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STAGE 2 BANKROLL MATRIX · 1-2-3-5 · 40U / 3-SHOE

1-2-3-5 Four-Step Ladder — 40-Unit Bankroll & 3-Shoe (216-Hand) Risk-of-Ruin Matrix

For a 40-unit roll spanning 216 hands (3 shoes), 1-2-3-5 Four-Step Ladder (1-2-3-5) tabulates a bankroll-constrained footprint under matrix M207-0, where the 60-unit table roof and -20u/+10u barriers yield 50.66% ruin versus 31.89% 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)
50.66%
Target Hit (+10u Cap)
31.89%
216-Hand Expected Hold
3.02u
Table Max (6-Step Depth)
60u
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference 8-deck shoe for Matrix Cell M207 (1-2-3-5 Four-Step Ladder, 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 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

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

Matrix cell M207 tests 1-2-3-5 Four-Step Ladder with a $50 base unit and -20u/+10u absorbing boundaries.

Stop-Loss Ruin Probability
50.66%

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

Stop-Win Target Completion
31.89%

Share of 216-hand trajectories reaching the +10u session ceiling, with 17.45% ending between barriers.

Table Limit Survival Depth
6 Steps (60u Cap)

A 60-unit house limit and 40-unit stack cap 1-2-3-5 escalation after 6 adverse coups.

Expected Session House Hold
3.02u ($151)

Derived from 257u total action (1.19x average wager) multiplied by the 1.0579% 8-deck Banker edge.

MATRIX CELL M207 · STOP-LOSS & STOP-WIN GEOMETRY

1-2-3-5 40u discrete-time capital-runway Across 216 Hands (M207)

Combinatorial ledger M207-1 quantifies 1-2-3-5 (1-2-3-5) at 40 units and 216 hands (3 shoes), proving that a 60-unit table ceiling and 1.19x average bet multiplier yield 50.66% ruin probability and 3.02u in theoretical house hold.

For a 40-unit roll spanning 216 hands (3 shoes), 1-2-3-5 Four-Step Ladder (1-2-3-5) charts a discrete-time cadence under matrix M207-2, where the 60-unit table roof and -20u/+10u barriers yield 50.66% ruin versus 31.89% upside completion.

M207 Parameter1-2-3-5 (40u)3-Shoe capital-runway
1-2-3-5 Ladder1-2-3-5 (4 steps)Peak 5u multiplier on M207
40u Stack Window216 hands (3 shoes)Barriers -20u / +10u
60u Ceiling & Ruin50.66% ruin vs 31.89% winDepth 6 steps (1 cap hits)
257u Handle & Hold3.02u ($151)Multiplier 1.19x (discrete-time drift)
STEP ESCALATION & TURNOVER AUDIT

60u Ceiling Collisions & 1-2-3-5 Turnover (3 Shoes)

Combinatorial ledger M207-3 profiles 1-2-3-5 (1-2-3-5) at 40 units and 216 hands (3 shoes), proving that a 60-unit table ceiling and 1.19x average bet multiplier yield 50.66% ruin probability and 3.02u in theoretical house hold.

For a 40-unit roll spanning 216 hands (3 shoes), 1-2-3-5 Four-Step Ladder (1-2-3-5) calibrates a asymmetric escalation under matrix M207-4, where the 60-unit table roof and -20u/+10u barriers yield 50.66% ruin versus 31.89% upside completion.

  • Cell M207 rule: lock the -20u stop on your 40u 1-2-3-5 stack across 216 hands.
  • Matrix M207 audits 3.02u ($151) in house hold over 257u of 1-2-3-5 action.
  • Scoreboard check M207: Big Eye Boy, Small Road, and Cockroach Pig use red for repeating symmetry (discrete-time capital-runway) 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 1-2-3-5 Four-Step Ladder overcome the 1.058% Banker house edge.
TruthNo bankroll size alters per-hand expectation: over 216 hands, 1-2-3-5 generates 257u in action, 3.02u in expected loss, and a 50.66% stop-loss ruin rate.
MythDerived road colors on the scoreboard tell 1-2-3-5 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