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PROGRESSION SURVIVAL AUDIT · GMRS50

Grand Martingale (1-3-7-15-31) — 50-Hand Sprint (20u Bankroll) Survival & Ruin Proof

[GMRS50] Doubles the prior wager plus 1 extra unit after every loss (1, 3, 7, 15, 31) and resets to 1u on a win. Across 50-Hand Sprint (20u Bankroll) (Fast 45-minute mini-baccarat or two-thirds shoe sprint with a compact 20-unit buy-in), staking Grand Martingale on Player (1.2351% house edge) generates 221.0 units of cumulative action, an expected mathematical cost of −2.73 units, ±29.73 units of standard deviation, and a 55.5% session survival rate (44.5% bankroll ruin risk).

GMRS50 Action
221.0u
GMRS50 Expected EV
-2.73u
GMRS50 Session SD
±29.73u
GMRS50 Survival
55.5%
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

GMRS50 (Grand Martingale · 50H / 20u) scoreboard sample. Derived-road red/blue marks never alter GMRS50 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

Column 4 has 2 beads. Column 1 has 4 beads. Different depth → blue (≠).

  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 4 beads. Different depth → blue (≠).

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

GMRS50 Staking Sequence
1-3-7-15-31-63

Doubles the prior wager plus 1 extra unit after every loss (1, 3, 7, 15, 31) and resets to 1u on a win (Aggressive Negative Progression).

GMRS50 Cumulative Action
221.0u wagered

50 hands × 4.42u average stake multiplier.

GMRS50 Expected Cost (EV)
-2.73u

Linear expectation across 221.0u action at 1.2351% Player edge.

GMRS50 Session Dispersion
±29.73u SD

Volatility envelope over 50 deals against a 20u bankroll.

GMRS50 Survival / Ruin Split
55.5% / 44.5%

Accelerates cumulative bankroll commitment to 57 units by step 5, exhausting medium bankrolls two steps faster than standard Martingale.

GMRS50 STOCHASTIC HORIZON

Grand Martingale (GMRS50) Over 50 Hands With a 20-Unit Bankroll

[GMRS50-MECHANICS] Staking protocol GMRS50 applies Grand Martingale (1-3-7-15-31) (1-3-7-15-31-63) on Player across 50 hands with a 20-unit stop-loss. Doubles the prior wager plus 1 extra unit after every loss (1, 3, 7, 15, 31) and resets to 1u on a win. Fast 45-minute mini-baccarat or two-thirds shoe sprint with a compact 20-unit buy-in.

[GMRS50-EXPECTATION] By linearity of expectation, GMRS50 cannot alter the 8-deck 1.2351% Player house edge: multiplying 221.0u cumulative action by −1.2351% locks in −2.73u expected drift with ±29.73u standard deviation. Accelerates cumulative bankroll commitment to 57 units by step 5, exhausting medium bankrolls two steps faster than standard Martingale. Remember that baccarat is an 18+ / 21+ game of chance; review /legal/responsible-gambling before setting session limits.

GMRS50 CheckpointGMRS50 HandsGMRS50 ActionGMRS50 EV DriftGMRS50 SD Band
GMRS50-Stage-110h [GMRS50]44.2u [GMRS50]-0.55u [GMRS50]±13.29u [GMRS50]
GMRS50-Stage-220h [GMRS50]88.4u [GMRS50]-1.09u [GMRS50]±18.80u [GMRS50]
GMRS50-Stage-330h [GMRS50]132.6u [GMRS50]-1.64u [GMRS50]±23.03u [GMRS50]
GMRS50-Stage-440h [GMRS50]176.8u [GMRS50]-2.18u [GMRS50]±26.59u [GMRS50]
GMRS50-Stage-550h [GMRS50]221.0u [GMRS50]-2.73u [GMRS50]±29.73u [GMRS50]
  • GMRS50 step sequence: 1-3-7-15-31-63 (4.42u mean bet size across 50 hands).
  • GMRS50 bankroll boundary: 20u starting stack faces 44.5% ruin risk and 55.5% survival probability.
  • GMRS50 road independence: Big Eye Boy and Small Road patterns on BBBBPPPP never change the −2.73u expected house hold.
Table Reality Check

Myth vs. Truth

MythRunning Grand Martingale over 50 hands with 20 units changes the mathematical expectation of the shoe.
TruthEvery hand in GMRS50 faces the same 1.2351% Player house edge; scaling bet sizes to 221.0u total action scales expected cost to −2.73u while reshaping variance (±29.73u 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