War of the Spark features a lot of cards that allow you to look at the top of your library and take one or more cards that satisfy a certain characteristic. Narset, Parter of Veils, God-Eternal Kefnet, Augur of Bolas, Vivien, Champion of the Wilds, Tamiyo, Collector of Tales, Vivien’s Arkbow, and Niv-Mizzet Reborn are examples of such cards, and all of them have already found themselves in successful Standard decks. Today, I will analyze how reliable these cards are in those decks. My main goal is to provide a handy reference for deck builders.

What I will determine, unless otherwise specified, is the expected hit probability when using such a card in a game. I model this by removing one copy of the card from the deck, drawing any number of cards (representing the opening hand and any number of draw steps), and finally putting the ability on the stack. This approach is justified in example 5 of my introductory article on the hypergeometric distribution.

Let’s start with the blue cards.

Dimir Control

Grzegorz Kowalski, Magic Pro League Week 1

8 Island
7 Swamp
4 Drowned Catacomb
4 Watery Grave
2 Blast Zone
2 Augur of Bolas
2 God-Eternal Kefnet
3 Narset, Parter of Veils
2 Liliana, Dreadhorde General
1 Ugin, the Ineffable
4 Thought Erasure
2 Cry of the Carnarium
3 Enter the God-Eternals
4 Opt
2 Cast Down
2 Negate
2 Tyrant's Scorn
3 Vraska's Contempt
1 Chemister's Insight
2 Search for Azcanta/Azcanta, the Sunken Ruin

Sideboard
4 Thief of Sanity
3 Duress
3 Unmoored Ego
2 Finale of Eternity
2 Moment of Craving
1 Enter the God-Eternals

Given the recent debut of MPL divisional play, I’m featuring a deck from that league. In Kowalski’s main deck, nearly half of the non-land cards stem from War of the Spark. With powerful spells like Enter the God-Eternals and Liliana, along with a colorless utility land in Blast Zone, a 2-color control shell without white has become a competitive option. Moreover, there are enough instants and sorceries to exploit Augur of Bolas, Kefnet, and Narset.

Augur of Bolas

Augur of Bolas
Instants/sorceries in your 60-card deck Augur hit probability
21 74.1%
22 76.1%
23 78.0%
24 79.9%
25 81.6%

When Shahar Shenhar won the 2013 World Championship, his Standard deck contained Augur of Bolas with 24 instants and sorceries. Kowalski’s list has 23. For both, that’s slightly below 80% to hit.

Given this low degree of consistency, I understand the joke “Augur of Bolas lets you look at the bottom three cards of your library.” Yet it is hard to increase this consistency without reducing the overall power level of your deck, and a defensive 1/3 body that draws a card nearly 4 out of 5 times does fit the strategy. I would caution against reducing the instant/sorcery count below 21, though.

God-Eternal Kefnet

God-Eternal Kefnet
Instants/sorceries in your 60-card deck Kefnet hit probability
21 35.6%
22 37.3%
23 39.0%
24 40.7%
25 42.4%

In Kowalski’s deck, Kefnet is 39.0% to yield a free card in your draw step, which is a sweet bonus on a creature whose base stats and ability to shrug off removal is appealing enough.

But it gets better. Did you know that Kefnet reads “each turn”? As a result, an Opt on your opponent’s turn becomes a huge value play. It’s even far more consistent due to scry—you’re 63.2% to hit an instant or sorcery in your top two cards. You still can’t reliably count on it, but the percentages add up over time. In Kowalski’s deck, given enough turns, Kefnet is a value machine.

Narset, Parter of Veils

Narset, Parter of Veils
Noncreature spells in your 60-card deck, including all copies of Narset Narset hit probability per activation
29 93.1%
30 94.0%
31 94.8%
32 95.5%
33 96.1%

Narset counts not only instants or sorceries—it also fetches planeswalkers or enchantments. And looking at the top 4 is a lot better than looking at your top 3. So it’s not a surprise that Narset is far, far more reliable than Augur of Bolas. In Kowalski’s deck, where 31 noncreature spells total yield a 94.8% hit rate per activation, comparisons to Dig Through Time are warranted.

What’s more, Narset’s static ability can cripple Esper Control and Simic Nexus, who can no longer fully exploit their Teferis and/or Chemister’s Insights. For a 3-mana planeswalker, that is an incredible deal, and I expect to see more and more control players adopt Narset in the near future. Once they do, more and more players should move from Chemister’s Insight to Narsets in order to dodge the static ability on opposing Narsets, so we may see a snowball effect in the coming weeks.

