AI for Bankroll Modelling: Simulating Your Strategy Before You Run It

[Betting Forum]

Most bettors discover the variance properties of their staking strategy the hard way. They run the strategy live, hit a drawdown they didn't anticipate, make emotional decisions about stake sizing mid-sequence, and then spend the next three months recovering ground they would have kept if they'd understood what they were running before they ran it.

Monte Carlo simulation is how every other industry that deals with uncertain outcomes - insurance, finance, engineering - stress-tests a strategy before committing real resources to it. You build a model of the process, run it thousands of times with randomised outcomes drawn from your probability estimates, and look at the distribution of results. Not the expected result. The distribution. The fifth percentile, the worst ten percent of runs, the probability of a drawdown of a specific magnitude before recovery. The things you'd only discover through live experience, surfaced in twenty minutes of computation instead.

This isn't new in betting theory. What's new is that you no longer need a quantitative background to build a meaningful simulation. An LLM can write the code. You provide the inputs. The combination produces something that no public betting content has actually walked through in practical terms - a simulation built from your specific strategy parameters rather than from generic assumptions about "a typical bettor."

This article covers how to do it. Specifically enough that you can implement it this week.

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What You're Simulating and Why It Matters

A Monte Carlo simulation of a betting strategy works like this. You define the parameters of your strategy - win rate by market type, average edge, stake sizing rule, starting bankroll, operator limit constraints. The simulation then runs thousands of independent sequences of bets drawn from those parameters, with outcomes randomised according to your probability estimates. At the end, you have thousands of possible trajectories your bankroll could take under your strategy. The distribution of those trajectories tells you things about your strategy that expected value calculations alone cannot.

Expected value tells you the average outcome over a very large number of bets. It doesn't tell you the probability of a fifty-unit drawdown before you reach that average. It doesn't tell you how long the worst ten percent of runs stay underwater before recovering. It doesn't tell you whether your stake sizing rule is likely to blow out your bankroll before the edge has time to express itself statistically.

Those are the things that determine whether a strategy is actually runnable given your psychological tolerance for variance, your actual bankroll size, and your operator limit constraints. A strategy with positive expected value but variance that regularly produces sixty-unit drawdowns is not a viable strategy for someone with a two-hundred-unit bankroll who will abandon the approach at minus forty. The EV calculation says it works. The simulation tells you whether it works for you specifically, under your specific conditions.

That specificity is the whole point.

The Inputs You Need Before Touching Any Code

The simulation is only as good as the inputs. Garbage in produces confident-looking garbage out, which is worse than no simulation because it looks like evidence.

You need four things, and you need to be honest about each of them.

Win rate and edge by market type. Not what you think your edge is - what your CLV tracker shows it actually is, by market category, over a sample size large enough to support a conclusion. The overfitting article established the threshold: roughly two hundred bets per category for a confident edge estimate, a hundred for a directional one you can use with appropriate uncertainty built in. If you're below a hundred bets in a category, your edge estimate for that category has wide error bars and the simulation should reflect that by running sensitivity analysis across a plausible range rather than treating your point estimate as fixed.

Stake sizing rule. The specific rule you apply, not the one you intend to apply. If you're running flat staking, what's the unit size as a percentage of bankroll? If you're running a Kelly fraction, what fraction and what's the input going into the Kelly calculation? If you're running a tiered system - larger stakes on higher confidence bets - what are the tiers and what confidence threshold separates them? The simulation will produce meaningless output if the staking rule it models doesn't match the one you actually execute.

Bet volume and frequency. How many bets per week, on average? How many per market type? The time dimension matters for drawdown analysis because a fifty-unit drawdown that resolves over four weeks is psychologically different from one that resolves over six months, even if the depth is the same. Volume determines how quickly variance resolves in either direction.

Operator constraints. This is the one most simulations ignore and the one that matters most for serious bettors. If your maximum stake at your primary operators is capped - either by explicit limits or by the stake sizes that avoid triggering review - that cap affects the compounding properties of your bankroll growth. A Kelly-based strategy that theoretically calls for a hundred-unit stake when your account is big enough is irrelevant if your operator caps you at fifteen. The simulation should model the constrained version of your strategy, not the theoretical unconstrained one.

Write these down before you ask the LLM to write any code. The prompting process is much cleaner when you're pasting specific numbers rather than describing a vague strategy and hoping the model fills in reasonable defaults.

Getting the LLM to Write the Code

You don't need to know Python to use this. You need to be able to run Python, which requires installing it and a couple of libraries - the prompt below handles the library specification. If you're on Windows, Python.org has a straightforward installer. If you're on Mac, it's likely already installed. The code runs in a terminal or in a free Jupyter notebook environment like Google Colab if you'd rather not run anything locally.

