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PROGRESSION SURVIVAL AUDIT · DALS500

D'Alembert Arithmetic (+1u / -1u) — 500-Hand High-Limit Marathon (200u Bankroll) Survival & Ruin Proof

[DALS500] Increases the wager by +1 unit after a loss and reduces the wager by −1 unit (minimum 1u) after a win. Across 500-Hand High-Limit Marathon (200u Bankroll) (Six-shoe salon marathon exposing long-run house-edge drift against a 200-unit reserve), staking D'Alembert on Player (1.2351% house edge) generates 1060.0 units of cumulative action, an expected mathematical cost of −13.09 units, ±45.09 units of standard deviation, and a 82.5% session survival rate (17.5% bankroll ruin risk).

DALS500 Action
1060.0u
DALS500 Expected EV
-13.09u
DALS500 Session SD
±45.09u
DALS500 Survival
82.5%
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 = ≠ ≠ ≠ ≠

DALS500 (D'Alembert · 500H / 200u) scoreboard sample. Derived-road red/blue marks never alter DALS500 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

DALS500 Staking Sequence
1-2-3-4-5-4-3

Increases the wager by +1 unit after a loss and reduces the wager by −1 unit (minimum 1u) after a win (Arithmetic Negative Progression).

DALS500 Cumulative Action
1060.0u wagered

500 hands × 2.12u average stake multiplier.

DALS500 Expected Cost (EV)
-13.09u

Linear expectation across 1060.0u action at 1.2351% Player edge.

DALS500 Session Dispersion
±45.09u SD

Volatility envelope over 500 deals against a 200u bankroll.

DALS500 Survival / Ruin Split
82.5% / 17.5%

Avoids exponential bet explosions but drifts into elevated 5u–10u flat exposure when Player losses outnumber wins over 50+ deals.

DALS500 STOCHASTIC HORIZON

D'Alembert (DALS500) Over 500 Hands With a 200-Unit Bankroll

[DALS500-MECHANICS] Staking protocol DALS500 applies D'Alembert Arithmetic (+1u / -1u) (1-2-3-4-5-4-3) on Player across 500 hands with a 200-unit stop-loss. Increases the wager by +1 unit after a loss and reduces the wager by −1 unit (minimum 1u) after a win. Six-shoe salon marathon exposing long-run house-edge drift against a 200-unit reserve.

[DALS500-EXPECTATION] By linearity of expectation, DALS500 cannot alter the 8-deck 1.2351% Player house edge: multiplying 1060.0u cumulative action by −1.2351% locks in −13.09u expected drift with ±45.09u standard deviation. Avoids exponential bet explosions but drifts into elevated 5u–10u flat exposure when Player losses outnumber wins over 50+ deals. Remember that baccarat is an 18+ / 21+ game of chance; review /legal/responsible-gambling before setting session limits.

DALS500 CheckpointDALS500 HandsDALS500 ActionDALS500 EV DriftDALS500 SD Band
DALS500-Stage-1100h [DALS500]212.0u [DALS500]-2.62u [DALS500]±20.16u [DALS500]
DALS500-Stage-2200h [DALS500]424.0u [DALS500]-5.24u [DALS500]±28.52u [DALS500]
DALS500-Stage-3300h [DALS500]636.0u [DALS500]-7.86u [DALS500]±34.93u [DALS500]
DALS500-Stage-4400h [DALS500]848.0u [DALS500]-10.47u [DALS500]±40.33u [DALS500]
DALS500-Stage-5500h [DALS500]1060.0u [DALS500]-13.09u [DALS500]±45.09u [DALS500]
  • DALS500 step sequence: 1-2-3-4-5-4-3 (2.12u mean bet size across 500 hands).
  • DALS500 bankroll boundary: 200u starting stack faces 17.5% ruin risk and 82.5% survival probability.
  • DALS500 road independence: Big Eye Boy and Small Road patterns on BBBBPPPP never change the −13.09u expected house hold.
Table Reality Check

Myth vs. Truth

MythRunning D'Alembert over 500 hands with 200 units changes the mathematical expectation of the shoe.
TruthEvery hand in DALS500 faces the same 1.2351% Player house edge; scaling bet sizes to 1060.0u total action scales expected cost to −13.09u while reshaping variance (±45.09u 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