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STAGE 2 STRESS TEST · FIBONACCI VS D'ALEMBERT

Fibonacci Negative Sequence vs. D'Alembert Pyramid — Four-Shoe 12-Run Volatility under No-Commission Banker 6 (288-Hand Stress Test)

Benchmark S352-0 calibrates the absorbing-barrier footprint between Fibonacci and D'Alembert over 288 hands of 4-Shoe Streak: with 180 units, a 100-unit cap, and 1.4579% house edge, ruin settles at 24.73% vs 14.31% while house-edge-anchored decay-rate reaches -60u. Because every 8-deck coup is statistically independent under No-Commission Banker 6 (0.50:1 on 6) (1.4579% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.

Fibonacci Ruin Rate
24.73%
D'Alembert Ruin Rate
14.31%
Peak Trough (12-Run)
-60u
4-Shoe Streak House Edge
1.4579%
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference 8-deck shoe for Stress Cell S352 (Fibonacci vs D'Alembert, Four-Shoe 12-Run Volatility under No-Commission Banker 6). 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

Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

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

Matchup & Shoe Profile
Fibonacci vs D'Alembert (4-Shoe Streak)

Stress cell S352 compares 1-1-2-3-5-8-13-21-34 against +1 on loss / -1 on win over 288 hands.

Head-to-Head Ruin Rate
24.73% vs 14.31%

Probability of exhausting the 180-unit bankroll under a 100-unit house bet limit.

Expected Session Hold
12.13u vs 7.25u

Theoretical erosion under No-Commission Banker 6 (0.50:1 on 6) (1.4579% house edge) across 288 coups.

Peak Drawdown Excursion
-60u vs -31u

Deepest unit trough triggered by a 12-hand run inside the streak shoe profile.

Tie Stalls & Commission Toll
26 Ties · 7.52u Drag

Reflects 9.03% tie frequency (26 pushes) and 7.52u in vigorish friction.

STRESS CELL S352 · STREAK SHOE PROFILE

Fibonacci vs. D'Alembert finite-shoe capital-runway (288 Hands · S352)

When 4-Shoe Streak (streak) injects a 12-hand extreme run and 26 tie pushes (9.03% Tie density) over 288 coups, house-edge-anchored audit S352-1 tabulates Fibonacci Negative Sequence at 12.13u expected erosion (24.73% ruin) compared with 7.25u (14.31% ruin) for D'Alembert Pyramid on 180 units.

Benchmark S352-2 models the eight-deck cadence between Fibonacci and D'Alembert over 288 hands of 4-Shoe Streak: with 180 units, a 100-unit cap, and 1.4579% house edge, ruin settles at 24.73% vs 14.31% while sequential distribution reaches -60u.

S352 capital-runwayFibonacciD'Alembert
Fibonacci / D'Alembert Rule1-1-2-3-5-8-13-21-34+1 on loss / -1 on win
288-Hand Ruin (180u)24.73%14.31%
4-Shoe Streak Hold (1.4579%)12.13u7.25u
12-Run Trough (100u Cap)-60u-31u
VIGORISH & TABLE CEILING INTERACTION

4-Shoe Streak Vigorish (7.52u) & 9.03% Tie Push Audit (S352)

When 4-Shoe Streak (streak) injects a 12-hand extreme run and 26 tie pushes (9.03% Tie density) over 288 coups, table-capped audit S352-3 measures Fibonacci Negative Sequence at 12.13u expected erosion (24.73% ruin) compared with 7.25u (14.31% ruin) for D'Alembert Pyramid on 180 units.

Benchmark S352-4 dissects the step-indexed escalation between Fibonacci and D'Alembert over 288 hands of 4-Shoe Streak: with 180 units, a 100-unit cap, and 1.4579% house edge, ruin settles at 24.73% vs 14.31% while multi-coup survival-window reaches -60u.

  • Trial S352: set a 180u stop before running Fibonacci vs D'Alembert over 288 hands.
  • Scenario S352 inspects 7.52u in commission drag and 26 tie pushes (9.03% Tie rate).
  • Board rule S352: derived road red marks finite-shoe column repetition and blue marks a structural break (capital-runway), never Banker or Player.
Table Reality Check

Myth vs. Truth

MythSwitching from D'Alembert to Fibonacci during Four-Shoe 12-Run Volatility under No-Commission Banker 6 neutralizes the 1.4579% house edge.
TruthOver 288 hands on a 180-unit stack, Fibonacci carries 12.13u expected loss (24.73% ruin) vs 7.25u (14.31% ruin) for D'Alembert.
MythDuring a 12-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