The prompt that produces working simulation code:

"Write a Python Monte Carlo simulation for a sports betting bankroll strategy. The simulation should accept the following parameters: starting bankroll, number of bets per simulation, number of simulation runs, win rate as a decimal, average odds on winning bets, average odds on losing bets, stake sizing rule (flat stake as percentage of current bankroll, OR fractional Kelly with fraction specified, OR fixed unit size), and a maximum stake cap in units to model operator limits. The simulation should run the specified number of runs, each consisting of the specified number of bets with outcomes randomised according to the win rate. For each run, track bankroll at every bet. After all runs complete, calculate and display: median final bankroll, fifth percentile final bankroll, ninety-fifth percentile final bankroll, probability of ruin (bankroll falling below twenty percent of starting bankroll at any point), median maximum drawdown in units, worst ten percent average maximum drawdown, and probability of being in drawdown at the midpoint of the simulation. Plot a chart showing the distribution of bankroll trajectories across all runs, with the median highlighted and the fifth to ninety-fifth percentile range shaded. Use matplotlib for the chart and numpy for the calculations. Include comments in the code explaining each section. Make the parameters easy to modify at the top of the script."

That prompt produces a complete, runnable simulation. Paste it into Claude or GPT-4, copy the code output, and run it. The first run will almost certainly produce an error related to a missing library - the model will tell you what to install and the install command is one line. After that it runs.

The parameters at the top of the script are where you input your actual strategy numbers. Change them, re-run the script, and the output updates. The whole cycle from changing a parameter to seeing the updated distribution takes about ten seconds.

Reading the Output Honestly

The simulation produces a distribution, not a prediction. The median final bankroll is the most likely single outcome if you run the strategy for the simulated number of bets. But "most likely" in a distribution with high variance means something different from what it means in conversation. If the fifth percentile outcome is minus sixty percent of your starting bankroll and the ninety-fifth percentile is plus four hundred percent, the median is technically the central estimate, but the lived experience of running this strategy has a wide range that the median doesn't capture.

The numbers to focus on, in order of importance for practical decision-making:

Probability of ruin. If the simulation shows a fifteen percent chance of your bankroll falling below twenty percent of its starting value at some point during the simulation run, that's a fifteen percent chance of being effectively knocked out of the strategy before the edge has time to express. For most bettors, a ruin probability above ten percent at their actual bankroll size is a signal to reduce stake sizing, not to accept the risk and run the strategy anyway.

Median maximum drawdown. This is the typical worst stretch you'll experience running this strategy over this many bets. Compare it to your actual tolerance. If the median maximum drawdown is forty units and you know from experience that a thirty-unit drawdown triggers emotional decision-making in you, the strategy's expected value is irrelevant - you won't execute it with discipline through the drawdown sequences the simulation predicts are normal.

Time in drawdown. The probability of being in drawdown at the midpoint of the simulation is the most psychologically useful number on the list. A strategy where you're more likely than not to be underwater halfway through the expected run requires genuine confidence in the edge and genuine commitment to the approach to survive intact. Most people don't have that level of conviction, and knowing you'll need it before you start is more useful than discovering it when you're thirty units down in month four.

The chart is worth spending time with. The distribution of trajectories across a thousand simulation runs shows you the shape of possible outcomes in a way that single statistics can't. A tight distribution clustered around the median is a low-variance strategy. A wide distribution with thin tails extending far in both directions is a high-variance one. A bimodal distribution - outcomes clustering around two separate values rather than one - is a warning sign that the strategy has some structural feature producing binary-ish outcomes, worth investigating before committing.

Sensitivity Analysis: The Part That Produces the Most Useful Information

Running the simulation once with your central estimates tells you the expected distribution under your best assumptions. Sensitivity analysis tells you how much the distribution changes when your assumptions are wrong.

Run the simulation three times for each uncertain parameter, using a low estimate, your central estimate, and a high estimate. For win rate, if your CLV tracker gives you a central estimate of fifty-three percent with meaningful uncertainty around it, run at fifty-one percent, fifty-three percent, and fifty-five percent. For edge, if your average CLV suggests an edge of around two percent but the sample is thin, run at one percent, two percent, and three percent.

The parameters that most change the output distribution when you vary them are the ones your strategy is most sensitive to. A simulation that looks viable at fifty-three percent win rate but produces ruin probabilities above twenty percent at fifty-one percent is a fragile strategy - one where a small overestimate of your edge produces materially different outcomes. A simulation that remains robust across the full sensitivity range is a more reliable strategy even if its central-estimate output looks less impressive.

This is where most betting strategy analysis stops short. The single-estimate simulation looks fine, the strategy gets implemented, and then actual win rates come in slightly below the estimate and the distribution of outcomes shifts dramatically in the wrong direction. The sensitivity analysis would have shown this. It takes twenty extra minutes to run. Do it.

