Force of Will is a more complicated spell than people give it credit for. Everything a person knows about the card, down to theory and deck construction, might be incorrect.

Believe it or not, I’ve also been wrong before. Want an example? The following is a simple thought experiment that I failed, as did my two doctorate-seeking, Magic-playing roommates. Apparently, many accomplished physicists also miss the correct answer. Can you do better?

The Men Who Err at Goats

You’re on a game show, say Let’s Make a Deal, and there are three doors. Behind one of the doors there is a car, and behind the other two there are goats. After you choose a door, the show host opens one of the other two doors, revealing a goat and giving you the option to switch.

Now, is it mathematically correct to switch doors or stay?

I’ll give you a moment.

 

Ok, ready?

The answer is to switch. Your initial guess, with one third chance of being correct, is less than that of the other two doors combined, which is two thirds. Now that the show host has shown you one of the other two doors is a goat, with zero chance, the door you would switch to retains a two thirds chance of being correct.

Still don’t believe me?

Your Pick Door B Door C Result if Staying Switching
Car Goat Goat Win Fail
Goat Car Goat Fail Win
Goat Goat Car Fail Win

As you can see, not switching is only correct one third of the time (when you correctly guess the car) and switching is correct two thirds of the time. This assumes, of course, that the show host always opens a door, instead of timing it in accordance with some scheme.

The reason that I opened with the above thought problem is because I found it somewhat humbling. As intelligent types, we can have difficulty admitting our own ignorance, especially when the problems are seemingly simple. The sheer volumes of people that get the goat puzzle wrong hints that we shouldn’t trust our instincts regarding probabilities. Part of the recent drive to avoid results-oriented thinking relates to the dangers of trusting experience over something more substantial. We delude ourselves into seeing patterns when there is only randomness. You can’t intuit how often your two land Belcher deck whiffs by goldfishing, you can’t feel out your average net worth of Lead the Stampede, and, regardless of how many games you’ve played, you can’t know how consistent your blue count for Force of Will is without doing a bit of math.

Ah, Force of Will. Back in the day, people debated whether it was worth the card disadvantage. Fortunately, general Magic theory realized that the gain in tempo (trading zero mana for however much mana the opponent has spent) is a valuable tool for countering the opponent’s win or forcing your own win through disruption.

These days, many err in that they don’t understand the function that the Force plays in a deck. Without this crucial knowledge, they won’t know when to spend it or when to hold it, or even the correct matchup to be shuffling the card away or even boarding it out.

You didn’t read that wrong. The best players in the world, established pros or Legacy ringers, board Force of Will out regularly, but certainly not willy-nilly. If you’re just learning a matchup, a good rule of thumb is that if both players consistently end the games with few to no cards in hand, the Force might have been better off as a card that at least trades one for one. If both players typically end with gas in hand, the tempo from Force is more likely to be critical.

Here are the better decks that I’ve brewed and championed since my breakout performance in Columbus with their respective blue counts. They’ve all had some success, and I’ve had a blast cashing events and shifting metagames. Due to their exposure, they’ve all received some commentary from the peanut gallery, and I’ve heard arguments ranging from weak matchups against fringe decks to citations of the lowest recommended blue count for Force of Will at twenty two: a number that, if it were true, would have shut me down before I even started.

UG Survival (17)

I liked the design behind this deck a lot, and so did a large segment of the Magic-playing community, and the deck was highly netdecked until it was eventually banned. Zack Strait ran my stock list to the top eight of multiple opens well after versions with Necrotic Ooze became popular, and Patrick Chapin claimed that, based on math taken from the open series, it was the best build for the Survival mirror match.

The popularity of the deck didn’t quiet the critics, however, and a few members of the insatiable Magic community condemned the low blue count, sometimes complaining about the power level of the blue cards in the next sentence. Apparently, my apple pie wasn’t using enough cinnamon, and what spice I did have sucked. The argument that seventeen blue cards were too few bewildered me at the time. Wasn’t fifteen the standardized minimum? Sure seventeen was less than Solidarity’s thirty eight or whatever, but it wasn’t unheard of.

Some cut the creature count to fit in Brainstorms, with the notion that the Brainstorm could simply find them a creature if they needed one. The argument reminds me of a Family Guy joke where Peter Griffin is given the choice between winning a boat or the contents of a mystery box.

“A boat’s a boat, but a mystery box could be anything. It could even be a boat!”

