The Game That Everyone Knows The Winning Strategy To (But Can't Win Without A Calculator)
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Tags: fibonaccigame-theorycombinatorial-game-theorynimfloor-functionlinear-equation
Wythoff’s Nim is a famous game that is (shockingly) under-explained here on YouTube. There are a few videos, but they all stop after the same point: “Here are the losing positions; good luck!”
This video attempts to go one step further and explain a winning strategy you can perform in your head. It goes through three different, seemingly unrelated, mathematical ideas that are each interesting in their own right, but then weaves them together one by one into a method for determining the best move at any given step. By the end you’ll want to go try out this game with one of your own friends!
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It had a lot to cover and was very ambitious. Keeping the winning strategy until the end as the dessert was a great strategy to keep viewers staying on but learning about the Beatty sequences in particular felt like eating vegetables. Of course we need that part both for the payoff and the lesson but I’d watch Mark Rober’s video about “hiding the vegetables” and try to incorporate that.
I won’t feign understanding of everything, but I can review what I do understand. This is a ~60 minute that goes very into depth on how to absolutely demolish others at the game “Wythoff’s Nim” by having a winning strategy. In comparison to the other videos I’ve already watched, this video does its topic justice. You’ve added a lot of examples, explained everything that needs to be explained. ~60 minutes is a lot, of course. But you make it clear that it’s a duration needed for proper explanation.
Motivation: If I want to dominate any Whythoff’s Nim game, I’m sure to watch this video a few times. It’ll allow me to win more often than not. It could be cool party trick.
Clarity: If you include hand-writing, please make sure it’s legible. I’m all for not all text being generated with computer fonts, but hand-writing always has the drawback that you have to write it as clear and close to the standard as possible, so that viewers don’t have to decipher it. I know that’s not easy, but I find it the absolute minimum to be able to read a text in a video (if it was meant to be read). Other than that, this is a very well done video! Really. Of course, with a professional film team and computer generated visuals, this video could be even better. But for the tools and technology you’ve had at your disposal, this is better than most. It’s clear how much time you yourself have spent understanding the topic and that you’ve put in a lot of effort in how to explain it to viewers who are unfamiliar with it.
Novelty: You’ve not just explained something that’s already been explain before, but you’ve gone a few steps further, to really ensure that the viewer understands what you’re trying to convey.
Memorability: The small skits are fun and memorable. You’ve done some of the explanations in real life with actual requisites and I find this important to showcase that it’s applicable to real life and not just an abstract concept.
Some more thoughts and considerations:
- You’re using a lot of red-green color coded visuals. People with red-green color vision deficiencies will have a difficult time following these visuals if there isn’t any other indicator for their difference. If I watch the video with a red-green CVD simulation, for example, some of the reds and greens look basically identical. Always implement redundancy when it comes to color coded visuals, or use colors that are distinguishable even for people with CVDs.
- Since you’ve already addressed the audio issues, I won’t give my opinion in this regard.
A bit long, of course, but overall I enjoyed watching this video and learning about something new.
good explanation, but a bit long.
Very nice contribution. I didn’t make it all the way to the end, but I’ll definitely return.
First off, congratulations on submitting the video on time! You were able to complete a very long explanation on a topic. The length itself shows how much work you must have put into the video. However, my main gripe with the submission is also that: it’s too long.
I watched the whole thing. If I were to summarize your video, it would be something like “I’ll teach you how to win at Nim. From the min-max recursive decision tree, the losing positions land on Fibonacci Beatty sequences.” I feel like it shouldn’t take one hour to get to that punchline.
Specific example at 3:50. You said
“The states I had an advantage are the red ones, 0 and 5, the states where I didn’t are the green ones. What does it mean that I had an advantage? Let’s dig into it. We say we’re in a winning position, I have an advantage. Whatever the opponent does, I can win. A losing position, conversely, is no matter what I do, if the person knows what they’re doing… ”, then talked about tying position, then “in the game we just played, the winning positions are 0 and 5, the losing are everything else.”
I feel like that you could’ve just said “I’m in a winning position if I can win even when my opponent plays perfectly. A losing position is the opposite. 0 and 5 are my winning positions, for example.”
That’s it. There aren’t ties in this game anyway. Inefficient phrasing is how a video blows up to 1 hour. I know you were just trying to be thorough with your explanation but I would have liked to learn the lesson more quickly. So again, great job on submitting on time. It would’ve been more enjoyable if you brought the wording in.
P.S. the ‘wtf’ at 38:33 caught me off guard xD
When you lay out the contents of the video at around 01:45 and I see the runtime of 1 hour, I immediately lost l interest in continuing.
I did continue, obviously, and the explanations were really good! (Even if you should have used coloured stones/marbles.) But overall, it was too technical.
Moreover, I really loved the little skits of you and your partner. Would have loved to see a version of this video that is boiled down to, like, 10 or 15 minutes and played out as a single dialogue between you two. (With some overlays for the technical stuff.)
I have to admit, when I saw the runtime, I almost didn’t watch it. I decided to give it a cautious try anyway, and I didn’t regret it. The subject matter is quite niche (personally, I wasn’t familiar with the game), but it turns out to be far richer than one might initially expect. I really liked how the arguments were presented—both rigorously and clearly (though I confess I lost the thread a bit right at the end with the “improved” strategy; I’ll watch that part again another day). I also really appreciate the “family-friendly” atmosphere; it’s very charming. The same goes for the minimalist production style, which in no way detracts from the clarity or rigor of the presentation. I sincerely hope this video gets a great reception—it is thoroughly deserved!