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PROGRESSION SURVIVAL AUDIT · GMRS250

Grand Martingale (1-3-7-15-31) — 250-Hand Weekend Horizon (100u Bankroll) Survival & Ruin Proof

[GMRS250] Doubles the prior wager plus 1 extra unit after every loss (1, 3, 7, 15, 31) and resets to 1u on a win. Across 250-Hand Weekend Horizon (100u Bankroll) (Three-plus shoe weekend trip horizon backed by a full 100-unit session bankroll), staking Grand Martingale on Player (1.2351% house edge) generates 1105.0 units of cumulative action, an expected mathematical cost of −13.65 units, ±66.47 units of standard deviation, and a 69.5% session survival rate (30.5% bankroll ruin risk).

GMRS250 Action
1105.0u
GMRS250 Expected EV
-13.65u
GMRS250 Session SD
±66.47u
GMRS250 Survival
69.5%
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

GMRS250 (Grand Martingale · 250H / 100u) scoreboard sample. Derived-road red/blue marks never alter GMRS250 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

Column 3 has 1 bead. Column 2 has 1 bead. Same depth → red (=).

  1. Column 4 starts, so use Rule 1: compare Column 3 with Column 2, 1 column further back.
  2. Column 3 has 1 bead. Column 2 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 2.

Small Road Mark #2

Column 4 has 1 bead. Column 2 has 1 bead. Same depth → red (=).

  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 1 bead. Same depth → red (=).

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 1 bead. Same depth → red (=).

  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 1 bead. Same depth → red (=).

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

GMRS250 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).

GMRS250 Cumulative Action
1105.0u wagered

250 hands × 4.42u average stake multiplier.

GMRS250 Expected Cost (EV)
-13.65u

Linear expectation across 1105.0u action at 1.2351% Player edge.

GMRS250 Session Dispersion
±66.47u SD

Volatility envelope over 250 deals against a 100u bankroll.

GMRS250 Survival / Ruin Split
69.5% / 30.5%

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

GMRS250 STOCHASTIC HORIZON

Grand Martingale (GMRS250) Over 250 Hands With a 100-Unit Bankroll

[GMRS250-MECHANICS] Staking protocol GMRS250 applies Grand Martingale (1-3-7-15-31) (1-3-7-15-31-63) on Player across 250 hands with a 100-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. Three-plus shoe weekend trip horizon backed by a full 100-unit session bankroll.

[GMRS250-EXPECTATION] By linearity of expectation, GMRS250 cannot alter the 8-deck 1.2351% Player house edge: multiplying 1105.0u cumulative action by −1.2351% locks in −13.65u expected drift with ±66.47u 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.

GMRS250 CheckpointGMRS250 HandsGMRS250 ActionGMRS250 EV DriftGMRS250 SD Band
GMRS250-Stage-150h [GMRS250]221.0u [GMRS250]-2.73u [GMRS250]±29.73u [GMRS250]
GMRS250-Stage-2100h [GMRS250]442.0u [GMRS250]-5.46u [GMRS250]±42.04u [GMRS250]
GMRS250-Stage-3150h [GMRS250]663.0u [GMRS250]-8.19u [GMRS250]±51.49u [GMRS250]
GMRS250-Stage-4200h [GMRS250]884.0u [GMRS250]-10.92u [GMRS250]±59.45u [GMRS250]
GMRS250-Stage-5250h [GMRS250]1105.0u [GMRS250]-13.65u [GMRS250]±66.47u [GMRS250]
  • GMRS250 step sequence: 1-3-7-15-31-63 (4.42u mean bet size across 250 hands).
  • GMRS250 bankroll boundary: 100u starting stack faces 30.5% ruin risk and 69.5% survival probability.
  • GMRS250 road independence: Big Eye Boy and Small Road patterns on PBPBPBPP never change the −13.65u expected house hold.
Table Reality Check

Myth vs. Truth

MythRunning Grand Martingale over 250 hands with 100 units changes the mathematical expectation of the shoe.
TruthEvery hand in GMRS250 faces the same 1.2351% Player house edge; scaling bet sizes to 1105.0u total action scales expected cost to −13.65u while reshaping variance (±66.47u 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