Times Square Familiar Face Meeting Likelihood Model
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Estimate the chance you meet someone you know in Times Square by simulating how many acquaintances are in NYC, their visit odds, and whether you notice them.
NOTEHow to use
Edit (1) how many acquaintances could plausibly be nearby that day, (2) the chance they visit Times Square during your time window, and (3) how likely you are to notice them. The output is the simulated chance of at least one run-in.
NOTEWhat this model ignores
It assumes acquaintances act independently and uses a Poisson approximation. It does not model coordinated plans, group travel, or time-of-day crowd effects (you can fold those into the input probabilities).
VARIABLEAcquaintances who could be in Midtown today
poisson(40)
Rough count of people you know who are in NYC and plausibly around Midtown on the same day as your visit.
acquaintances_nearby
VARIABLEChance a given acquaintance is in Times Square during your visit
beta(2, 98)
Probability (0-1) that one acquaintance ends up in Times Square within your visit window (e.g., about an hour). Mean here is ~2% but can be edited.
p_at_times_square
VARIABLEChance you notice and recognize them if they are there
beta(6, 4)
Accounts for crowd density, visibility, distraction, and whether you both look up. Mean here is ~60% but can be edited.
p_notice
FORMULAPer acquaintance encounter chance
p_at_times_square * p_notice
A given acquaintance both overlaps your visit window and you notice them.
p_at_times_square
p_notice
p_encounter_per_acq
FORMULAExpected number of encounters
acquaintances_nearby * p_encounter_per_acq
How many familiar-face encounters you would expect on average for the visit.
acquaintances_nearby
p_encounter_per_acq
expected_encounters
FORMULAProbability of at least one encounter
1 - exp(-expected_encounters)
Poisson approximation for the chance of meeting at least one person you know during the visit.
expected_encounters
meet_probability
OUTPUTMeeting probability
Chance you meet someone you know
Probability (0-1) of running into at least one acquaintance during your Times Square visit window.
OUTPUTExpected encounters
Expected number of familiar-face encounters
Average number of acquaintances you would meet (can be >1 even if meeting probability is <1).
What is Carlo?
Carlo is a visual tool for Monte Carlo simulation. Model uncertainty by dragging probability distributions, connecting them visually, and running thousands of scenarios instantly.