How to Mathematically Prove Your Strategy Isn't LuckBitcoin / U.S. dollarBITSTAMP:BTCUSDVertexQoreYou run a backtest on a strategy, and it makes 40% over two years. You get excited and go live with it, only to realize that one question almost no retail trader considers is: how likely is it that such a result happened by chance, and the strategy has no edge at all? Quant funds answer this question every day using a Monte Carlo simulation , something almost no retail trader has ever heard of. This article describes what this tool is, why it's useful, and how you can run a simple one yourself. The Trap of a Single Backtest Run A backtest, the one you ran on your strategy, represents a single possible outcome of a series of trades in the form of a single equity curve. The problem is that this is a single possibility out of thousands that exist. The order in which wins and losses fall within the same set of trades has a tremendous impact on the shape of the equity curve and the drawdowns it produces, even assuming the overall win rate, average win, and average loss across all trades are the same. A losing streak early in the series of trades will produce an equity curve that looks far worse than the same losing streak later in the series, or evenly distributed throughout the series. A single backtest only represents one ordering of trades, and it's possible, even likely, that you've selected one that favours your strategy unfairly. What a Monte Carlo Simulation Is, and What It Does A Monte Carlo simulation is essentially a tool that takes your set of wins and losses from your backtest and randomly orders them thousands of times, each time building an equity curve of the performance of your strategy if the trades had occurred in that particular ordering. Instead of having one single equity curve from your backtest, you end up with a distribution, sometimes a thousand or more different possibilities, that all represent realistic orderings of your trades, and thus realistic outcomes for your strategy. The basic idea is simple: One backtest → Randomize the trade order → Repeat hundreds or thousands of times → Analyze the distribution of outcomes. What You Can Do Once You Have a Distribution of Outcomes to Consider Instead of asking the relatively useless question of how much money your strategy can make, you can start asking much more useful questions: What's the worst possible drawdown this strategy could have, given the trades it has? What percentage of the possible outcomes of this strategy are profitable? How wide is the range between the best and worst possible outcome? These questions give you a much better understanding of the distribution of possible outcomes, rather than focusing on one historical equity curve. If 95% of outcomes for your strategy are profitable, that provides stronger evidence of robustness than a result where only 55% of simulated paths are profitable. But this should not be interpreted as a guarantee that the strategy has a genuine edge. Monte Carlo testing helps evaluate the robustness of the observed trade set; it does not prove future profitability. A Simple Example to Illustrate How This Works Your backtest consists of 100 trades: 45 winning trades, averaging +$200 55 losing trades, averaging −$120 Your original backtest, when ordered in the way it is, may have a nice, smooth equity curve that grows steadily throughout, with a maximum drawdown of only 15%. The basic arithmetic is: 45 × $200 = +$9,000 55 × $120 = −$6,600 Therefore: +$9,000 − $6,600 = +$2,400 So the complete set of 100 trades produces a +$2,400 net result before considering the order in which those trades occurred. You can now shuffle this set of trades, and if you place more losing trades at the beginning of the series, you end up with an equity curve that looks far worse than the one in your original backtest, potentially with a 35% drawdown at the beginning before recovering. The important point is that the trades themselves did not change. Only their order changed. Shuffling the Same Trades 1,000 Times Shuffling this set of trades a total of a thousand times will give you a distribution of outcomes for this strategy, some of which are better than your original backtest, and some far worse. Imagine two possible distributions: Scenario A 95% of simulated paths are profitable This suggests that profitability is relatively common across the simulated trade sequences. Scenario B 55% of simulated paths are profitable This indicates much greater uncertainty. Your original profitable backtest could simply be one of the favorable paths. The closer the percentage gets to 50%, the less convincing the result becomes as evidence of robustness. Again, these percentages should be treated as simulation evidence, not literal probabilities that the strategy will succeed in live markets. Why Almost No Retail Trader Actually Uses This A Monte Carlo simulation is normally done in code, often in Python, where a simple script is written to shuffle your list of trades thousands of times and record the results. Most retail trading platforms do not offer such a tool, and so it's left up to quant funds and more serious systematic traders to do the necessary work. The reality is that it's actually an incredibly useful tool, and the concepts behind it are easy to grasp. This also ignores the fact that people love the looks of a single backtest. A smooth green equity curve going steadily upward looks convincing. The looks of a thousand simulations, some of which are losing and some of which experience much larger drawdowns, are not nearly as attractive. But they tell a far more realistic story. How to Actually Apply This Do not trust a strategy based on a single backtest equity curve, and especially not one based on a backtest with a smaller number of trades, as such backtests are far more likely to produce a single outcome that looks good. If you can actually run a simple Monte Carlo simulation yourself, and you can run even 500 shuffles of a given set of trades, you should treat the percentage of them that are profitable as a rough robustness metric, rather than as a guaranteed probability of future success. Focus on the worst-case drawdowns across your shuffled outcomes, and not just the overall average outcome. The worst-case drawdown can provide a more useful picture of the type of risk your strategy may expose you to than simply looking at the smooth original equity curve. Before risking real money, a useful checklist is: 1. Run hundreds or thousands of randomized simulations. 2. Check what percentage of simulated paths remain profitable. 3. Examine the worst simulated drawdown. 4. Test the strategy across different periods and market conditions. Remember that a strategy that has survived a Monte Carlo test is not guaranteed to perform well in real markets either. This type of analysis only reduces the risk that you select a losing strategy based on a single backtest outcome. It does not remove this risk entirely. My conclusion A great-looking backtest is exciting, but it can simply be one favorable realization among many less favorable possibilities hidden behind it. Monte Carlo simulations give traders a way to evaluate a strategy based on the distribution of outcomes, rather than relying entirely on one ordering of trades. The next time you have a great backtest, ask yourself the far more important question: Would this strategy still look this great if I were to run a few hundred more backtests in random order instead of just one? That is the question that turns a simple backtest into a much deeper test of robustness, uncertainty, and risk. Thank you @VertexQore on @TradingView