EV (5% Vig)
-0.8594%
Player EV (1:1)
-1.4386%
Rank-2 in 16-Card Stub
1/4
Single-Hand Std Dev
0.9371
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 DEP024 (1D Rank-2 at 70% 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 (DEP024)
16 / 52 Cards

70% penetration depth in 1D (single-deck laboratory benchmarks and historical pitch audits).

Rank-2 Remaining
1 of 4 Cards

3 2-pip cards across all four suits removed from the 1D pack.

Banker EV (5% Vig)
-0.8594%

Resolved at 45.9615% Banker win rate under 5% settlement.

Player EV (1:1)
-1.4386%

Resolved at 44.5228% Player win rate with 0.9371 unit standard deviation.

Tie Incidence (8:1)
9.5157%

Produces a 14.3589% house hold on the 8-to-1 Tie wager in state DEP024.

FINITE-SHOE ENUMERATION · DEP024

How Two-Pip (Deuce) Depletion at 70% Depth Impacts 1D (5% Vig)

Depletion matrix entry DEP024 pairs 1D (52 cards) at 70% penetration with 3 removed Two-Pip (Deuce) cards (1 left in 16 cards), fixing per-hand volatility at 0.9371 and Banker house hold at 0.8594% (5% Vig).

Comparing initial 52-card 1D weights against stub DEP024 (16 cards, 70% depth, 1 Rank-2 left) illustrates how on banker total 4, (dep024) banker draws against player third-card (1d-70%) 2 through 7; removing 2s (dep024·1d-70%) trims low-pip player third-card triggers (+0.52 bps slope, 0.8594% 5% Vig edge).

State DEP024 (1D, 70% depth, 1/4 Rank-2 left, 5% Vig)
Wager / MetricState DEP024 Value1D BaselineSettlement Note
DEP024 Banker (5% Vig)45.9615% (-0.8594% EV)45.9595%DEP024 1D 70% (1 Rank-2)
DEP024 Player (1:1)44.5228% (-1.4386% EV)44.5249%DEP024 16-card 1D stub (0.9371 SD)
DEP024 Tie (8:1)9.5157% (-14.3589% EV)9.5156%DEP024 Rank-2 (3 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP024

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP024 · 1D)

In DEP024, the 16-card 1D stub (70% penetration, 3 of 4 Rank-2 dealt) yields 45.9615% Banker, 44.5228% Player, and 9.5157% Tie outcomes with 0.9371 dispersion under 5% Vig.

  • DEP024 (1D 70%): 16/52 cards with 1/4 Rank-2 (6A).
  • DEP024 (Rank-2 split): 45.9615% Banker, 44.5228% Player, 9.5157% Tie in 16 1D cards (6B).
  • DEP024 (5% Vig EV): -0.8594% Banker, -1.4386% Player, -14.3589% Tie, 0.9371 SD at 70% (6C).
  • DEP024 (1D roads): red/blue marks log Big Road columns, never 1 Rank-2 stub count (6D).
Table Reality Check

Myth vs. Truth

MythWhen 3 Two-Pip (Deuce) cards leave a 1D shoe by 70% depth (DEP024), 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-2 stub counts (1/4 in 16 cards); Banker carries a -0.8594% expectation under 5%.
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