Bant Aggro

Ken Yukuhiro, Magic Pro League Week 1

3 Forest
4 Breeding Pool
4 Temple Garden
4 Sunpetal Grove
4 Hallowed Fountain
3 Glacial Fortress
1 Hinterland Harbor
4 Pelt Collector
4 Huatli's Raptor
4 Venerated Loxodon
4 Llanowar Elves
4 Growth-Chamber Guardian
2 Emmara, Soul of the Accord
4 Chamber Sentry
2 Deputy of Detention
2 Knight of Autumn
4 Vivien, Champion of the Wilds
3 Teferi, Time Raveler

Sideboard
4 Baffling End
3 Negate
2 Deputy of Detention
2 Nissa, Who Shakes the World
1 Teferi, Time Raveler
1 Trostani Discordant
1 Disdainful Stroke
1 Ajani, Adversary of Tyrants

Yukuhiro’s masterpiece is capable of all kinds of sweet tricks. For example, if you control Vivien, Champion of the Wilds, then you can cast Huatli’s Raptor, put its proliferate trigger on the stack, and convoke Venerated Loxodon in response. The end result is that all creatures you tapped, including Huatli’s Raptor, will have gained two +1/+1 counters. It’s just like Aether Vialing in a Human in response to the Thalia’s Lieutenant trigger.

But what’s even more important than her static ability is that Vivien can provide a lot of free creatures over time.

Vivien, Champion of the Wilds

Vivien, Champion of the Wilds
Creatures in your 60-card deck Vivien hit probability
28 86.2%
29 87.5%
30 88.8%
31 89.9%
32 91.0%

You’re looking at the top 3, not the top 4, so two Vivien activations aren’t as close to a double Dig Through Time as Narset. But with 30 creatures in the deck, a Vivien activation will yield a creature 88.8% of the time, get you closer to your key creatures at worst, and always put the fear in your opponent.

Vannifar Pod

Will Erker, MCQ Winner at Moonbase Market

4 Forest
1 Island
1 Plains
4 Breeding Pool
4 Hallowed Fountain
2 Hinterland Harbor
1 Sunpetal Grove
4 Temple Garden
2 Deputy of Detention
2 District Guide
4 Elite Guardmage
2 Fblthp, the Lost
3 God-Eternal Oketra
2 Knight of Autumn
1 Kraul Harpooner
4 Llanowar Elves
3 Militia Bugler
4 Paradise Druid
4 Prime Speaker Vannifar
1 Shalai, Voice of Plenty
2 Spark Double
1 Tolsimir, Friend to Wolves
1 Trostani Discordant
3 Neoform

Sideboard
4 Negate
3 Frilled Mystic
2 Teferi, Time Raveler
2 The Wanderer
2 Vivien's Arkbow
1 Kraul Harpooner
1 Vivien, Champion of the Wilds

This MCQ winning deck list features a mind-boggling 36 creatures, so the Vivien in the sideboard should pretty much always hit.

Vivien’s Arkbow

But her Arkbow is even more interesting. If you board in the artifact against Esper Control, you may want to board out Neoform since getting Neoform countered is a disaster, so let’s suppose we retain the same creature curve as in the main deck.

Vivien's Arkbow
Value for X Probability to hit a creature Probability to find Fblthp
1 6.8% 3.4%
2 34.1% 6.7%
3 71.9% (62.0% to hit CMC 2 or 3) 10.0%
4 95.5% (81.9% to hit CMC 3 or 4) 13.2%
5 99.3% (80.8% to hit CMC 4 or 5) 16.4%
6 99.8% (86.5% to hit CMC 4 or 5) 19.5%
7 99.9% (90.6% to hit CMC 4 or 5) 22.5%

Poring over these numbers, I’d say that you don’t want to start activating Vivien’s Arkbow for less than 4 if you can help it, and the difference between an activation for 6 and an activation for 7 is relatively small, so playing out your 7th land is unlikely to be worth it.

Sadly, finding Fblthp won’t be a regular occurrence. (But honestly I wouldn’t pick him over God-Eternal Oketra, even if drawing two cards is sweet.)