Prompt the LLM to extend the original code:

"Modify the simulation to run a sensitivity analysis. Create three versions of the simulation using the following parameter sets: [paste your low, central, and high estimates for the two or three most uncertain parameters]. Run all three versions and display their output statistics side by side for comparison. Add a combined chart showing the median trajectory for each version."

The comparison output tells you whether your strategy is robust or fragile across reasonable uncertainty in your input estimates.

Modelling Operator Limit Constraints Specifically

This deserves its own section because it's the input most bettors get wrong, and getting it wrong produces a simulation that models a strategy you can't actually run.

If you're betting at soft operators with stake restrictions, your effective maximum bet size isn't a function of your bankroll - it's a function of what the operator will accept. A Kelly calculation that says bet twelve percent of a five-hundred-unit bankroll means sixty units. If your operator caps you at eight units on this market, the Kelly number is irrelevant. The simulation should model eight units, not sixty.

The compounding implication of this is significant and underappreciated. Kelly staking's edge over flat staking comes from increasing bet size as the bankroll grows. If operator limits cap your bet size at a fixed amount regardless of bankroll growth, you're effectively running flat staking with extra steps - and the simulation's output for Kelly staking dramatically overstates the actual growth trajectory your constrained strategy will produce.

Prompt the LLM to add this constraint:

"Add a maximum stake cap to the simulation. The cap should operate as follows: calculate the Kelly or percentage stake based on current bankroll using the normal formula, then apply the cap so the actual stake is the minimum of the calculated stake and the maximum cap value. Run the simulation with the cap active and compare output to the unconstrained version."

The comparison between constrained and unconstrained versions is illuminating. For strategies where the cap binds frequently, the constrained trajectory looks substantially flatter than the unconstrained one - which is the honest representation of what you're actually running.

When to Rerun the Simulation

The simulation isn't a one-time exercise. Rerun it when any of the inputs change materially.

When your CLV tracker produces a meaningfully updated edge estimate after a larger sample - every hundred additional bets or so in each market category. When your operator limit situation changes - a restriction at a primary operator, a new operator added to your portfolio, a limit reduction that changes your effective maximum stake. When you change your staking rule - moving from flat to fractional Kelly, adjusting the fraction, changing your tier thresholds. And when you're considering a scope expansion - adding a new competition or market type with different edge estimates from your existing coverage.

The other time to rerun it is when you're in a significant drawdown and considering changing your approach. The emotional impulse in a drawdown is to do something - change the strategy, increase stake size to recover faster, narrow scope to the most confident bets. Run the simulation before acting on any of those impulses. Show the simulation what you're considering changing to and look at its distribution relative to the current strategy. The emotional response to a drawdown is rarely pointing toward the better strategy. The simulation output usually isn't either - but at least it's not emotional.

Anyway. The tool won't tell you whether your edge is real. Nothing will tell you that except a large enough sample of bets over time. What it tells you is whether your edge, if it is real, is being deployed in a way that gives it room to express itself - or whether your stake sizing and variance tolerance are likely to end the experiment before the sample is large enough to mean anything.

That's a different and more practically useful question than most bankroll analysis addresses. And it's one that used to require a quant background to answer. It no longer does.

FAQ

Q: My CLV sample is too small for confident edge estimates. Is the simulation still useful?

Yes, but differently. With a thin sample, the value of the simulation shifts from "here's what my strategy will do" to "here's what my strategy would need my edge to be for the variance to be survivable." Run the simulation at several edge estimates across a plausible range and find the breakeven point - the edge level below which the ruin probability crosses your tolerance threshold. Then ask whether your current evidence is good enough to be confident you're above that breakeven. If the answer is uncertain, the simulation has told you the most useful thing it can: you need more evidence before committing to this strategy at this stake size.

Q: How many simulation runs should I use?

Ten thousand is the standard for stable output. A thousand runs produces results that vary noticeably between separate runs of the same script - the variance in the simulation output itself is too high to trust the statistics. At ten thousand runs the output stabilises and re-running the same parameters produces essentially identical statistics. The computation time difference between a thousand and ten thousand runs is trivial - a few seconds at most on any modern laptop. Default to ten thousand.

Q: Can I model multiple market types with different edge estimates in the same simulation?

Yes, and it's worth doing if your betting is meaningfully split across market types with genuinely different edge profiles. Prompt the LLM to extend the code: specify the proportion of bets in each market type, the win rate and average odds for each, and the simulation draws from the appropriate parameters depending on which market type each simulated bet is assigned to. The combined output reflects the actual mixed strategy you're running rather than an average that obscures the differences between categories. The additional prompt is about a paragraph of specification and produces code that handles the mixing automatically.