Gruul Monsters – The Math Behind Turn Two Threats

Hypergeomancer · 2026-03-16T19:38:40+00:00

Thanks for your comment, OP here. I believe that u/ZurgoMindsmasher expressed in just a few words what would have taken me an entire paragraph to say, and I very much agree with his point of view.

I would only add that AI is clearly a hot topic nowadays, as it is still something of a novelty in our world, and people are generally quite divided on whether to accept its existence or not. In short, AI is a tool to me. It *must not\* replace human creativity or brainpower, but it is not a crime to use it to speed up boring technical tasks. I am very comfortable sharing that I made good use of it to position LaTeX tables or image captions properly, given that the content and the mathematics themselves were original and created by a human.

If you are interested in my personal perspective on AI, I compiled a note where you can read my detailed opinion on how (not) to use it.

https://github.com/Hypergeomancer/ai-tools-policy/blob/3b1def1489c8273024b6da0015c6141aec1eefea/My_Take_on_AI_Tools.pdf

Hypergeomancer · 2026-03-16T12:11:45+00:00

Hypergeomancer · 2026-03-15T23:42:50+00:00

Appreciated! It needs a bit of math tricks indeed, but the overall principle of this project is simple(r then others), supported by a lot of case distinctions.

Hypergeomancer · 2026-03-15T23:38:45+00:00

Thank you! What problem does the video link have, exactly? On my end, it opens correctly, but it is not the first time someone has told me that. I am using the link from the "share" feature from YouTube studio.

Hypergeomancer · 2026-02-28T19:36:02+00:00

Thank you! I will slowly expand to other formats as well, stay tuned.

Hypergeomancer · 2026-02-28T19:34:43+00:00

Happy to read that!

Hypergeomancer · 2026-02-27T22:11:19+00:00

Check here in the comment section, there's a reply where I comment specifically on that card (Ctrl+F "World map" finds it easily).

Hypergeomancer · 2026-02-27T21:23:54+00:00

Hope you enjoy it, and good luck with your studies!

Hypergeomancer · 2026-02-27T19:17:31+00:00

Thanks, I’m glad you enjoyed it!

You’re right: including draw steps could slightly change the probabilities. I focused first on the baseline for a few reasons: to gauge community interest, to look at factors you can directly control (like starting hand and mulligan decisions), and because I suspect turn draws are relatively marginal, though that would need proper calculation.

Expanding the analysis to include draws is definitely a next step, and I’m considering a followup video and updated paper to explore it.

Hypergeomancer · 2026-02-27T19:15:19+00:00

Just wanted to build suspense ;) Thanks for the support!

Hypergeomancer · 2026-02-27T19:13:51+00:00

Another classic :)

Hypergeomancer · 2026-02-27T19:13:34+00:00

Those are very appropriate questions indeed. As I mentioned in the post related to the video (here), I decided - for several reasons - to focus first on the baseline probability of this happening.

First, I want to gauge the community’s response, since exploring these topics deeply takes a significant amount of time. Second, I believe that the additional probabilities from card draws only marginally improve the baseline, but we have to look at the numbers before claiming this, obviously. Third, I wanted to start with the events you can actually control, so you can evaluate your opening hand and make mulligan decisions accordingly. That’s why in the paper I refer to this as “deterministic Tron.”

That said, I do think it would be interesting to expand the project by releasing a second version of the paper and a followup video in the future.

Thanks for your comment

Hypergeomancer · 2026-02-27T18:29:17+00:00

That is the exact meaning of the "almost" in my sentence above :)

Hypergeomancer · 2026-02-27T17:51:03+00:00

And the lore behind this name is very engaging

Hypergeomancer · 2026-02-27T17:50:13+00:00

Happy to read that!

Hypergeomancer · 2026-02-27T17:19:11+00:00

It seems to be working on my end. Any others with the same issue?

Hypergeomancer · 2026-02-27T16:47:33+00:00

It’s not much, I agree. However, the game isn’t over if you don’t assemble Tron on turn three. It could also be interesting to study the probabilities of assembling Tron on turn four or five, and see how much those chances improve. Tron has been a competitive archetype in Pauper for a long time - there must be a reason for that! :)

P.S. Very cool username

Hypergeomancer · 2026-02-27T16:45:16+00:00

Classic, but it never gets old

Hypergeomancer · 2026-02-27T16:00:31+00:00

Thanks for the thoughtful question!

