For #thisweeksfiddler by @xaqwg.bsky.social , we find the probability that you win a best-of-N series, given that you win vs. lose the very first game.

For #thisweeksfiddler, we race among randomly selected loops of length 1, 3, 3.5, 4.5 miles at a 10 min/mi pace. If unfinished loops don't count and we have 65 min left to race, how can we maximize the avg total distance completed?

For #thisweeksfiddler by @xaqwg.bsky.social , we start with a set of vouchers ($10, $10, $10, $25), and can bet any of them on either side of an even odds game.

For #thisweeksfiddler, we're blocking our friend from placing their square on a board of side length B using 3 of our own.

#thisweeksfiddler @xaqwg.bsky.social Other bikers will sprint if their strength >0.5, while we sprint if our leg strength >t. What is our chance of winning?

For #thisweeksfiddler, what's the maximum score we can reach in bowling if we knock down a given number of pins? @xaqwg.bsky.social

For @xaqwg.bsky.social 's #thisweeksfiddler, we're in a race where we increase our speed continuously to the end. (1+b)v(2x) = v(x), where x is the distance remaining in the race and b is the factor we increase our speed.

My attempts for #thisweeksfiddler by @xaqwg.bsky.social : how often can each point in a square be covered by a randomly placed, long line? Simulated (Left) and analytical.

My findings for #thisweeksfiddler by @xaqwg.bsky.social : How long is a river of spaces in a text? thefiddler.substack.com/p/how-long-i...

For #thisweeksfiddler by @xaqwg.bsky.social thefiddler.substack.com/p/can-you-pe..., my approach: We consider separately the number of ways to descend to a point in the next layer and the ways to travel between two points in a given layer.

For #thisweeksfiddler by @xaqwg.bsky.social , we evaluate win probabilities for a best of 7 series. My graphical approach:

My findings for #thisweeksfiddler: thefiddler.substack.com/p/how-many-r...

My findings for #Thisweeksfiddler, looking through the coprime forest. thefiddler.substack.com/p/can-you-se... @xaqwg.bsky.social

For #ThisWeeksFiddler: Another graph! @xaqwg.bsky.social

For #thisweeksfiddler by @xaqwg.bsky.social , how often will a 1-seed win a single elimination tournament, if in any matchup between teams with seeds M and N, the M-seed wins with probability N/(M+N)?

My findings for #Thisweeksfiddler by @xaqwg.bsky.social , where we try to escape pie, only to find pi. colab.research.google.com/drive/1ZTfQc...

For #thisweeksfiddler by @xaqwg.bsky.social : Setting up a chain of dominoes, using the geometric distribution:

For #ThisWeeksFiddler, picking rabbits out of a hat. A near linear trend.