D'Alembert System

A linear betting progression with a fixed step applied after each result.

1 → 2 → 3 → 4 → 5...

How It Works

STEP 01

Base Bet

Set the initial bet amount. This serves as the starting point for the entire progression.

STEP 02

After a Loss

One fixed step is added to the current bet.

STEP 03

After a Win

One step is subtracted from the current bet, but the bet cannot fall below the base bet.

Progression Feature

D'Alembert uses a linear increase in bet size. The sequence therefore grows gradually: 1 → 2 → 3 → 4 → 5, rather than doubling after each loss.

Important Limitation

The progression does not change the expected value of the underlying event and does not guarantee recovery of losses. Bankroll size and the maximum bet remain key constraints of the model.

Model Parameters

These values are used for bankroll safety calculations, the manual trainer, and the simulation.

Starting Bankroll ($)

Base Bet ($)

Bet Step ($)

Win Probability (%)

Event Odds (Decimal)

Maximum Bet ($)

Bet limit: a value of 0 means no limit is set.

Bankroll Safety Margin

This calculation shows how many consecutive losses the current bankroll can withstand.

Maximum Streak

consecutive losses

Streak Probability

0.001%

at the specified win probability

Bankroll Usage by StepSpent: $945.00

#1$10($10)

#2$15($25)

#3$20($45)

#4$25($70)

#5$30($100)

#6$35($135)

#7$40($175)

#8$45($220)

#9$50($270)

#10$55($325)

#11$60($385)

#12$65($450)

#13$70($520)

#14$75($595)

#15$80($675)

#16$85($760)

#17$90($850)

#18$95($945)

Interactive Trainer

Run the sequence manually and observe how the bankroll and bet size change.

Current Bankroll

$1000.00

Next Bet

$10.00

After a win, the bet decreases by one step but cannot fall below the base bet. After a loss, it increases by one step, subject to the maximum bet limit.

Strategy Simulation

Repeated simulations of random sequences allow you to explore how the strategy behaves under the specified parameters.

D'Alembert Simulator (Monte Carlo Simulation)

Analysis of 30 independent simulation sessions with 100 iterations

Distance (number of operations):

Liquidation frequency (30 sessions)10.0% (3 из 30)

Calculated ruin risk (100 steps)0.0%Threshold: 18 consecutive losses

Expected capital (without liquidation)$1000.00

Median / Maximum balance$915.00 / $1355.00

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What This Section Shows

The calculator demonstrates the mathematical behavior of the linear progression: changes in bet size, bankroll requirements, the maximum tolerable losing streak, and the impact of the specified limits. Model results do not guarantee a positive outcome for any individual betting session.