Magic Math: Hour of Devastation

Hour of Devastation contains several cards that I found interesting from a mathematical perspective. Let’s run some numbers!

Do We Have a Reason to Believe?

This card has the potential to cheat an Ulamog, the Ceaseless Hunger into play ahead of time, so it at least deserves consideration for that. Unfortunately, without a Mortuary Mire to fix the top of your deck, the numbers aren’t great.

Click to enlarge.

There is only a 19.3% probability of seeing said Ulamog in your top 3 cards, even if you run 4 Ulamog in your deck. What’s more, you don’t even get the cast trigger.

If you add 4 Kozilek, the Great Distortion to your deck, then you can scry into at least 1 of your 8 Eldrazi with probability 35.9%, but that’s still not exactly consistent enough to build a deck around. I am not a believer.

How Many Deserts Do You Need for Ramunap Hydra?

Once upon a time, Juzam Djinn was one of the best creatures in Magic. Times have changed. Woodland Wanderer, for example, has only seen a little bit of Standard play, despite being a 6/6 for 4 mana.

Ramunap Hydra is somewhat similar to Woodland Wanderer. Both creatures have vigilance and trample, and require a specific mana base. Although Ramunap Hydra can grow no larger than 5/5, it does have reach. That is a useful ability in a format where the best threats include various 4/4 flyers. As long as Heart of KiranArchangel Avacyn, and Glorybringer remain popular in Standard, Ramunap Hydra deserves consideration.

But to make it a 5/5 consistently, say with 90% probability on turn 4 on the draw, how many Deserts would you need?

Here are some numbers.

I made things relatively easy on myself by using basic hypergeometric probabilities after 1 Ramunap Hydra was removed from the deck. The results are at least close to the conditional probability of having a certain number of Deserts and at least 1 Ramunap Hydra on turn 4 on the draw, but it doesn’t take into account that (1) there are mulligans, (2) you are only interested in scenarios where you have at least 4 lands, (3) cycling lands draw additional cards, and (4) you can’t afford to cycle/sacrifice a Desert if you are land-light. The first three issues would make it easier to get a big Ramunap Hydra in practice—the fourth issue makes this more difficult than the above table suggests. Yet, the ease with which you could cycle a Desert in the early game will heavily depend on the rest of your deck and your mana base, so I decided to give you the above, easy-to-interpret numbers.

What the numbers tell us is that if you would start the game with a Ramunap Hydra on the battlefield and are always able to cycle/sacrifice any Desert, then you need 18 Deserts to get a 5/5 Ramunap Hydra with at least 90% probability on turn 4 on the draw. But Ramunap Hydra may already be playable with 14 Deserts—its expected size at that point in the game would be a reasonable 4.77/4.77.

Yet, it is hard to fit a large number of non-embarrassing (and preferably sacrificable or cyclable) Deserts into your mana base. Most Deserts are mediocre, so the only realistic home would be an Hour of Promise deck. You may count 4 copies of that sorcery as approximately 6 Deserts for the purpose of Ramunap Hydra. Here’s a rough idea.

Green-White Deserts

This doesn’t look like it will break Standard anytime soon, but it’s at least worth exploring the new Desert theme.

How Likely Are You to Face a Drafter in the Same Colors?

If I assume that every drafter picks two distinct colors at random, then the average 8-player pod has 3.2 white drafters, 3.2 blue drafters, and so on. If you’re drafting white yourself, then out of the 7 possible opponents there are 2.2 white drafters on average, which means that you have a 31.4% chance of facing another white drafter in an arbitrary match.

In Magic Online Leagues, you can play opponents outside of your draft pod. In this case, an arbitrary opponent will be white 3.2 out of 8 times in expectation, which comes out to 40.0%.

Either way, I wouldn’t run Gideon’s Defeat in my main deck. It’s a potent sideboard card, but you simply cannot afford to run a situational removal spell that is dead against more than half of your opponents.

Hazoret Is Still Alive, but How About Her Undying Fury?