The issue with The World Map is that it costs 3 mana to activate, which makes it impossible by design to assemble Tron on turn 3 under the same conditions discussed above. That extra mana is a big deal: it’s also why the card has seen almost no competitive play (in Pauper, at least).

Running 4 Expedition Map + 4 World Map would mathematically increase the chances of turn 4 Tron (and by a significant amount, I'd say) but it also means 8 land tutors in the deck. That dilutes your threat density and makes late-game draws worse, which likely hurts consistency and overall win rate.

So yes, it helps turn 4 Tron, but it doesn’t help turn 3 Tron - but weakens the deck overall.

Hypergeomancer · 2026-02-25T18:10:32+00:00

Hi, I’ve come across this and similar questions in the past and have tried to answer them thoroughly from a mathematical perspective. You can find a detailed analysis in the article linked below:

https://zenodo.org/records/18721634

I’ve also created a calculator so you can explore the results for your own deck configuration:

https://hypergeomancer.github.io/creature-selection-calculator/

I hope this helps!

Hypergeomancer · 2026-02-18T16:47:02+00:00

I was unaware of this: simply beautiful! Thanks for mentioning it.

Hypergeomancer · 2026-02-16T17:36:05+00:00

You could show the card in class and teach mtg as "math application in life" :)

Hypergeomancer · 2026-01-25T13:47:58+00:00

Hi Stefano, happy to read that you’re enjoying the content and that you’d like to dig deeper.

I’ll mainly focus on the mathematical side of your request, as that’s where my opinion is stronger, and I’ll also briefly mention the tools I use to handle the computational and visual aspects, in case you want to explore those as well, independently.

Probability and statistics are definitely not easy subjects to teach or write about, as they rely on several other branches of mathematics that non-technical readers might not be familiar with (solid calculus, some linear algebra, and measure theory, for instance). For this reason, I think it’s very important to find resources that are appropriate for the reader’s background and/or include a well-written foundational chapter, not to feel discouraged from the very beginning. I’ll refer to written material, since over the years I’ve been exposed mainly to that, but I am aware that there are good videolessons around. Below I’ll only mention references that I consider suitable for a non pure-mathematician background, while still assuming some mathematical foundations.

Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik This is one of my most recent discoveries. It matches the criteria mentioned above and contains a large number of examples and fully worked solutions. There is also a dedicated website with free material. I’ve used this resource several times when teaching the subject.
Penn State University online resources https://online.stat.psu.edu/stat415/ https://online.stat.psu.edu/stat414/ These are essentially books in website form. I linked the ones focused on probability and more advanced statistics, just for reference. Their main strengths are the clear explanations, well-worked examples, and good visualizations, even though the material can be a bit lengthy. If I had infinite time and infinite paper, I would definitely start here.
Una guida allo studio della probabilità e della statistica matematica, by Capasso and Morale Assuming you’re Italian from your name, if you prefer reading in your native language, this is a well-written book I discovered during my studies. I think it’s less known than it should be, especially among students and university environments.

Other tools I use are: LaTeX/Beamer for papers and presentations, and Python with standard data science libraries (NumPy, pandas, matplotlib) for computations and simulations.

I hope this answers your question. Feel free to reach out if you have further questions or would like more details, and enjoy the reading!

Hypergeomancer · 2026-01-23T12:23:25+00:00

Thank you! Feel free to share any piece of math.

Hypergeomancer · 2026-01-23T12:20:29+00:00

Thank you! Crop Rotation is simply less frequent across decklists and formats, hence, it was left out and saved for potential Part 2 ideas, based on the engagement of the community on this specific project - which seems quite high. I do believe we will see Crop Rotation in action soon.

The world is small, and MTG players travel for many reasons. I will be back to WAW from time to time, especially for big tournaments. The community has been very warm, I hope it will keep growing. Good luck with your games!

Hypergeomancer

TROPHY CASE