Change the wording, keep your experiment. Saved in this browser when storage is available.
A Monte Carlo decision lab Interactive simulation
Which route wins
in your world?
Which route would you choose before knowing the weather? Monte Carlo means trying many randomly chosen possibilities and comparing the results. A rough estimate can help you choose. Telling two very close options apart takes more samples. Here, every route faces the same weather in each trial.Deliver more on average, or bring something home reliably? Monte Carlo planning uses repeated random sampling to compare possible outcomes before choosing. Each trial draws one weather pair and tests all three routes against it.
You design the rules.
The simulation tests the possibilities.
Choose a route and commit. The trip’s hidden weather is drawn separately from the simulations.
Your last ten voyages
Exploration under these rules, not a controlled comparison. Changing the world clears this log.
- No voyages yet.
Make it your world
Try a different question
These controls change a real local simulation. AI helped build this lesson; no model runs here.
Try possible futures before choosing
Compare the routes
Run a batch to compare the average cargo delivered by each route.
Dock
?points / trip
Waiting for your experiment.Channel
?points / trip
Waiting for your experiment.Outer passage
?points / trip
Waiting for your experiment.Each trial uses one randomly drawn weather pair for all routes. Count × cargo shows how many trials returned each amount. Each average is total cargo divided by the number of trials. Dock’s return is exact; Channel and Outer use sampled averages. The separate exact-answer panel calculates probabilities from your rules.
A sampled leader is a clue. Check uncertainty before treating it as a clear winner.
How uncertain is the estimate?
Run a batch first. Dock is deterministic; its score is known exactly.
More trials usually narrow the range of plausible averages. The estimate itself can still move away from the exact answer on a particular run. These cautious ranges allow for checking three routes at four fixed sample counts. They rely on bounded scores and independent weather draws, approximated here by a repeatable random-number generator. They describe sampling noise, not whether your forecast is right. Editing or restarting begins a separate experiment.More samples generally reduce sampling uncertainty, but an individual estimate can move farther from the exact answer at a later checkpoint. These conservative bands describe sampling error under your chosen model. They do not test whether the model is right. The calculation uses bounded returns and a correction for three routes at four fixed sample counts. It assumes independent draws within a route; seeded pseudorandom draws approximate that assumption. Repeated edits and restarts are separate experiments.
Plan for reliable cargo and a changing forecast
These exact calculations explain your small world. They use the forecast, not the weather secretly drawn for an actual trip. On narrow screens, scroll the tables sideways. With a keyboard, focus a table and use the arrow keys.
Open this section to compare goals and stress-test the forecast.
What must arrive?
| Route | Target met | Zero cargo |
|---|
If the forecast shifts
Try ten percentage points less or more calm weather. These are scenarios, not confidence limits on a forecast.
| Calm | Dock | Channel | Outer | Best |
|---|
How your estimate changed
Each row adds trials to the same repeatable run. Compare the sampled average with the exact average for these rules. Their gap is the error. More samples help overall, but this gap does not have to shrink at every row.Each row extends the same seeded sequence. The error is distance from the exact average for this model; it need not shrink at every checkpoint.
| Samples / route | Dock | Channel | Outer |
|---|
Inspect a particular possibility
Follow one of the futures.
The first 16 sampled weather pairs stay available. Every completed sample contributes to the averages.
Run a batch, then inspect a future.
A precise answer to the wrong question
What if the forecast is wrong?
Keep the sampler’s calm chance at 75%, but change the actual toy world to 50%. More samples cannot repair the old assumption.
The simulator and actual trips currently use the same weather model.
Small enough to solve completely
The four weather patterns
There are only four possible weather pairs here. Multiply each pair’s cargo by how often that pair is expected, then add. Because the two legs are independent, their chances multiply. This gives the exact long-run average for your rules. In larger problems, listing every possibility may be impractical, which is where sampling helps.Weight each pattern’s cargo by its probability, then add. The two legs are independent. This gives the exact expected score under your rules, without sampling.
| First / second leg | Probability | Dock | Channel | Outer |
|---|
At 75% calm, both legs are calm in 9 of 16 equally likely four-face weather pairs. Outer averages 14 × 9 / 16 = 7.875 cargo points.
Try the idea somewhere else
A delivery robot has three choices.
Park for 5 points. Pass one gate for 9. Pass two for 14. Each independent gate opens 60% of the time. Which choice has the highest average score?
Make a prediction. You can change your answer.