Does Every Game have a Winner?
Why can a computer always win in tic-tac-toe? Is it true for games in general?
Introductory
Posts that do not assume prior knowledge of mathematics beyond some basic concepts and notations (e.g. derivatives, summation notation)
A Devious Bet 2: Law of Large Numbers
You meet up with a slightly familiar mustached squid “man” He may or may not have bankrupted you infinitely times over in the past, but you’re over it. In fact he has a new deal for you! Every day he will modify your bank balance in one of two ways. With probability 0.6, your balance … Read more
5 Holiday Math Puzzles
Happy Holidays! Here are a couple Christmas and Hanukkah puzzles just for you: The 2n-Menorah: In an alternate universe, instead of the flask in the temple lasting for just 8 days, it lasted for 2n days for a positive integer n. Thus, Hanukkah in that universe is celebrated for 2n days, and the menorah has … Read more
The Harmonic Series and Friends
A lot of times, math can be deceptive and unexpected A few examples are the Monty Hall problem, the Banach-Tarski paradox, and the Weierstrass function. Today we will look at one of the most famous and classic counterexamples, that is that if a sequence converges to zero, it’s series does not necessarily converge. What does … Read more
A Tale of Drunk Worms and Random Walks
Meet Larry the worm. Larry had a wonderful night drinking at a bar with his friends. Alas, Larry got a bit too drunk, so when he and his friends finished drinking, he went to walk (err, crawl) home, drunk. Larry and his friends live on a one dimensional road. As Larry is drunk, he walks … Read more
Necklaces and Groups. The Burnside Lemma
Here is a fun riddle: suppose you have beads in n different colors, and you want to make a necklace with say, 5 beads. How many different ways are there to do this? Well, you can first look at the possible colors for the beads: Each position can have n different colors, and there are … Read more
Stable pairings and how to find them (Gale-Shapley algorithm and also puppies)
From dating apps to matchmaking in video games, and matching computers to the best servers, matching problems have a notable presence in computer science and game theory nowadays. So let’s look at one of this problems, which has a rather simple premise and a surprisingly simple solution. The problem deals with finding stable pairing (say, … Read more
Why “almost surely” a math blog?
So why is this only “almost surely” a math blog? For technical reasons, it’s because maybe in the future some posts will not be about math but related subjects (or unrelated, perhaps in 2026 this blog will be about pistachios, who knows honestly). But the major reason I chose this title is as a reference … Read more
Newton’s Method
Let’s look at a very common problem where the use of math is needed, solving equations. We have an expression using some variable x on one side of the ‘=’ sign and another expression using x on the other. We want to find for which values of x the equation holds.
How do we choose things? (at random)
Don’t you just hate it when you are asked to pick something “at random”? No? Well let me show you what I mean.