Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math & Odds Hub
  3. Fibonacci 40u 3-Shoe Matrix
STAGE 2 BANKROLL MATRIX · FIBONACCI · 40U / 3-SHOE

Fibonacci Negative Sequence — 40-Unit Bankroll & 3-Shoe (216-Hand) Risk-of-Ruin Matrix

For a 40-unit roll spanning 216 hands (3 shoes), Fibonacci Negative Sequence (1-1-2-3-5-8-13-21-34) profiles a step-indexed distribution under matrix M232-0, where the 60-unit table roof and -20u/+10u barriers yield 81.74% ruin versus 23.19% upside completion. Every 8-deck hand remains statistically independent (45.86% Banker, 44.62% Player, 9.52% Tie), meaning progression sizing reshapes session variance without altering the house edge.

Ruin Rate (-20u Stop)
81.74%
Target Hit (+10u Cap)
23.19%
216-Hand Expected Hold
4.65u
Table Max (6-Step Depth)
60u
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference 8-deck shoe for Matrix Cell M232 (Fibonacci Negative Sequence, 40u bankroll, 216 hands). Big Road and Bead Plate show Banker (red) and Player (blue); derived roads record structural 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

Session Bankroll & Horizon
40u / 3 Shoes (216 Hands)

Matrix cell M232 tests Fibonacci Negative Sequence with a $50 base unit and -20u/+10u absorbing boundaries.

Stop-Loss Ruin Probability
81.74%

Probability of hitting the -20u drawdown barrier before completing 216 hands or reaching +10u.

Stop-Win Target Completion
23.19%

Share of 216-hand trajectories reaching the +10u session ceiling, with 0.50% ending between barriers.

Table Limit Survival Depth
6 Steps (60u Cap)

A 60-unit house limit and 40-unit stack cap Fibonacci escalation after 6 adverse coups.

Expected Session House Hold
4.65u ($233)

Derived from 341u total action (1.58x average wager) multiplied by the 1.0579% 8-deck Banker edge.

MATRIX CELL M232 · STOP-LOSS & STOP-WIN GEOMETRY

Fibonacci 40u absorbing-barrier absorption-curve Across 216 Hands (M232)

Combinatorial ledger M232-1 calibrates Fibonacci (1-1-2-3-5-8-13-21-34) at 40 units and 216 hands (3 shoes), proving that a 60-unit table ceiling and 1.58x average bet multiplier yield 81.74% ruin probability and 4.65u in theoretical house hold.

For a 40-unit roll spanning 216 hands (3 shoes), Fibonacci Negative Sequence (1-1-2-3-5-8-13-21-34) dissects a absorbing-barrier envelope under matrix M232-2, where the 60-unit table roof and -20u/+10u barriers yield 81.74% ruin versus 23.19% upside completion.

M232 ParameterFibonacci (40u)3-Shoe absorption-curve
Fibonacci Ladder1-1-2-3-5-8-13-21-34 (9 steps)Peak 34u multiplier on M232
40u Stack Window216 hands (3 shoes)Barriers -20u / +10u
60u Ceiling & Ruin81.74% ruin vs 23.19% winDepth 6 steps (9 cap hits)
341u Handle & Hold4.65u ($233)Multiplier 1.58x (absorbing-barrier drift)
STEP ESCALATION & TURNOVER AUDIT

60u Ceiling Collisions & Fibonacci Turnover (3 Shoes)

Combinatorial ledger M232-3 evaluates Fibonacci (1-1-2-3-5-8-13-21-34) at 40 units and 216 hands (3 shoes), proving that a 60-unit table ceiling and 1.58x average bet multiplier yield 81.74% ruin probability and 4.65u in theoretical house hold.

For a 40-unit roll spanning 216 hands (3 shoes), Fibonacci Negative Sequence (1-1-2-3-5-8-13-21-34) audits a capital-bounded trajectory under matrix M232-4, where the 60-unit table roof and -20u/+10u barriers yield 81.74% ruin versus 23.19% upside completion.

  • Cell M232 rule: lock the -20u stop on your 40u Fibonacci stack across 216 hands.
  • Matrix M232 charts 4.65u ($233) in house hold over 341u of Fibonacci action.
  • Scoreboard check M232: Big Eye Boy, Small Road, and Cockroach Pig use red for repeating symmetry (absorbing-barrier absorption-curve) and blue for pattern breaks—never for Banker or Player.
Table Reality Check

Myth vs. Truth

MythBringing 40 units to a 3-shoe session lets Fibonacci Negative Sequence overcome the 1.058% Banker house edge.
TruthNo bankroll size alters per-hand expectation: over 216 hands, Fibonacci generates 341u in action, 4.65u in expected loss, and a 81.74% stop-loss ruin rate.
MythDerived road colors on the scoreboard tell Fibonacci bettors whether Banker (red) or Player (blue) is due during a 216-hand run.
TruthOn Big Eye Boy, Small Road, and Cockroach Pig, red indicates repeating column structure and blue indicates breaking structure; neither color represents Banker or Player.
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