Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math Hub
  3. D'Alembert (250H / 100u)
PROGRESSION SURVIVAL AUDIT · DALS250

D'Alembert Arithmetic (+1u / -1u) — 250-Hand Weekend Horizon (100u Bankroll) Survival & Ruin Proof

[DALS250] Increases the wager by +1 unit after a loss and reduces the wager by −1 unit (minimum 1u) after a win. Across 250-Hand Weekend Horizon (100u Bankroll) (Three-plus shoe weekend trip horizon backed by a full 100-unit session bankroll), staking D'Alembert on Player (1.2351% house edge) generates 530.0 units of cumulative action, an expected mathematical cost of −6.55 units, ±31.88 units of standard deviation, and a 85.4% session survival rate (14.6% bankroll ruin risk).

DALS250 Action
530.0u
DALS250 Expected EV
-6.55u
DALS250 Session SD
±31.88u
DALS250 Survival
85.4%
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

DALS250 (D'Alembert · 250H / 100u) scoreboard sample. Derived-road red/blue marks never alter DALS250 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

DALS250 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).

DALS250 Cumulative Action
530.0u wagered

250 hands × 2.12u average stake multiplier.

DALS250 Expected Cost (EV)
-6.55u

Linear expectation across 530.0u action at 1.2351% Player edge.

DALS250 Session Dispersion
±31.88u SD

Volatility envelope over 250 deals against a 100u bankroll.

DALS250 Survival / Ruin Split
85.4% / 14.6%

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

DALS250 STOCHASTIC HORIZON

D'Alembert (DALS250) Over 250 Hands With a 100-Unit Bankroll

[DALS250-MECHANICS] Staking protocol DALS250 applies D'Alembert Arithmetic (+1u / -1u) (1-2-3-4-5-4-3) on Player across 250 hands with a 100-unit stop-loss. Increases the wager by +1 unit after a loss and reduces the wager by −1 unit (minimum 1u) after a win. Three-plus shoe weekend trip horizon backed by a full 100-unit session bankroll.

[DALS250-EXPECTATION] By linearity of expectation, DALS250 cannot alter the 8-deck 1.2351% Player house edge: multiplying 530.0u cumulative action by −1.2351% locks in −6.55u expected drift with ±31.88u 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.

DALS250 CheckpointDALS250 HandsDALS250 ActionDALS250 EV DriftDALS250 SD Band
DALS250-Stage-150h [DALS250]106.0u [DALS250]-1.31u [DALS250]±14.26u [DALS250]
DALS250-Stage-2100h [DALS250]212.0u [DALS250]-2.62u [DALS250]±20.16u [DALS250]
DALS250-Stage-3150h [DALS250]318.0u [DALS250]-3.93u [DALS250]±24.70u [DALS250]
DALS250-Stage-4200h [DALS250]424.0u [DALS250]-5.24u [DALS250]±28.52u [DALS250]
DALS250-Stage-5250h [DALS250]530.0u [DALS250]-6.55u [DALS250]±31.88u [DALS250]
  • DALS250 step sequence: 1-2-3-4-5-4-3 (2.12u mean bet size across 250 hands).
  • DALS250 bankroll boundary: 100u starting stack faces 14.6% ruin risk and 85.4% survival probability.
  • DALS250 road independence: Big Eye Boy and Small Road patterns on BPBPBPBB never change the −6.55u expected house hold.
Table Reality Check

Myth vs. Truth

MythRunning D'Alembert over 250 hands with 100 units changes the mathematical expectation of the shoe.
TruthEvery hand in DALS250 faces the same 1.2351% Player house edge; scaling bet sizes to 530.0u total action scales expected cost to −6.55u while reshaping variance (±31.88u 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