Summer of Math Exposition

Motivation Calculating all the possible options at the beginning was really effective!

Clarity Yes - excellent

Novelty Well animated and a variety, yet clear animation.

Memorability Yes. It helps I enjoy games. Great video!

That was nice! You had quite a few long stretches where the scoreboard is on-screen and nothing happens besides you talking. Would have preferred to see you on screen more in these cases.

The presentation quality is excellent. I’m not terribly interest in Yahtzee, however, so the long stretches of dice rolling talk was hard for me to engage with. However, the cut to the whiteboard where you struggled to read the large number was a great addition to increase engagement.

This video was informational, well-organized, and had visuals that properly complemented the topic at hand. For this reason, I think it is a great video. However, the steps were at times monotonous and repetitive. But this is not unexpected from a longer video, so I view it as a symptom of its length rather than as an inherent flaw of the presentation style.

I wish you could have explained a bit more the programmatic side of the reduction of cases and the DP, but that’s a bit out of the mathsy scope of the whole thing

Great usage of visualisation for explaining different strategies, my favourite takeaway being the frequency graph with many peaks, it was also nice to see that graph return at the end. Content organisation was impressive.

One example of game play for people who don’t know about the game would have been nice, and the video’s fast pacing did make it difficult to follow at some times

Great deep dive! Definitely learned some things I’ll now apply when playing.

I saw this video before I knew it was a SoME entry. I thought it was a delight then, and a quick review reminds me that I was right. I do not have any criticism, but I will spend a moment recounting what I liked most about it.

My main praise is that this is a fantastically complete analysis. It would already have been a good video had it cut off around 10:00— a gentle introduction, nice description of the combinatorics, broad strategic principles and tricks for reducing to a laptop-computable space of positions. But then you not only go on to give a thorough endgame analysis, a fantastic middle-height view of the strategic principles of the middle game, and simple advice for the opening. All of this at a patient pace with appropriate levels of detail and a good dose of enthusiasm. It would already have been a great video if it cut off around 27:00, but you then go on to rattle off an extremely succinct description of the difficulties involved in multiplayer analysis, show how to use the heuristic scoring to estimate positionality, and benchmarks for winning, all in a breezy five minutes (and still have enough time for the meme-worthy quntillion-player distribution).

Stylistically, I thought the animations were quite nice, and they were deployed well. The figure at 21:20 may have genuinely been the most interesting plot I have seen all year. And the interspersed segments of you on the couch added a great texture— you come off as easygoing and a little mischievous; plus there’s something to those shots (maybe the spacing between you and the camera, and the table?) that made me feel present in the room.

I think this vide does a pretty nice job, indeed the rules of the games are pretty complicated and withitu him guiding htorugh the ones that actually matter it would have been real difficult to grasp.

Visuals are good, your narration is fine. And while personally I love probability, I’ve never played Yahtzee so it was hard to sustain my interest.

Love the thorough analysis. Well narrated too.

too specific. took me to much efford to undestand the rools. I have a filing that afterwrds the explantion will be OK, but I did not get there, and so are will the vast majority of the viwers. It seems that you have high explanating abilities, but you need to chose a different topic. Good luck!

Perfect balance of explaining without going too deep (and thus, boring)

Really nice narrative and production.

Thanks for the video, it was a fun watch, I didn’t realize that the average and median score was so high. The video felt fairly narrow, which is fine, but that prevents me from scoring higher.

I like the transition from the animations to you sitting on a sofa with a board showing the same number. A nice way to transition!

Good to see the math behind a game I played growing up!

The colours are quite clashy, maybe this is your style but aesthetics could benefit from a bit more focus. There’s lots of good detail, but this also means it’s useful to spend some time recapping or revisiting the big picture - I think presenting the overall argument more often would’ve helped me understand better

Good. I don’t know where he came up with the 4, 3, 2 1 bonus point system (I watched that part a couple of times). I get that Yahtzee is more valuable than a straight but who assigned the bonus point designation and why was the 4, 3, 2, 1 point system devised? Over all good and something to keep in mind when I play Yahtzee next. I especially liked the set up at the end saying that if you played against all employees of Yahtzee someone would get Yahtzees, then if you played against 80 people you would probably need 3 Yahtzees, if against 5000 people you would need 4 yahtzees to win, etc…

The creator says it himself: the goal is not so much to explain the mathematics as to show how mathematics can be used to solve a problem that people might care about. I think the application to Yahtzee is interesting, and using dynamic programming to find an optimal strategy is a good example of mathematics being used to solve a concrete and relatable problem.

However, for an online math exposition competition, I would expect a minimum level of mathematical explanation. The video does a good job explaining how dynamic programming is actually used to solve the Yahtzee problem, but it seems to assume that the viewer already knows what dynamic programming is. For someone encountering the concept for the first time, a brief introduction to the basic idea - what dynamic programming is, why it works, and how the idea of breaking a problem into smaller subproblems applies here - would make the exposition much more accessible.

I particularly liked seeing the resulting optimal strategy analyzed in different phases of the game, as well as the adjustments needed for multiplayer games. These sections show very well what mathematics can reveal about a game that people already care about.

Overall, this is a good example of a mathematical method being applied to an engaging problem. The main thing I would improve is the accessibility of the mathematical concept itself. Adding a short, intuitive introduction to dynamic programming would make the video much stronger for viewers who are not already familiar with the technique, while still keeping the focus on the application.

I would encourage a faster rythm, with less cumbersome details about the rules and the details and more about the high level ideas.

I love that you distinguished expectation guarantees and high probability guarantees! Though it could use a bit more emphasis, the natural instinct of “play aggressive when you’re behind, conservative when you’re ahead” contradicting merely trying to get a high average score was great. That could even be tied with algorithmic guarantees, where “the fastest algorithm” does not always mean the same thing: does one want it fast in expectation? Over adversarial instances? etc etc. More analogies to chess (too many states to count, the variability of opponent skill levels maybe) would also be interesting, since it is maybe a more straightforward game of skill than yahtzee. The pacing was good, the animations natural, and the enthusiasm of the narration was communicative. However, this video was quite long. I understand that the point of the video was to give a general strategy for Yahtzee, but that does mean that some parts are not too interesting for someone who does not care much about the game; for example, the point strategies at the last turn for each box was a bit much, and distracted from the many interesting tools that were brought up.

With some quite simple maths and pretty good explanations, I think you’ve managed to really capture the imagination of a few people, which is what a math exposition should be about. I think it’s cool to see the algorithm in action to explore the decision making process and how probabilities can be used to make the optimal decision, and how the analysis can extend to cool outcomes near the end. One of the things I wanted to see more was how the weights were calculated for the particular bonuses. I think it’d be good to see some more derivation or rationale on how that came about.