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How Many Cards Can You Exile With Tasha’s Hideous Laughter?

Previews for Adventures in the Forgotten Realms have already started, and one of the previews is an awesome high-variance sorcery – Tasha’s Hideous Laughter.

 

 

While you could describe it as a “mill” card, Tasha’s Hideous Laughter actually exiles the cards. That’s great news for Oblivion Sower aficionados but bad news for mill players who rely on Crypt Incursion. Nevertheless, when your game plan is to reduce your opponent’s library to zero cards as quickly as possible, then Tasha’s Hideous Laughter could fit right in.

But how many cards can you expect to exile with this spell on average, what’s the distribution like, and how does this depend on the format?

 

 

Alright, requests received. I’ll run the numbers.

 

Header - Approximating the Amount Exiled

If you know what you’re playing against, then a very easy approximation works as follows. First, determine the average mana value of all cards (including lands) in the opposing deck. Then the expected number of cards exiled is approximately 20 divided by that average mana value. For example, an opposing deck with 20 lands, seven one-mana spells, 10 two-mana spells and 23 three-mana spells would have an average mana value of 1.6. Then the expected number of cards exiled with Tasha’s Hideous Laughter is approximately 20 / 1.6 = 12.5. This is not exact, but it’s a decent, quick approximation.

An exact calculation is more difficult. Given a deck list, you’d enumerate all permutations (i.e. all ways in which the deck can be ordered) and for each, you’d determine the number of cards exiled. From this, the entire probability distribution can be obtained. While it’s not difficult to define this mathematically, a practical problem is that the number of permutations of a 60-card deck is in the quadrillion vigintillions – the same order of magnitude of the number of atoms in the observable universe. We could employ some clever tricks to reduce this by observing that many permutations are effectively identical, but the calculation would still be tedious, error-prone and time-consuming.

It’s easier to resort to simulation. We’d take an opposing deck list, shuffle and exile from the top until we’ve exiled cards with total mana value 20 or more. We could make things more complicated by incorporating an opponent’s mulligan process, fetch lands and so on, but this would only make a tiny difference. Let’s just treat the opponent’s opening hand as a random sample, and then we can simulate Tasha’s Hideous Laughter against shuffled 60-card deck.

 

Header - Deck List Source Data

To simulate, we need an opposing deck or a sample of opposing decks. For five popular formats, I obtained a variety of decklists.

  • Standard: I used all 250 deck lists from the recent Strixhaven Championship and I simulated each deck for 40,000 games.
  • Historic: I used all 250 deck lists from the recent Strixhaven Championship and I simulated each deck for 40,000 games.
  • Modern: I used all downloadable deck lists from the June 7, June 13 and June 14 Modern Challenges. I then added enough top decks from the June 6 Challenge to get up to 100 decks total. I simulated each deck for 100,000 games.
  • Legacy: I used all downloadable deck lists from the June 7, June 13 and June 14 Legacy Challenges. I then added enough top decks from the June 6 Challenge to get up to 100 decks total. I simulated each deck for 100,000 games.
  • Vintage: I used all downloadable deck lists from the June 7, June 13, and June 14 Vintage Challenges. I then added enough top decks from the June 6 Challenge to get up to 100 decks total. I simulated each deck for 100,000 games.

I did not include Commander because I wasn’t sure where to obtain a reasonable sample of deck lists. I will just mention that Tasha’s Hideous Laughter says “each opponent,” which makes it appealing in a multiplayer format. And if anyone in your play group is running a 97+ land deck with Borborygmos Enraged or Maelstrom Wanderer as their commander, then you now have the perfect way to punish them.

 

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