Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. 1-2-3-5 Staircase (500H / 200u)
PROGRESSION SURVIVAL AUDIT · S1235S500

1-2-3-5 Staircase Sequence — 500-Hand High-Limit Marathon (200u Bankroll) Survival & Ruin Proof

[S1235S500] Steps up 1u, 2u, 3u, 5u on consecutive wins (+11u on four wins) and resets immediately to 1u on any loss. Across 500-Hand High-Limit Marathon (200u Bankroll) (Six-shoe salon marathon exposing long-run house-edge drift against a 200-unit reserve), staking 1-2-3-5 Staircase on Player (1.2351% house edge) generates 760.0 units of cumulative action, an expected mathematical cost of −9.39 units, ±32.33 units of standard deviation, and a 87.4% session survival rate (12.6% bankroll ruin risk).

S1235S500 Action
760.0u
S1235S500 Expected EV
-9.39u
S1235S500 Session SD
±32.33u
S1235S500 Survival
87.4%
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

S1235S500 (1-2-3-5 Staircase · 500H / 200u) scoreboard sample. Derived-road red/blue marks never alter S1235S500 progression expectation.

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

This bead is at Row 3. Column 1 has a bead at Row 3 too → red (=).

  1. Column 2 goes down to Row 3, so use Rule 2: look 1 column back, at Column 1.
  2. Column 1 has a bead at Row 3 too → red (=).

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.

Small Road Mark #2

This bead is at Row 3. Column 1 has a bead at Row 3 too → red (=).

  1. Column 3 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 has a bead at Row 3 too → red (=).

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 has a bead at Row 3 too → red (=).

  1. Column 4 goes down to Row 3, so use Rule 2: look 3 columns back, at Column 1.
  2. Column 1 has a bead at Row 3 too → red (=).

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

S1235S500 Staking Sequence
1-2-3-5

Steps up 1u, 2u, 3u, 5u on consecutive wins (+11u on four wins) and resets immediately to 1u on any loss (Stepped Positive Progression).

S1235S500 Cumulative Action
760.0u wagered

500 hands × 1.52u average stake multiplier.

S1235S500 Expected Cost (EV)
-9.39u

Linear expectation across 760.0u action at 1.2351% Player edge.

S1235S500 Session Dispersion
±32.33u SD

Volatility envelope over 500 deals against a 200u bankroll.

S1235S500 Survival / Ruin Split
87.4% / 12.6%

Smooths out step-2 exposure (2u instead of 3u in 1-3-2-6), lowering two-hand variance across short 50-to-80 hand sessions.

S1235S500 STOCHASTIC HORIZON

1-2-3-5 Staircase (S1235S500) Over 500 Hands With a 200-Unit Bankroll

[S1235S500-MECHANICS] Staking protocol S1235S500 applies 1-2-3-5 Staircase Sequence (1-2-3-5) on Player across 500 hands with a 200-unit stop-loss. Steps up 1u, 2u, 3u, 5u on consecutive wins (+11u on four wins) and resets immediately to 1u on any loss. Six-shoe salon marathon exposing long-run house-edge drift against a 200-unit reserve.

[S1235S500-EXPECTATION] By linearity of expectation, S1235S500 cannot alter the 8-deck 1.2351% Player house edge: multiplying 760.0u cumulative action by −1.2351% locks in −9.39u expected drift with ±32.33u standard deviation. Smooths out step-2 exposure (2u instead of 3u in 1-3-2-6), lowering two-hand variance across short 50-to-80 hand sessions. Remember that baccarat is an 18+ / 21+ game of chance; review /legal/responsible-gambling before setting session limits.

S1235S500 CheckpointS1235S500 HandsS1235S500 ActionS1235S500 EV DriftS1235S500 SD Band
S1235S500-Stage-1100h [S1235S500]152.0u [S1235S500]-1.88u [S1235S500]±14.46u [S1235S500]
S1235S500-Stage-2200h [S1235S500]304.0u [S1235S500]-3.75u [S1235S500]±20.45u [S1235S500]
S1235S500-Stage-3300h [S1235S500]456.0u [S1235S500]-5.63u [S1235S500]±25.04u [S1235S500]
S1235S500-Stage-4400h [S1235S500]608.0u [S1235S500]-7.51u [S1235S500]±28.92u [S1235S500]
S1235S500-Stage-5500h [S1235S500]760.0u [S1235S500]-9.39u [S1235S500]±32.33u [S1235S500]
  • S1235S500 step sequence: 1-2-3-5 (1.52u mean bet size across 500 hands).
  • S1235S500 bankroll boundary: 200u starting stack faces 12.6% ruin risk and 87.4% survival probability.
  • S1235S500 road independence: Big Eye Boy and Small Road patterns on PPPBBBPP never change the −9.39u expected house hold.
Table Reality Check

Myth vs. Truth

MythRunning 1-2-3-5 Staircase over 500 hands with 200 units changes the mathematical expectation of the shoe.
TruthEvery hand in S1235S500 faces the same 1.2351% Player house edge; scaling bet sizes to 760.0u total action scales expected cost to −9.39u while reshaping variance (±32.33u SD).
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