Simic Nexus

Jeremy Payen, MCQ Winner at Magic Bazar

3 Blast Zone
4 Breeding Pool
4 Hinterland Harbor
2 Memorial to Genius
6 Forest
6 Island
1 Blink of an Eye
1 Callous Dismissal
4 Chemister's Insight
4 Growth Spiral
1 Negate
4 Nexus of Fate - Foil - Buy-a-Box Promo
4 Root Snare
1 Narset, Parter of Veils
3 Search for Azcanta/Azcanta, the Sunken Ruin
4 Tamiyo, Collector of Tales
4 Wilderness Reclamation
4 Opt

Sideboard
2 Arboreal Grazer
2 Biogenic Ooze
2 Incubation Druid
2 Kraul Harpooner
2 Negate
2 Thrashing Brontodon
1 Carnage Tyrant
1 Crushing Canopy
1 Spell Pierce

In War of the Spark, Simic Nexus received enormous upgrades. As Jeremy Payen’s MCQ winning deck list shows, Narset is finding her way into more and more decks—a recurring theme—but the most important upgrades are Callous Dismissal (the slimmest of win conditions), Blast Zone (free removal that can be put in play with Growth Spiral and untapped with Wilderness Reclamation), and Tamiyo, Collector of Tales (an absurdly powerful way to find and rebuy your key pieces).

Tamiyo, Collector of Tales

Tamiyo, Collector of Tales
Deck size Probability of hitting Nexus of Fate
40 35.5%
36 39.0%
32 43.1%
28 48.1%
24 54.4%
20 62.4%
16 72.8%
12 85.9%

Assuming your deck always contains four Nexus of Fates any time you activate Tamiyo (which, given the self-shuffling ability, seems reasonable), an early-game +1 activation is worth about 1/3rd of a Nexus of Fate. But as each activation decreases your library size, the hit probability grows rapidly. After activating Tamiyo for several turns, you should be able to take all the turns.

Neo Niv

Iam3DHomer, 5-1 in an Traditional Standard Event on MTG Arena

1 Glacial Fortress
2 Hallowed Fountain
2 Godless Shrine
1 Isolated Chapel
1 Drowned Catacomb
1 Watery Grave
1 Steam Vents
1 Sulfur Falls
1 Blood Crypt
1 Dragonskull Summit
1 Overgrown Tomb
1 Woodland Cemetery
1 Rootbound Crag
2 Stomping Ground
1 Sacred Foundry
1 Sunpetal Grove
3 Temple Garden
3 Breeding Pool
1 Hinterland Harbor
4 Paradise Druid
1 Deputy of Detention
2 Knight of Autumn
2 Elite Guardmage
1 Seraph of the Scales
4 Niv-Mizzet Reborn
2 Hostage Taker
1 Aurelia, Exemplar of Justice
1 Prime Speaker Vannifar
1 Trostani Discordant
1 Sorin, Vengeful Bloodlord
1 Tamiyo, Collector of Tales
4 Neoform
4 Chromatic Lantern
1 Teferi, Time Raveler
1 Domri, Anarch of Bolas
1 Rhythm of the Wild
1 Collision/Colossus
1 Find/Finality

Sideboard
2 Teferi, Time Raveler
1 Mortify
1 Oath of Kaya
1 Rhythm of the Wild
1 Elite Guardmage
2 Deafening Clarion
1 Underrealm Lich
2 Hydroid Krasis
2 Dovin's Veto
2 Assassin's Trophy

While reaching the top prize in an MTG Arena event is not in the same league as winning an MCQ, this list is super sweet and deserves recognition. It was brewed up by Iam3DHomer.

Thanks to Paradise Druid and Chromatic Lantern, the deck is capable of hardcasting Niv-Mizzet on turn 4. Using Neoform to turn Elite Guardmage into the Dragon is perhaps even more satisfying.

Niv-Mizzet Reborn

Niv-Mizzet Reborn

Given this specific deck list, the distribution of the number of cards provided by Niv-Mizzet can be found by combining multivariate hypergeometric probabilities. I wrote a quick Python script to run the calculations.

Number of hits Probability
0 1.8%
1 12.5%
2 30.2%
3 32.8%
4 17.4%
5 4.6%
6 0.6%
7+ 0.0%

Overall, the expected number of cards put in your hand by Niv-Mizzet is 2.68. That’s nice, even it may not be enough to make for a top-tier competitive deck. But when you submit this deck, you’re in it for the dream of hitting eight cards. With Iam3DHomer’s list, this happens once per 210,438 games. Be sure to clip it if that happens.

In conclusion, out of all cards I analyzed today, Narset is easily the most reliable, as long as you play at most a handful of creatures. Given that, she really is Dig Through Time with the bonus of preemptive stopping opposing card draw effects, and I expect her popularity to increase as more and more players start to realize how much power and reliability you’re getting for 1UU.