FUN: TOILET SEAT

How much work do you spend by moving the toilet seat up and down? Does it change based on the ratio of men to women? Does it change based on the fraction of times you perform business 1 or 2? How much more work is it if you always left the toilet seat down as opposed to being lazy and just leaving it in the position you finished your business in? Click to find out!

FUN: SECRETARY PROBLEM OR DATING PROBLEM

Let's say that you need to interview a series of candidates and at the end of each interview you need to decide if you wanted to hire or pass on the candidate. How should you strategize to maximize the probability of finding the best candidate? Such problems occurs all the time in real life situations. While not every aspect of the real-world can be reduced to simulations, maybe you can gain some intuition by realizing how to trade-off between waiting to find the best person and being decisive and hiring the person in front of you.

PUZZLE: MONTY HALL PROBLEM

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

PUZZLE: COIN TOSS PATTERNS

How many coin tosses do you need to perform on an average to get a single head? Seems straight-forward and the answer is indeed 2 as intuition would suggest. How about the number of coin tosses until we see hh (two consecutive heads)? Is that the same as the average number of tosses before we see ht (heads followed by tails)? What about hth (heads-tails-heads) versus hhh (heads-heads-heads) versus htt (heads-tails-tails)? Are they all equally likely? Find out in this simulation to see if your intuition is guiding you or misleading you!

BIOLOGY: HARDY-WEINBERG EQUILIBRIUM

Would a dominant genetic trait automatically increase in frequency? Would the rare variant get wiped out quickly? Do we expect the dominant trait to systematically increase in frequency generation after generation until it wipes out the rare variant?

ENTERPRISE: FLIGHT BOARDING

How long does it take to board a flight in random order? How does boarding by zones help speed up? How bad can things be in worst case and how does this compare with other cases? What happens if you board from window to aisle instead?

SOCIAL: GENTRIFICATION OF NEIGHBORHOODS (COMING SOON)

What happens if each individual decides to move if less than a certain fraction of their neighbors are 'like' them? How does this affect the overall neighborhood distribution? How long does it take for patterns of gentrification to emerge with such schemes?

SOCIAL: BRAESS'S PARADOX (COMING SOON)

Does building roads always help with traffic congestion? Could it in fact hurt to add a road? Could it actually help to remove an existing road? Seems counter-intuitive that this would be true right?

ENTERPRISE: RENTAL SCOOTER PLACEMENT (COMING SOON)

Where should you place your rental scooters in San Francisco? Based on your policy of collecting and replacing scooters into different locations, how much revenue do you lose? How do patterns change during the course of the day and during the week?