Or, as I now imagine it,

“A crit’s a crit, but a Brainstorm could draw into anything. It could even draw a crit!”

People also ridiculed the lone Gaea’s Cradle, comparing it to a Forest with fading when they should’ve been thinking of it as a cross between a green Dark Ritual and a City of Traitors. To be fair, the accomplished Brian Kibler was of that number, so maybe they were right.

Painter (14)

This deck falls below my own recommended minimum of fifteen blue sources. Still, people haven’t questioned it much, perhaps because of the group of fellow ringers that began the season running the deck alongside me, or perhaps because Painter’s Servant allows for Lion’s Eye Diamond and City of Traitors to be pitched to Force of Will. That doesn’t help resolve Goblin Welder or the Painter itself, however, which comes up often.

The main reason this deck gets away with so few blue sources is because it is, primarily, a Sensei’s Divining Top deck. If it needs a blue card, it can typically find one, and it can always just let Force of Will chill on top of the deck until one shows up.

Why is it in this deck? To “force” the combo through disruption. Once, in testing, I had a friend move to Force of Will an Aether Vial on turn one against a Merfolk opponent, until I stopped him. Since the deck doesn’t typically need Force until turn three, if ever, and because it sees more cards with top, and because Painter’s Servant can turn blanks into Force fodder, the deck gets away with an extremely low blue count.

Bant (16)

Like UG Survival, Bant is another Noble Hierarch deck, and can actually get away with hardcasting Force of Will on occasion. Unlike UG Survival, Bant isn’t trying to protect an engine, but it still needs the card for several matchups. Hitting a turn one Aether Vial or Goblin Lackey is important, especially on the draw. Also, it can be a stopper for otherwise unbeatable cards like Replenish, Pernicious Deed, or Humility.

Note that, as the Pithing Needles come in against Aether Vial decks, the Force of Wills lose importance, and often aren’t what you want to be doing. I leave them in against goblins, since countering Goblin Ringleader or Goblin Warchief is still a fine play, but I pull them against Merfolk, where the plan is to kill their key creatures, needle the right card, and crush them with equipment.

While a Bant deck could be made to run more blue spells, since there are plenty of blue playables like Stifle, Daze, and Preordain that I’m not utilizing, this isn’t necessarily the path to success. Running do-nothing or underpowered blue cards to “make Force good” is a poor mentality to take towards deckbuilding. You want good threats, ones that win if they resolve, to protect with Force, and you want to be able to win if you don’t draw Force too. Gerry Thompson recently made the finals of a Legacy event with Dazes in his deck, though he didn’t remember Dazing anything all day long. If Gerry Thompson doesn’t like a card, I probably don’t want it in my deck, blue count be damned.

This means that there are times when I have to hold the Brainstorm rather than cast it, or hardcast the Force on turn three or four as my last card in hand, or even bounce a Vendilion Clique with Karakas to pitch. Typically, however, I have a three or four drop to pitch on turn zero. The math works out that the card is consistent, the blue count adequate.

The Math

On the left is the number of blue cards in a deck, including four Forces. The number on the right is approximately the chance to open with Force of Will and a blue card to pitch to it.

15: 31.4% (My recommended minimum)
16: 32.6%
17: 33.6%
18: 34.5%
19: 35.3%
20: 35.9%
21: 36.5%
22: 37.0% (A seemingly arbitrary minimum I heard once)

Since we start with a forty percent chance of opening with at least one Force, subtraction allows us to figure out the percentage of hands where we open with a Force but no other blue card.

Note the diminishing returns involved with adding more blue cards for the Force of Will math. Moving from fifteen to sixteen changes the percentages by over a full percent, while going from twenty one to twenty two increases our odds by a mere half percent. Clearly, the blue count matters more the lower it goes.

These numbers are useful if the Force of Will is necessary on turn zero, but often it isn’t. Painter, for example, is a deck that typically only needs protection on turn three, and most decks even later.

By multiplying the above numbers by .4, since forty percent is the likelihood of getting a Force in the opening hand, we get the odds of having the card and something to fuel it. The missing percentage (100-the number) is equal to how often we have the Force in our opener without being able to cast it.

15: 78.5%
16: 81.5%
17: 84%
18: 86.25%
19: 88.25%
20: 89.75%
21: 91.25%
22: 92.5%

This means that, with fifteen blue cards in the deck, twenty one and a half percent of the time we draw Force in our opening grip we won’t be able to cast it. Is this a relevant number? Yes. Is this the final number? No.

