Times Square Meeting Likelihood Probability Model
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Estimate the chance of meeting someone you know in Times Square by simulating how many acquaintances might visit, your visit duration, and encounter rates.
NOTEHow to use
Tune inputs to fit your situation:
- If you know lots of NYC locals or tourists, increase `acquaintances_potential` lambda.
- If you go at a peak time, raise `encounter_rate_per_hour`.
- If you are only passing through, lower `duration_hours`.
The result is a simplified estimate using a Poisson approximation (best when each individual encounter chance is small).
NOTELimitations
Does not model coordinated meetups (texts/calls), meeting at a specific landmark, or correlated friend behavior; treat it as a rough estimate.
VARIABLEPotential acquaintances who might visit
poisson(3)
How many people you know could plausibly be in NYC and consider Times Square around the same time.
acquaintances_potential
VARIABLEChance an acquaintance visits during your window
beta(2, 18)
Uncertainty in how likely a given acquaintance is to be in Times Square during your visit window.
p_visit
VARIABLEYour time in Times Square hours
uniform(0.5, 3)
Longer stays create more opportunity for an encounter.
duration_hours
VARIABLEEncounter rate per hour if both are there
triangular(0.05, 0.15, 0.4)
Effective crossing paths rate given crowd flow, visibility, and movement.
encounter_rate_per_hour
FORMULAMeet chance if a specific acquaintance is present
1 - exp(-encounter_rate_per_hour * duration_hours)
Probability you run into a particular acquaintance assuming they are present during your visit.
encounter_rate_per_hour
duration_hours
meet_given_present
FORMULAExpected number of acquaintance encounters
acquaintances_potential * p_visit * meet_given_present
Average number of meet opportunities across all potential acquaintances during your visit.
acquaintances_potential
p_visit
meet_given_present
expected_meets
FORMULAChance of meeting at least one acquaintance
1 - exp(-expected_meets)
Poisson approximation for probability of at least one encounter.
expected_meets
prob_meet_someone
FORMULAChance of meeting at least one acquaintance percent
100 * prob_meet_someone
Same result expressed as a percentage.
prob_meet_someone
prob_meet_someone_pct
OUTPUTLikelihood of meeting someone you know
Chance percent
Simulated probability (percent) of meeting at least one acquaintance during your visit.
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.