How Many Cards Can You Expect to Play Each Turn With Experimental Frenzy?

Experimental Frenzy has quickly proven itself to be one of the most powerful card draw engines from Guilds of Ravnica. The red Future Sight lets you look at and play cards from the top of your library, enabling a steady flow of spells that can rapidly bury an opponent in card advantage.

In Guilds of Ravnica Standard, its power is best harnessed by Mono-Red Aggro decks with Runaway Steam-Kin and a low mana curve. With such a deck, you can usually keep playing spells from the top of your library until you hit the second land of the turn. An example list is the following, which found success in the hands of Max McVety during the first weekend of the new Standard.

Mono-Red Aggro

Max McVety, 3rd at SCG Team Open Columbus

The same weekend, a tournament in Japan was won by a player named Kouchi Daiki, whose main deck was identical to Max McVety’s except that it relied even more on the enchantment, with zero Rekindling Phoenix and four Experimental Frenzy. That’s a clear vote of confidence.

But how many cards can you expect to play each turn with Experimental Frenzy?

Doing the Math: The Negative Hypergeometric Distribution

Let’s start with the general distribution for the amount of spells you can play off of Experimental Frenzy on any given turn, assuming you have unlimited mana to keep chaining spells. This is a reasonable assumption if you control one or more Runaway Steam-Kin with a low-curve deck.

Suppose you start the turn with N cards in your library, L of which are lands and N-L of which are spells. We then draw cards one after the other until we encounter two lands, at which point the drawing stops and the number of spells is counted. The outcome of seeing S spells requires that we observe S spells in S+1 draws, immediately followed by a land on top. If you’re familiar with probability theory, you may recognize this as a negative hypergeometric distribution.

Therefore, the probability of seeing S spells before seeing the second land is described by HYPERGEOMDIST(S, S+1, N-L, N) * (L-1)/(N-S-1), where:

• HYPERGEOMDIST(S, S+1, N-L, N) represents the hypergeometric probability of hitting S spells in a sample of size S+1 given a population of size N containing N-L spells, without replacement.
• (L-1)/(N-S-1) represents the probability of having a land on top after you have drawn S+1 cards, exactly one of which was a land, from the original N-card library containing L lands.

Given an N-card library containing L lands, the expected number of spells you see before seeing the second land is 2(N-L)/(L+1).

Running the Numbers

Let’s apply this to a typical situation on turn 6 where you have N=48 cards left in your library, L=18 of which are lands. You won’t encounter this specific situation every time, but it’s still a good approximation for any game where you drew Experimental Frenzy by turn 5, along with at least 4 lands, from a deck with 22 or 23 Mountains.

Supposing that mana availability is not a limitation, the probability distribution for the number of spells we would be able to play on that turn is given in the following table.

 Number of spells you see before second land Probability of seeing exactly so many spells Probability of seeing at least so many spells 0 13.6% 100.0% 1 17.7% 86.4% 2 17.1% 68.7% 3 14.5% 51.6% 4 11.4% 37.1% 5 8.5% 25.7% 6 6.0% 17.3% 7 4.1% 11.3% 8 2.7% 7.1% 9 1.8% 4.4% 10 1.1% 2.6%

As you see, the fail rate is small. The probability of immediately seeing two lands in a row without seeing a single spell is only 13.6%. In the other 84.6% of the cases, you’ll hit at least one spell, and you’ll usually be able to rattle off several spells each turn. According to the above cumulative distribution, you’re 51.6% to hit 3 or more spells before seeing the second land. And if you’re lucky, in 7.1% of the cases, you’ll hit 8 spells or more.

The expected value for the number of spells you can play per turn is 3.16. That means that Experimental Frenzy is like a triple Phyrexian Arena without the life loss!

Admittedly, a substantial part of that expected value comes from the tail of the distribution, i.e., from the scenarios where you’d hit 8 or more spells. In practice, unless you control two Runaway Steam-Kin, you would get stuck way before that point due to mana limitations. But we can account for that. If I would relax my infinite-mana assumption by instead assuming that you can cast no more than 3 spells per turn, then the result would be an expected number of 2.07 spells cast on that turn. That may not be as impressive as a triple Phyrexian Arena, but a double Phyrexian Arena still represents a very powerful card draw engine.

I should note that, so far, I’ve only counted spells—I haven’t included the guaranteed and free land drop each turn. But in terms of card economy, it seems fair to ignore this free land drop because you are also effectively missing your draw step (since you can’t play cards from your hand). It’s the spells that represent the number of additional cards per turn.

Conclusion

In the right deck, Experimental Frenzy basically reads “draw 2-3 extra cards every turn,” which is better than Outpost Siege, better than Vance’s Blasting Cannons, and arguably better than most 4 mana planeswalkers. The card is the real deal.

As the numbers showed, Experimental Frenzy is reliable enough by itself—to reap the benefits, you don’t need cards like Treasure Map or Dismissive Pyromancer to clear out land pockets from the top of your deck.

If you’re a Mono-Red Aggro player in Standard, then I recommend putting Experimental Frenzy in your 75. For your main deck, you have to choose between Experimental Frenzy and The Flame of Keld, and that’s a close call. Experimental Frenzy gives late-game staying power, but if you want to embrace the fiery aggro role, at least in Game 1, then The Flame of Keld might be better: It’s faster, costs less mana, can close out the game with its explosive third chapter, and has better synergy with Risk Factor. But at least for Games 2 and 3, which tend to be grindier and may put you in a control role, I prefer Experimental Frenzy.

If you’re not a Mono-Red Aggro player, then you need to have a plan against Experimental Frenzy because it attacks from a different angle. If you merely bring in creature removal and life gain spells against them, then you might easily lose to the enchantment. On the other hand, you also don’t want to bring in overly specific answers like Demystify that might be dead. Instead, emphasize answers that still do something if your Mono-Red Aggro opponent didn’t draw Experimental Frenzy. The best ones are Conclave Tribunal, Ixalan’s Binding, Assassin’s Trophy, Status // Statue, Thrashing Brontodon, Knight of Autumn, Teferi, Hero of Dominaria, Vivien Reid, and Vraska, Relic Seeker. Since they’re all green or white, you’re out of luck if you’re Grixis. Better draw Duress or Negate in time, or Experimental Frenzy will bury you in card advantage.

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