If this card had cost 4 mana and looked at the top 6 six cards (like Collected Company and Aetherworks Marvel) then it would have very powerful. Likewise, if it didn’t have a converted mana cost restriction (so that you could cast expensive spells or chain Hazoret’s Undying Fury in the same way as Mind’s Desire), then it would have been very strong as well. Alas, with the numbers and restrictions on the card that saw print, I don’t see that much potential.

As an example, consider a deck with 40% lands—that’s 24 lands for a 60-card deck. You can’t realistically play less with 6-mana cards. I’ll be generous and ignore the presence of Hazoret’s Undying Fury in the deck. With this distribution, you’ll hit 1.6 lands and 2.4 spells on average. This means that to fully recoup your 6-mana investment, you need an average converted mana cost of 2.5. That’s reasonable and in line with most Standard decks, but Hazoret’s Undying Fury isn’t just a 6-mana card—it ties up at least 12 lands in total.

To break even on your 12-mana investment, you need a converted mana cost of 5.0. In other words, every nonland card in your deck has to be a 5-drop. That’s completely unreasonable.

To be fair, the “truth” is somewhere in between: Hazoret’s Undying Fury costs more than 6 mana, but since you get the full effect up front and pay in installments, it’s not the same as a 12-mana card. But if I evaluate it as, say, a 9-mana card, then you would still need an average converted mana cost of 3.75 in your deck to break even, which is too top-heavy for Standard. Besides, various 2-mana and 3-mana cards are virtually worthless by the time you have progressed to 6 mana, there is a randomness involved, and you might hit a second copy of a legend or a removal spell without a target. The list of downsides is too large for my taste.

How Many Creatures Do You Need in Your Deck for Gate to the Afterlife?

6 creatures in the graveyard, eh? Well, you could at least give it a try. To get 6 creatures in the bin, you need to draw (and/or mill) 6 creatures in the first place. Supposing that you can easily discard or kill any creature at will and that you start the game with Gate to the Afterlife on the battlefield, I can figure out this likelihood after seeing various numbers of cards. The following table is brought to you by the hypergeometric distribution.

So if you have a deck with, say, 32 creatures, then after seeing 16 cards you’ll have seen at least 6 creatures with probability 90.0%. In a deck with plenty of cycling creatures, you could easily see 16 cards by turn 4. Imagine the following, on the draw.

Turn 1 – Cast Insolent Neonate. (Seen 8 cards)
Turn 2 – Cast Wharf Infiltrator. (Seen 9 cards)
Turn 3 – Attack with Wharf Infiltrator for a draw/discard trigger, then cast Gate to the Afterlife. (Seen 11 cards)
Turn 4 – Sacrifice Insolent Neonate for a discard/draw trigger and a discard/draw effect. Cycle Curator of Mysteries and Desert Cerodon. You can now have 6 creatures in your graveyard and the mana to activate Gate to the Afterlife! (Seen 16 cards)

So in the right deck, you should be able to fetch God-Pharaoh’s Gift on turn 4 or 5 with reasonable consistency. Here’s a rough idea.

Blue-Red Gift

I considered various other versions (with input from Danny de Rooij) as well. One of the options was a more spell-heavy, self-mill version with Strategic Planning, Cathartic Reunion, Pieces of the Puzzle, and Refurbish. That one didn’t have many cycling creatures and instead had Champion of Wits, Angel of Invention, and Ulamog, the Ceaseless Hunger as its sweet reanimation targets. But Gate to the Afterlife was a bit out of place there, and I figured that if I wanted to make use of Minister of Inquiries as well, then I just had to maximize the number of creatures. Eventually, I settled on the above list with Glint-Nest Crane and Hollow One.

I’m not sure if a stream of hasty 4/4s (sometimes with relevant abilities) will actually be enough to lock up the game, and the whole deck is questionable if Abrade becomes popular. But let’s just add this to the ever-growing list of ambitious Standard brews. Math is my muse.

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