Of that twenty one and a half percent, now we need to subtract mulliganed hands, since a hand with a dead card is essentially a mulligan anyway, and if the rest of the cards are weak it’s likely to get shipped. Of the kept hands, the Force will only be necessary at all times in game ones against Belcher, which constitutes a small portion of the metagame. Against other, slower decks we have to approximate the turn we need a Force, and how often we’ll have the extra blue card by that turn. Now, of all the remaining games in which we never have the blue card for Force of Will, we can subtract the games in which the card isn’t necessary to win. This would include games in which we get an active Umezawa’s Jitte against a creature deck, Wasteland an opponent into oblivion, or simply have threats the opponent can’t handle.

What we’re left with is the number of times we actually needed more blue cards in our deck, which is a very small number indeed, and one that shrinks even further with tight play and proper mulliganing.

If you’re interesting in getting the numbers yourself, but you’re no math wiz, the deep analysis option on Magic Workstation has a probability function that I found quite useful, and can let you do anything you need to do (though it rounds to whole numbers.)

Excel is the more typical math-y program, and you can accomplish most of your probability goals with hypergeometric distribution. Simply open up excel and punch in =HYPGEOMDIST(A,B,C,D)

Now, simply replace A with the number of times you draw the card in question, B is the starting hand (7 as an opener, 6 after a mulligan, etc,) C is the number of the card that you can draw (1-4 unless a basic land,) and D is the number of cards in your library before you start drawing.

This means that =HYPGEOMDIST(0,7,4,60) should punch out 60%, or rather the chances of not drawing a four of in our opening grip.

But the topic of this article is Force of Will, not math, and I’m sure some statistics major has already covered this in depth.

Moving on.

Forceful Play

Our play changes the way Force of Will functions in the different matchups.

Something that surprises a lot of newer Legacy players is that you can actually hardcast Force of Will if the situation calls for it. In some matchups the play might even be ideal. The first time I encountered the need was when I first started getting into Vintage back in 2004. I netdecked a storm combo deck that supported Force off of a meager fourteen blue cards, but the designer of the deck noted that Force could often be cast off of a Dark Ritual. While such a play is not ideal, I did learn that decks with lots of mana acceleration, such as City of Traitors, Moxen, Noble Hierarch, or Green Sun’s Zenith, are able to get away with running Force with fewer blue cards because they’ll be able to hardcast Force more often when it matters.

When a matchup consistently reaches the long game, two for oneing yourself to counter an opponent’s spell only makes sense if the card is otherwise dead, like a Sower of Temptation against a control deck. If you pitch relevant cards, like Brainstorm and Jace, you’ll probably regret it when the game reaches the point where your more powerful cards might’ve pulled you ahead. Now you’re stuck with a hand full of Sower of Temptations, and, in all that time, you could’ve found a spot to hardcast the Force anyway, netting an additional card towards the battle of attrition.

This is clearly different than where your opponent leads with a turn one Aether Vial, or goes for the Show and Tell. Here, simply staying alive takes priority, the games are more likely to be brutally short, and any old blue card will do. In matchups where Force of Will is most important, say against Belcher or other types of combo, casting Brainstorm when it’s your only blue card to pitch is a suicidal move.

Speaking of Brainstorm, it’s clear that a deck that stockpiles cards, like Landstill or High Tide, is going to have a much easier time paying for Force than a deck that dumps a hand full of cantrips, such as Tempo Thresh. Counterspell will chill in hand longer than Preordain, and you should plan your turns accordingly.

Finally, but not unimportantly, your sideboard should have a good mixture of blue spells for the matchups where Force of Wills are important. If you’re pulling a blue card against combo, say Sower of Temptation, you need a good blue replacement, such as Spell Pierce or Meddling Mage.

This is an advantage to running a deck with a higher blue count. A deck with twenty-two blue spells can lose seven in sideboarding and still have a consistent Force of Will, while a deck with only fifteen needs to manage its blue count more carefully. If sideboarding nulls the efficiency of Force of Will, perhaps the Forces were the cards you should’ve been pulling in the first place!

And at that, I’ll leave you. The Wescoe has yet another theory on how the game show host can scum people into choosing goats, and from his excitement it should be a good one.

Reach me in the comments or at CalebDurward@hotmail.com.

-Caleb Durward