Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. Flat Player (50H / 20u)
PROGRESSION SURVIVAL AUDIT · FPLS50

Flat Betting Player (1u Constant) — 50-Hand Sprint (20u Bankroll) Survival & Ruin Proof

[FPLS50] Wagers a constant 1 unit on Player every hand with even-money 1:1 settlement and zero vig breakage. Across 50-Hand Sprint (20u Bankroll) (Fast 45-minute mini-baccarat or two-thirds shoe sprint with a compact 20-unit buy-in), staking Flat Player on Player (1.2351% house edge) generates 50.0 units of cumulative action, an expected mathematical cost of −0.62 units, ±6.73 units of standard deviation, and a 89.9% session survival rate (10.1% bankroll ruin risk).

FPLS50 Action
50.0u
FPLS50 Expected EV
-0.62u
FPLS50 Session SD
±6.73u
FPLS50 Survival
89.9%
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 = = = ≠ ≠ ≠ = =

FPLS50 (Flat Player · 50H / 20u) scoreboard sample. Derived-road red/blue marks never alter FPLS50 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

FPLS50 Staking Sequence
1-1-1-1-1

Wagers a constant 1 unit on Player every hand with even-money 1:1 settlement and zero vig breakage (Constant-Unit Baseline).

FPLS50 Cumulative Action
50.0u wagered

50 hands × 1.00u average stake multiplier.

FPLS50 Expected Cost (EV)
-0.62u

Linear expectation across 50.0u action at 1.2351% Player edge.

FPLS50 Session Dispersion
±6.73u SD

Volatility envelope over 50 deals against a 20u bankroll.

FPLS50 Survival / Ruin Split
89.9% / 10.1%

Eliminates 5% commission accounting at the cost of a 1.2351% house edge per unit staked.

FPLS50 STOCHASTIC HORIZON

Flat Player (FPLS50) Over 50 Hands With a 20-Unit Bankroll

[FPLS50-MECHANICS] Staking protocol FPLS50 applies Flat Betting Player (1u Constant) (1-1-1-1-1) on Player across 50 hands with a 20-unit stop-loss. Wagers a constant 1 unit on Player every hand with even-money 1:1 settlement and zero vig breakage. Fast 45-minute mini-baccarat or two-thirds shoe sprint with a compact 20-unit buy-in.

[FPLS50-EXPECTATION] By linearity of expectation, FPLS50 cannot alter the 8-deck 1.2351% Player house edge: multiplying 50.0u cumulative action by −1.2351% locks in −0.62u expected drift with ±6.73u standard deviation. Eliminates 5% commission accounting at the cost of a 1.2351% house edge per unit staked. Remember that baccarat is an 18+ / 21+ game of chance; review /legal/responsible-gambling before setting session limits.

FPLS50 CheckpointFPLS50 HandsFPLS50 ActionFPLS50 EV DriftFPLS50 SD Band
FPLS50-Stage-110h [FPLS50]10.0u [FPLS50]-0.12u [FPLS50]±3.01u [FPLS50]
FPLS50-Stage-220h [FPLS50]20.0u [FPLS50]-0.25u [FPLS50]±4.25u [FPLS50]
FPLS50-Stage-330h [FPLS50]30.0u [FPLS50]-0.37u [FPLS50]±5.21u [FPLS50]
FPLS50-Stage-440h [FPLS50]40.0u [FPLS50]-0.49u [FPLS50]±6.02u [FPLS50]
FPLS50-Stage-550h [FPLS50]50.0u [FPLS50]-0.62u [FPLS50]±6.73u [FPLS50]
  • FPLS50 step sequence: 1-1-1-1-1 (1.00u mean bet size across 50 hands).
  • FPLS50 bankroll boundary: 20u starting stack faces 10.1% ruin risk and 89.9% survival probability.
  • FPLS50 road independence: Big Eye Boy and Small Road patterns on PPPBBBPP never change the −0.62u expected house hold.
Table Reality Check

Myth vs. Truth

MythRunning Flat Player over 50 hands with 20 units changes the mathematical expectation of the shoe.
TruthEvery hand in FPLS50 faces the same 1.2351% Player house edge; scaling bet sizes to 50.0u total action scales expected cost to −0.62u while reshaping variance (±6.73u 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