Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math & Odds Hub
  3. Contra D'Alembert vs Flat Betting (5% Comm Streak)
STAGE 2 STRESS TEST · CONTRA D'ALEMBERT VS FLAT BETTING

Contra D'Alembert Press vs. Flat 1-Unit Baseline — 9-Hand Dragon Streak Shoe under 5% Banker Commission (75-Hand Stress Test)

Under 5% Comm Streak (1.0579% effective edge), capital-bounded stress run S214-0 over 75 hands and a 80-unit treasury dissects a -39u drawdown (10.42% ruin) for Contra D'Alembert Press against -20u (4.80% ruin) for Flat 1-Unit Baseline inside a 60-unit cap. Because every 8-deck coup is statistically independent under 5% Banker Commission (0.95:1) (1.0579% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.

Contra D'Alembert Ruin Rate
10.42%
Flat Betting Ruin Rate
4.80%
Peak Trough (9-Run)
-39u
5% Comm Streak House Edge
1.0579%
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P B B B B P P P P B B P B
Big Eye Boy = = = ≠ = ≠ = = = = = = ≠ ≠
Small Road = ≠ = ≠ = ≠ = ≠ = = ≠ ≠
Cockroach Pig = ≠ = ≠ = ≠ ≠ ≠

Reference 8-deck shoe for Stress Cell S214 (Contra D'Alembert vs Flat Betting, 9-Hand Dragon Streak Shoe under 5% Banker Commission). Big Road shows Banker (red) and Player (blue); derived roads track symmetry.

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

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 3 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Cockroach Pig Mark #2

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 4 goes down to Row 3, so use Rule 2: look 3 columns back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

Matchup & Shoe Profile
Contra D'Alembert vs Flat Betting (5% Comm Streak)

Stress cell S214 compares +1 on win / -1 on loss against 1-1-1-1 constant unit over 75 hands.

Head-to-Head Ruin Rate
10.42% vs 4.80%

Probability of exhausting the 80-unit bankroll under a 60-unit house bet limit.

Expected Session Hold
1.38u vs 0.83u

Theoretical erosion under 5% Banker Commission (0.95:1) (1.0579% house edge) across 75 coups.

Peak Drawdown Excursion
-39u vs -20u

Deepest unit trough triggered by a 9-hand run inside the streak shoe profile.

Tie Stalls & Commission Toll
6 Ties · 0.66u Drag

Reflects 8.4% tie frequency (6 pushes) and 0.66u in vigorish friction.

STRESS CELL S214 · STREAK SHOE PROFILE

Contra D'Alembert vs. Flat Betting step-indexed volatility-band (75 Hands · S214)

In sequential comparative trial S214-1, running Contra D'Alembert against Flat Betting for 75 hands of 5% Comm Streak (streak) on 80 units quantifies 1.38u vs 0.83u in expected toll and 10.42% vs 4.80% ruin under a 60-unit pit limit.

Under 5% Comm Streak (1.0579% effective edge), bankroll-constrained stress run S214-2 over 75 hands and a 80-unit treasury computes a -39u drawdown (10.42% ruin) for Contra D'Alembert Press against -20u (4.80% ruin) for Flat 1-Unit Baseline inside a 60-unit cap.

S214 volatility-bandContra D'AlembertFlat Betting
Contra D'Alembert / Flat Betting Rule+1 on win / -1 on loss1-1-1-1 constant unit
75-Hand Ruin (80u)10.42%4.80%
5% Comm Streak Hold (1.0579%)1.38u0.83u
9-Run Trough (60u Cap)-39u-20u
VIGORISH & TABLE CEILING INTERACTION

5% Comm Streak Vigorish (0.66u) & 8.4% Tie Push Audit (S214)

In stochastic comparative trial S214-3, running Contra D'Alembert against Flat Betting for 75 hands of 5% Comm Streak (streak) on 80 units maps 1.38u vs 0.83u in expected toll and 10.42% vs 4.80% ruin under a 60-unit pit limit.

Under 5% Comm Streak (1.0579% effective edge), absorbing-barrier stress run S214-4 over 75 hands and a 80-unit treasury evaluates a -39u drawdown (10.42% ruin) for Contra D'Alembert Press against -20u (4.80% ruin) for Flat 1-Unit Baseline inside a 60-unit cap.

  • Trial S214: set a 80u stop before running Contra D'Alembert vs Flat Betting over 75 hands.
  • Scenario S214 benchmarks 0.66u in commission drag and 6 tie pushes (8.4% Tie rate).
  • Board rule S214: derived road red marks step-indexed column repetition and blue marks a structural break (volatility-band), never Banker or Player.
Table Reality Check

Myth vs. Truth

MythSwitching from Flat Betting to Contra D'Alembert during 9-Hand Dragon Streak Shoe under 5% Banker Commission neutralizes the 1.0579% house edge.
TruthOver 75 hands on a 80-unit stack, Contra D'Alembert carries 1.38u expected loss (10.42% ruin) vs 0.83u (4.80% ruin) for Flat Betting.
MythDuring a 9-hand streak sequence, red marks on Big Eye Boy or Small Road indicate Banker is favored next.
TruthDerived road colors never represent Banker or Player: red denotes repeatingBig Road structure and blue denotes breaking structure.
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