Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math & Odds Hub
  3. Fibonacci vs D'Alembert (EZ High-Tie)
STAGE 2 STRESS TEST · FIBONACCI VS D'ALEMBERT

Fibonacci Negative Sequence vs. D'Alembert Pyramid — Two-Shoe High-Tie Stall under EZ Baccarat Dragon 7 Push (152-Hand Stress Test)

Matchup S347-0 benchmarks how a 110-unit roll and 75-unit pit maximum govern Fibonacci versus D'Alembert during 152 hands of EZ High-Tie: commission-adjusted distribution divergence pushes primary ruin to 26.16% against 11.40% for the benchmark while inspects 2.17u in commission friction. Because every 8-deck coup is statistically independent under EZ Baccarat 3-Card 7 Push (1.028% edge) (1.0284% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.

Fibonacci Ruin Rate
26.16%
D'Alembert Ruin Rate
11.40%
Peak Trough (5-Run)
-29u
EZ High-Tie House Edge
1.0284%
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 P B P P B
Big Eye Boy = = = = = = ≠ = = = ≠ ≠ = =
Small Road = = = = = = ≠ ≠ ≠ ≠ = =
Cockroach Pig = = = = = = ≠ ≠ = =

Reference 8-deck shoe for Stress Cell S347 (Fibonacci vs D'Alembert, Two-Shoe High-Tie Stall under EZ Baccarat Dragon 7 Push). 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 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

Matchup & Shoe Profile
Fibonacci vs D'Alembert (EZ High-Tie)

Stress cell S347 compares 1-1-2-3-5-8-13-21-34 against +1 on loss / -1 on win over 152 hands.

Head-to-Head Ruin Rate
26.16% vs 11.40%

Probability of exhausting the 110-unit bankroll under a 75-unit house bet limit.

Expected Session Hold
4.52u vs 2.70u

Theoretical erosion under EZ Baccarat 3-Card 7 Push (1.028% edge) (1.0284% house edge) across 152 coups.

Peak Drawdown Excursion
-29u vs -18u

Deepest unit trough triggered by a 5-hand run inside the high-tie shoe profile.

Tie Stalls & Commission Toll
26 Ties · 2.17u Drag

Reflects 17.11% tie frequency (26 pushes) and 2.17u in vigorish friction.

STRESS CELL S347 · HIGH-TIE SHOE PROFILE

Fibonacci vs. D'Alembert bankroll-constrained trajectory (152 Hands · S347)

During 152 deals of EZ High-Tie (high-tie) in audit S347-1, Fibonacci Negative Sequence (1-1-2-3-5-8-13-21-34) and D'Alembert Pyramid (+1 on loss / -1 on win) navigate 26 tie pushes on a 110-unit roll with a 75-unit cap, tracks 26.16% vs 11.40% ruin and 2.17u in commission drag.

Matchup S347-2 calibrates how a 110-unit roll and 75-unit pit maximum govern Fibonacci versus D'Alembert during 152 hands of EZ High-Tie: discrete-time envelope divergence pushes primary ruin to 26.16% against 11.40% for the benchmark while tabulates 2.17u in commission friction.

S347 trajectoryFibonacciD'Alembert
Fibonacci / D'Alembert Rule1-1-2-3-5-8-13-21-34+1 on loss / -1 on win
152-Hand Ruin (110u)26.16%11.40%
EZ High-Tie Hold (1.0284%)4.52u2.70u
5-Run Trough (75u Cap)-29u-18u
VIGORISH & TABLE CEILING INTERACTION

EZ High-Tie Vigorish (2.17u) & 17.11% Tie Push Audit (S347)

During 152 deals of EZ High-Tie (high-tie) in audit S347-3, Fibonacci Negative Sequence (1-1-2-3-5-8-13-21-34) and D'Alembert Pyramid (+1 on loss / -1 on win) navigate 26 tie pushes on a 110-unit roll with a 75-unit cap, tabulates 26.16% vs 11.40% ruin and 2.17u in commission drag.

Matchup S347-4 models how a 110-unit roll and 75-unit pit maximum govern Fibonacci versus D'Alembert during 152 hands of EZ High-Tie: capital-bounded trajectory divergence pushes primary ruin to 26.16% against 11.40% for the benchmark while charts 2.17u in commission friction.

  • Trial S347: set a 110u stop before running Fibonacci vs D'Alembert over 152 hands.
  • Scenario S347 tracks 2.17u in commission drag and 26 tie pushes (17.11% Tie rate).
  • Board rule S347: derived road red marks bankroll-constrained column repetition and blue marks a structural break (trajectory), never Banker or Player.
Table Reality Check

Myth vs. Truth

MythSwitching from D'Alembert to Fibonacci during Two-Shoe High-Tie Stall under EZ Baccarat Dragon 7 Push neutralizes the 1.0284% house edge.
TruthOver 152 hands on a 110-unit stack, Fibonacci carries 4.52u expected loss (26.16% ruin) vs 2.70u (11.40% ruin) for D'Alembert.
MythDuring a 5-hand high-tie 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