Times Square Chance Encounter Probability Calculator
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Estimate the chance you meet someone you know in Times Square by simulating how many acquaintances could be nearby, timing overlap, and recognition odds.
NOTEHow to tune this model
Key knobs to personalize:
- acquaintances_total: how many people you’d recognize who could plausibly be in NYC.
- p_known_in_area: chance any one of them is in Times Square during your exact time window.
- visibility_radius_m and p_notice_given_close: how easy it is to spot each other.
Assumptions: independence and a simplified encounter process; ignores repeat visits, coordinated plans, and friend-group clustering.
VARIABLEAcquaintances who could plausibly be in NYC count
triangular(30, 120, 300)
How many people you might recognize who could plausibly be in NYC during your broader visit period.
acquaintances_total
VARIABLEChance any one acquaintance is in Times Square in your window
beta(1.5, 60)
Per-person probability of being in Times Square during your specific time window; increase for holidays/events, decrease for random hours.
p_known_in_area
VARIABLEVisibility radius to recognize someone meters
triangular(5, 15, 30)
How far you can reliably recognize someone in a dense crowd.
visibility_radius_m
VARIABLENotice each other given you are within range
beta(8, 2)
Accounts for distractions and missed recognition even when close.
p_notice_given_close
CONSTANTEffective Times Square area considered square meters
20000
Order-of-magnitude effective area for the encounter region; adjust if you mean a larger/smaller zone.
area_times_square_m2
FORMULAVisibility area square meters
3.141592653589793 * visibility_radius_m^2
Area of a circle with the visibility radius.
visibility_radius_m
visibility_area_m2
FORMULAProbability a random person is within range
1 - exp(-visibility_area_m2 / area_times_square_m2)
Smoothly bounded approximation that rises with visibility area.
visibility_area_m2
area_times_square_m2
p_within_range
FORMULAPer acquaintance encounter probability
p_within_range * p_notice_given_close
Chance you get close enough and successfully recognize each other.
p_within_range
p_notice_given_close
p_encounter_per_known
FORMULAExpected acquaintances present
acquaintances_total * p_known_in_area
Expected number of acquaintances in the area during your time window.
acquaintances_total
p_known_in_area
expected_known_present
FORMULAProbability meet at least one acquaintance
1 - exp(-expected_known_present * p_encounter_per_known)
Poisson thinning approximation for meeting one or more acquaintances.
expected_known_present
p_encounter_per_known
meet_probability
OUTPUTMeet probability
Meet probability 0 to 1
Main result: probability you run into at least one person you know.
OUTPUTExpected known present
Expected acquaintances present
Intermediate result: expected number of acquaintances in the area during your window.
OUTPUTPer known encounter probability
Per acquaintance encounter probability
Intermediate result: chance of meeting a specific acquaintance if they are there.
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.