Educational information, not individual financial advice.
Key Takeaways
Most real financial questions are comparisons: "What if I retire two years later?" "What if I convert $50k a year to Roth?" "What if the market underperforms?" The best way to answer them is to run two scenarios and look at the difference — in median net worth, success probability, and the percentile bands.
A Monte Carlo result isn't one number — it's a distribution drawn from thousands of randomized futures. So when you compare two Monte Carlo scenarios, you're differencing two independent sets of random draws, and the reported gap carries the sampling noise of both runs.
With, say, 200 trials each, a genuine "+$50k median" improvement can be swamped by ±$40k of pure simulation noise. Run the comparison again and the sign of the difference can even flip for a small change. That's not your decision moving the number — it's the dice.
The cure is common random numbers (CRN): run both scenarios on the same underlying random draws. The shared luck cancels out, so the difference you see reflects the plan change itself, not the randomness. Combined with a related trick (antithetic variates), CRN can make 200 trials behave like 400+ for comparison purposes.
This is what turns scenario comparison from two fuzzy fan charts into a trustworthy decision tool. Under CRN, "converting $50k/yr to Roth adds +$182k median terminal wealth, and +$60k even at the 5th percentile" is a near-noise-free answer you can act on.
A change that improves the median but worsens the downside deserves a second look.
Horizons saves each simulation run and compares them side by side, surfacing the deltas in net worth, success probability, and percentiles so you can isolate the impact of a single decision.
You compare two Monte Carlo scenarios and a small change shows a +$30k median gain on one run but −$10k on a re-run. What's most likely going on?
Try it in your scenario
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Monte Carlo Simulation Explained
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