Analyzing roulette strategies - my insights from a simulation

Roulette strategies have been the subject of extensive discussion, but how do they hold up when subjected to rigorous testing? I conducted two simulations with 1,000 spins each, starting with a $1,000 bankroll and a $10 base bet. These simulations provide a clear picture of how different strategies perform over time. Let us dissect the data logically.

Key Strategies Defined:​

1. Constant Bet: Betting consistently on the same outcome (e.g., Red).
2. Martingale: Doubling bets after losses to recover losses and secure a profit.
3. Reverse Martingale: Doubling bets after wins, aiming to capitalize on streaks.
4. D’Alembert: Incrementing bets by one unit after losses and decrementing after wins.

Simulation 1: Observations​

• Constant Betting:
  The most stable strategy, as expected. Bets on colors (e.g., Red) proved reasonably reliable, yielding returns up to +20%. However, straight bets (single numbers) highlighted extreme volatility, with the longest losing streak at 136 spins.
  
  
• Martingale:
  Predictably disastrous. All simulations failed to complete due to bankroll depletion, highlighting the inherent flaw in the strategy: exponential losses. This underscores the futility of attempting to outpace the house edge with aggressive doubling.
  
  
• Reverse Martingale:
  Highly volatile with a single standout—betting on the first dozen yielded a 251% ROI. However, the vast majority of variations led to complete bankruptcy, showcasing the dangers of over-leveraging during winning streaks.
  
  
• D’Alembert:
  More conservative but equally prone to failure over extended spins. Incremental betting provided some buffer against rapid losses, but the house edge prevailed in every scenario tested.

Simulation 2: Additional Insights​

• Constant Betting:
  Consistently the most sustainable approach. Betting on the first dozen emerged as a top performer, with a +26% ROI. While this strategy does not defy the house edge, it maximizes longevity.
  
  
• Martingale:
  Short-lived and prone to catastrophic failure. While rare instances yielded marginal gains (+2% ROI on Even bets), the overall outlook remained grim.
  
  
• Reverse Martingale:
  Once again, highly volatile. Successes were few and far between, with most strategies resulting in bankruptcy within 200 spins.
  
  
• D’Alembert:
  This strategy consistently underperformed. Though less aggressive than Martingale, it failed to mitigate the house edge in any meaningful way.

Conclusions:​

1. Sustainability: Constant betting is by far the most practical for players aiming to extend their session.
2. Volatility: Both Martingale and Reverse Martingale strategies amplify the risk of bankruptcy.
3. House Edge: No strategy completely offsets this inevitability. Over time, the casino retains its statistical advantage.

While simulations provide clarity, real-world play introduces additional variables such as table limits and psychological factors. However, for those committed to logical decision-making, avoiding progressive systems like Martingale is imperative. Stick with consistent betting if longevity matters to you.

I welcome any thoughts or critiques on these findings. Is there a strategy you’ve tested that defies these results? Let us debate this logically.