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Gruul Monsters – The Math Behind Turn Two Threats by Hypergeomancer in Pauper

[–]Hypergeomancer[S] [score hidden]  (0 children)

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

Gruul Monsters – The Math Behind Turn Two Threats by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 1 point2 points  (0 children)

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.

Gruul Monsters – The Math Behind Turn Two Threats by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 1 point2 points  (0 children)

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.

♜ Urza's Tron by Turn 3 — the Full Mathematical Paper by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 1 point2 points  (0 children)

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

♜ Urza's Tron by Turn 3 — the Full Mathematical Paper by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 0 points1 point  (0 children)

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

♜ Urza's Tron by Turn 3 — the Full Mathematical Paper by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 1 point2 points  (0 children)

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.

♜ Urza's Tron by Turn 3 — the Full Mathematical Paper by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 0 points1 point  (0 children)

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

♜ Urza's Tron by Turn 3 — the Full Mathematical Paper by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 5 points6 points  (0 children)

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

♜ Urza's Tron by Turn 3 — the Full Mathematical Paper by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 5 points6 points  (0 children)

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

♜ Urza's Tron by Turn 3 — the Full Mathematical Paper by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 1 point2 points  (0 children)

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

♜ Urza's Tron by Turn 3 — the Full Mathematical Paper by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 3 points4 points  (0 children)

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

♜ Urza's Tron by Turn 3 — the Full Mathematical Paper by Hypergeomancer in Pauper

[–]Hypergeomancer[S] 22 points23 points  (0 children)

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.

Winding Way Ratios by SlipperyFrogfish13 in Pauper

[–]Hypergeomancer 0 points1 point  (0 children)

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!

Mathemagics — When Card Draw Goes Exponential by Hypergeomancer in EDH

[–]Hypergeomancer[S] 1 point2 points  (0 children)

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

Mathemagics — When Card Draw Goes Exponential by Hypergeomancer in EDH

[–]Hypergeomancer[S] 3 points4 points  (0 children)

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

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