# How Many Blue Cards Do You Need for Force of Negation?

Old-school players will remember this cycle of free spells from Alliances.

Modern Horizons introduces a new cycle of free spells, with lower costs and an updated design that prevents abuse during your own turn.

These cards naturally lead to a deckbuilding challenge: how many spells of the corresponding color do you need to consistently cast a Force for its alternative cost?

# How Many Blue Cards Do You Need for Force of Negation?

## Methodology and Assumptions

To run some numbers, I must make some assumptions. First, I will assume that we want to cast a Force without paying its mana cost on our opponent’s second turn. This is typically the turn where Goryo’s Vengeance or Neoform may be cast or where an Affinity or Hollow One player may dump multiple creatures onto the battlefield.

The second assumption I will make (for analytical tractability and ease) is that there are no mulligans, card selection spells, opposing discard spells, and so on. Hence, regardless of whether you were on the draw or on the play, when your opponent takes their second turn, you will have seen 8 cards. This helps to establish a baseline number. For concreteness, let’s focus on Force of Negation in a 60-card deck. The number that I’m interested in is the probability of drawing at least one other blue card in the top eight cards conditional on having at least one Force of Negation in the top eight as well.

There are two tricky elements to determining this probability:

• I only care whether I have another blue card when I have at least one Force, and in that case the Force is taking up one slot somewhere in the top 8 cards.
• A second Force is just as good as any other blue spell for pitching purposes, so the result may depend on how many Forces there are in the deck.

Given this, I want to look at all possible 8-card sequences of Forces (F), other blue cards to pitch (P), and non-blue cards (C), such as FPCCCFPPC, assign a probability to each, sum up the probabilities for all combinations with at least one F and either at least one P or another F, and then divide that by the sum of probabilities for all combinations with at least one F. As this is just a garden variety conditional cumulative multivariate hypergeometric, I coded a simple Python script to run the calculation.

## Results

Here are the results.

 Number of other blue spells Success rate, 2 Force deck Success rate, 4 Force deck 4 46.1% 53.0% 5 53.3% 59.3% 6 59.7% 64.9% 7 65.4% 69.8% 8 70.3% 74.1% 9 74.7% 77.9% 10 78.4% 81.2% 11 81.7% 84.1% 12 84.6% 86.5% 13 87.0% 88.7% 14 89.1% 90.5% 15 90.9% 92.1% 16 92.5% 93.4% 17 93.8% 94.6% 18 94.9% 95.6% 19 95.9% 96.4% 20 96.6% 97.1% 21 97.3% 97.6% 22 97.8% 98.1%

In this table, “success rate” refers to the probability of having a blue card to pitch when you hold Force of Negation in hand during your opponent’s second turn. For example, in a 60-card deck with 2 Force of Negation and 14 other blue spells, this probability is 89.1%. In a 60-card deck with 4 Force of Negation and 14 other blue spells, this probability is 90.5% (because you could pitch one Force to another). Naturally, you can replace “blue” and Force of Negation by “green” and Force of Vigor, etc., in which case all numbers will remain the same.

Although I focused solely on the probability of casting Force during your opponent’s second turn, I can give a bit more insight for other turns in the context of a 60-card deck with 4 Force of Negation and 14 other blue spells. With this deck, the corresponding success rate would be 86.4% on your opponent’s first turn and 93.4% on your opponent’s third turn.

## What is a good percentage?

In the matchups where Forces of Negation is at its best (e.g., against Goryo’s Vengeance or Neoform) you really need to be able to cast them early and cast them for free. Otherwise, you may be better off with something like Spell Pierce. From this perspective, I would like to see a high likelihood of at least 90% to have a blue card for Force of Negation on my opponent’s second turn.

According to the above table, you would reach 90% consistency in a deck with 2 Force of Negation and 15 other blue spells or in a deck with 4 Force of Negation and 14 other blue spells. These are good to keep in mind as guidelines. The more, the better, of course.

## All 5 Forces are seeing play in Modern

After sifting through the first week of Magic Online decklists since the release of Modern Horizons, I already encountered all 5 Forces. Let’s look at one example list for each.

### Orim67, 5-0 in a Modern League on June 12

```2 Field of Ruin
16 Plains (331)
3 Windbrisk Heights
4 Ajani's Pridemate
3 Martyr of Sands
4 Ranger of Eos
4 Serra Ascendant
4 Soul Warden
3 Soul's Attendant
2 Proclamation of Rebirth
4 Spectral Procession
3 Path to Exile
4 Force of Virtue

Sideboard
4 Damping Sphere
2 Disenchant
2 Grafdigger's Cage
1 Ratchet Bomb
4 Rest in Peace
2 Stony Silence```

I have also spotted Force of Virtue in Mono-White Eldrazi, but Soul Sisters seems like the perfect home. This deck not only swarms the board with one-drops and Spectral Processions but also easily recoups the card disadvantage via Squadron Hawk or Ranger of Eos. As a result, a “free” Force of Virtue is an excellent way to improve the damage clock. And with 35 other white spells, paying the alternate cost will almost never be a problem.

### Ragingtiltmonster, 5-0 in a Modern League on June 14

```1 Cavern of Souls
14 Island (335)
4 Mutavault
1 Oboro, Palace in the Clouds
4 Cursecatcher
1 Harbinger of the Tides
4 Lord of Atlantis
4 Master of the Pearl Trident
4 Merfolk Trickster
3 Merrow Reejerey
2 Mistcaller
4 Force of Negation
2 Vapor Snag
4 AEther Vial

Sideboard
4 Ceremonious Rejection
2 Deprive
4 Grafdigger's Cage
3 Master of Waves
1 Phyrexian Revoker
1 Ravenous Trap```

Force of Negation is the best Force in the cycle. It has seen a lot of play already in U/W Control decks, where it can protect a turn-4 Jace or counter an opposing threat while you’re tapped out. I showed such a list last week in my article on Fact or Fiction.

