Stake Progression Simulator

The mathematical fallacy of betting systems

Since the inception of the modern casino, players have searched for the perfect betting progression—a systematic rule to scale bet sizes to guarantee a win. The most famous is the Martingale, where you double your bet after every loss, believing that a win will eventually recover all previous losses and secure a one-unit profit.

The math behind these progressions is simple: **they do not change the house edge.** Every bet you place still carries the exact same negative expected value. Betting systems simply alter your volatility profile, exchanging a high probability of making small, short-term gains for a tiny probability of experiencing a catastrophic loss that wipes out your entire bankroll.

How progressions grow: The Martingale cliff

To understand why progressions fail, let’s examine the exponential stake growth of the Martingale system:

1. Exponential stake equation

After a streak of $L$ consecutive losses, your required bet size on the next round is:

Bet_Size = Base_Bet * 2^L

Your total accumulated loss after $L$ rounds is:

Total_Loss = Base_Bet * (2^L - 1)

2. The table limit barrier

If you start with a base bet of $5, your wagers scale as follows after consecutive losses:

• 1 Loss: $10
• 3 Losses: $40
• 5 Losses: $160
• 7 Losses: $640
• 9 Losses: $2,560

If your casino has a standard table limit of $1,000, you will hit the table maximum after just 7 consecutive losses. At this point, the system breaks: you cannot double your bet, your accumulated losses cannot be recovered, and your session ends in ruin.

Step-by-step audit: Simulating a system

Let’s audit the Martingale system over 1,000 spins of European Roulette:

1. Set your starting bankroll (e.g., $1,000) and base bet (e.g., $10).
2. Choose the game type (e.g., European Roulette) and the bet type (e.g., Red/Black).
3. Select the “Martingale” progression from the dropdown.
4. Set the table limit (e.g., $500).
5. Run the simulator. The tool will execute 1,000 rounds and plot the bankroll trajectory on the chart.

Watch how the chart behaves. You will see a slow, steady upward trend of small profits, followed by an abrupt, vertical drop to zero. This vertical drop is the “cliff of ruin”—the mathematical certainty that ruins every progression player.

Frequently asked questions