The full code for the simulation is available on GitHub if anyone is curious.

github.com/birchmd/mtg-...

I don't think any of this data is useful in practice; this deck is clearly not competitive in standard (where aggro decks can regularly win on turn 4 or 5 and control decks will have ample answers for the namesake card). But I had fun putting all this together regardless!

Other mulligan heuristics will have to be a topic for future research.

The deck can also lose by decking before killing the opponent. This happens around 0.1% of the time. Losing to a goldfish is kind of funny, but again the simulation doesn't ever attack, which obviously makes a difference.

Since this is a combo deck, I tried adding mulligan heuristics to try to have Claim in the opening hand. But this also made things worse, increasing the average to 11.57. I am not sure why this makes things worse and I think it should be true that a mulligan heuristic exists to improve performance.

The average is winning on turn 11.38 (+/- 0.01). The scry/surveil logic used when playing lands is important. If I disable this in the simulation (always top) then the average increases by almost half a turn to 11.86. I think this means including those lands in the mana base is good deck building!

About 61% of the time, the deck wins between turns 7 and 10 (inclusive). It wins on turn four 0.03% of the time. The turn 4 win happens by playing Claim on turn 3, hitting a big spell on end step then playing a second copy on turn 4 with both copies hitting big spells (7 x 3 = 21 damage).

That said, I think this simulation should still give a bit of a sense of how quickly the deck deals damage on average and how important certain decisions are. The main result is the plot showing the distribution of turn number on which the deck wins (deals lethal damage with Claim).

First, some caveats. The simulation is vastly simplified relative to the actual complexity of playing magic. Notably, there is no combat because the main goal of this deck is to drain the opponent out with Duskmourn's Claim. Also the decision making follows simple (not optimal) heuristics.

If you're wondering where these came from, the real ones are titles presented at ETAPS 2025, which I had the pleasure of attending this year. I didn't present anything myself, but I enjoyed the presentations I saw and I'm looking forward to digging more into formal verification!

Disclaimer: this is just a bit of fun! I am not disparaging any of the real talk titles. They are clear and technically accurate, which is exactly what you want from an academic talk title.

C. Two-sorted algebraic decompositions of Brookes's shared-state denotational semantics

D. Reachability for Nonsmooth Systems with Lexicographic Jacobians

So I suspect, though haven't looked at the numerical data to double check, that away from (0.5,0.5) a+b is positive so that the equilibria are unstable and thus allows the state to move towards the stable equilibrium in the center. And this is what the numerical trajectories showed as well.

I realized one more thing about the linearization and stability analysis. There is a whole line of equilibria y=x and the linearization applies to all of them. Since -1 is always an eigenvalue, the line is stable along one direction. The other eigenvalue is a+b, which changes along the line.

So if your deck is a little better than your opponent (p>0.5) then on average you add cards to your deck, making it worse until they're evenly matched. This is reversed if you're a little behind your opponent. And so the game continues until a large enough variation randomly pushes someone to win.