Summer of Math Exposition

Great video! The motivation is clear, the animation illustrates the points well, the color is helpful and not distracting, and you cover a lot of interesting topics in one video. You probably could have skipped over some of the cases where binary search was dominant, and I would have liked to see the first tree where it wasn’t, but these are pretty minor issues.

This was very enjoyable and very well made. I was surprised by the results and by many of the different topics that came out along the video and I wasn’t expecting, such as the simplex algorithm.

Vet clearly animated and narrated video with the perfect pacing, the result was surprising and the methods introduced gave me new ideas. Excellent video.

Interesting video! I really enjoyed the use of Guess Who as a framing device to make the discussion of search decision trees more concrete. The visuals in the video were helpful, although sometimes there was too much information on the screen to look at before the next visual appeared. The last minute of the video was my favorite part, you did a good job reviewing the key takeaways while still staying high level. Overall good video!

Audio could be improved. A little difficult to follow for high-school level, since the presentation goes too fast in the beginning.

So I do think this is a very interesting topic, and not enough people quite understand the distinction between optimizing an expected long-term outcome as opposed to taking long-term risks to create short-term opportunities, especially in the context of games where the long-term prospects don’t matter if you win or lose. (I just got back from playing Magic the Gathering, where that sort of decision is sort of a huge theme)

That said, I think there are a few things about your explanation which are a bit opaque. First off, I’m not sure if this example really captures the depth of this phenomenon, because all of the optimal strategies involve very slight deviation from the naive solution of maximizing the average value. I also think that the number of strategies present in the game, focusing on sprawling decision trees rather than an individual choice, hampers your ability to communicate clearly about the differences between strategies by the end: for instance, I know that strategy 1 is binary search, but I don’t actually know what strategy 3, 5, and 8 are, so I don’t get to check whether the result we end up with ends up making any intuitive sense. You also never substantiate the claim that binary search is always best for the average result, you run through exactly what it is we’re minimizing a little quickly, and I think that results in the claim of a Nash equilibrium feeling a little shaky.

That said, I think the setup that you have in this demonstration is interesting, I haven’t seen someone do this exact sort of calculation for this exact sort of game, and thank you for sharing.

Simple yet original topic

Loved the content. But the visuals are hard to see and the audio isn’t that good.