Force of Negation has also shown up in Vannifar Pod, Saheeli combo, U/R Kiln Fiend, and U/W Spirits. But above all, I think it fits Merfolk quite well. Thanks to Silvergill Adept, it’s not too hard to recoup the card disadvantage of pitching a blue spell, and the ability to keep adding Lords to the battlefield while holding free protection against nonsense like Karn Liberated, Wrath of God, or Scapeshift fits the game plan perfectly. And unsurprisingly for a mono-blue deck, you’re 99.9% to have drawn another blue card for Force of Negation on your opponent’s second turn.

### Heilagur, 5-0 in a Modern League on June 12

Force of Despair is somewhat like Counterspell, and it can wreck an Affinity or Hollow One player when they dump multiple creatures onto the battlefield in one turn. A pure control deck would probably be better off with Damnation, but in a creature-based midrange deck like Mardu Pyromancer or Sultai Snow, Force of Despair seems good. In Mardu Pyromancer specifically, it has great synergy with Bedlam Reveler, as Force of Despair puts another instant in your graveyard for free. And having to exile a card from your hand is not a big downside when you’re refilling with Bedlam Reveler anyway.

In the above list, it’s a one-of in the main deck with 16 other black spells. This yields a 92.0% probability of having a black card to pitch when you hold Force of Despair in hand during your opponent’s second turn. That’s fine, but it relies on the assumption that you wouldn’t cast a black discard or removal spell on turn one, which seems questionable in the context of this deck. In practice, casting Force of Despair will be more awkward than the numbers might suggest.

### Seky, 5-0 in a Modern League on June 15

```4 Arid Mesa
2 Bloodstained Mire
3 Mountain (343)
2 Sacred Foundry
1 Stomping Ground
4 Sunbaked Canyon
3 Wooded Foothills
4 Eidolon of the Great Revel
4 Goblin Guide
1 Grim Lavamancer
4 Monastery Swiftspear
4 Lava Spike
4 Rift Bolt
4 Boros Charm
4 Force of Rage
4 Lightning Bolt
4 Lightning Helix
4 Searing Blaze

Sideboard
4 Cindervines
2 Ensnaring Bridge
3 Path to Exile
2 Ravenous Trap
2 Rest in Peace
2 Tormod's Crypt```

If Force of Rage had said “sacrifice at the beginning of your next end step,” it would have been busted: that would have allowed you to pitch a red card for 6 free damage. Alas, if you want to attack with the tokens, you have to pay full retail, making the card similar to Ball Lightning. Six damage for three mana is a good deal for Burn, but Ball Lightning never saw any play. One reason for that is that Ball Lightning was too easily stopped by a single spot removal spell or first-striking blocker. However, Force of Rage creates two tokens, so it might turn out to be a substantial upgrade.

While you’re usually going to pay three mana during your own turn, it’s useful to have access to the alternative cost. This could come up, for example, when you have a land-light draw and are in a damage race against an opposing creature deck. Or when you need to ambush Primeval Titan. And there’s also the super-secret mode of exiling your opponent’s Bridge from Belows in your next upkeep. All these fringe options combined make for an intriguing card.

### Boland, 5-0 in a Modern League on June 14

```1 Bojuka Bog
1 Boros Garrison
1 Cavern of Souls
1 Crumbling Vestige
4 Gemstone Mine
1 Ghost Quarter
1 Gruul Turf
1 Khalni Garden
4 Selesnya Sanctuary
4 Simic Growth Chamber
1 Slayers' Stronghold
3 Snow-Covered Forest
1 Sunhome, Fortress of the Legion
1 Vesuva
3 Tolaria West
4 Arboreal Grazer
4 Azusa, Lost but Seeking
1 Hornet Queen
4 Primeval Titan
2 Trinket Mage
1 Walking Ballista
4 Ancient Stirrings
2 Sylvok Explorer
4 Summoner's Pact
4 Amulet of Vigor
1 Engineered Explosives

Sideboard
1 Cavern of Souls
4 Force of Vigor
1 Grafdigger's Cage
1 Obstinate Baloth
1 Ramunap Excavator
1 Reclamation Sage
1 Ruric Thar, the Unbowed
1 Spell Pierce
1 Tireless Tracker
1 Tormod's Crypt
1 Wheel of Sun and Moon```

Force of Vigor is the perfect answer to Blood Moon. For Amulet Titan players, it reduces the need for such cards as Coalition Relic, Karn, the Great Creator, and Negate. And with 19 green cards in the main deck, you should nearly always have a green card to pitch: it’s 96.4% on your opponent’s second turn and 97.9% on their third turn.

I have also seen Force of Vigor in the sideboard of Infect, where it might deal with cards like Chalice of the Void. Oh, and Affinity players hate this new Force. It’s not as bad as Stony Silence, but a zero-mana double Ancient Grudge is still unfair.

As a final note, remember that Force of Vigor doesn’t get around the Karn, the Great Creator plus Mycosynth Lattice lock because Lattice makes all green cards in hand colorless.

## Conclusion

If you want to be at least 90% to have a blue card to pitch when holding Force of Negation during your opponent’s second turn, then you can accomplish this by running 2 Force of Negation and 15 other blue spells.

All in all, the new Forces are much-needed safety valves, and Modern Horizons is shaking up the Modern format in various ways. I can’t wait to see what comes out of the Red Bull Untapped tournaments on 6 & 7 July—the first major Modern events with the London mulligan rule—but several Forces in the Top 8 wouldn’t surprise me.

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