Mathed Up: Once Upon A Time

This is probably the largest statistical dataset we have managed to jam into one article to date. Once Upon A Time is such a simple card at face-value. An effect we have seen before but never for free. It comes out to an odd hybrid of a Leyline and an Ancient Stirrings. This hybridization really complicates the effect and leaves a ton to be calculated. Today we will cover the odds of opening with one, drawing into one, finding lands, and finding creatures in various builds. It is a lot to take in but we have done our best to condense it for you.

Opening Hand
Well let’s start at the beginning. Obviously this card is at it’s best when it is in your opening hand. The probability of this occurrence depends on how many copies you run. These are the probabilities that you will find at least one in your opening hand:

Four Copies: 39.95%
Three Copies: 31.54%
Two Copies: 22.15%
One Copy: 11.67%

I must say that beginning two out of every five games by digging five deep for a creature or land sounds great. Running three copies is reasonable as well; it gives you almost a third of your games that boost. Even two copies seems nice if the deck is tight for slots. The sharp decline down at one copy is just to steep for me though; you likely have better options available.

How to Interpret the Following: We do not look at the exact number of your cards in your library as this varies from hand to hand. For example, sometimes your opening hand from your twenty-four land deck has four lands so the probability is looking at twenty lands in a fifty-three card deck. Sometimes that hand has two lands so the probability is looking at twenty-two lands in a fifty-three card deck. It varies greatly so it is not particularly useful to know the exact numbers. Instead, we run the numbers for the full count of lands in your full sixty card deck to give the true average. Sometimes your opening hand has more lands so the probability is actually lower, sometimes the opposite. For all of these, with a large enough sample size, your hands will be true samples of your deck and the fifty-three cards left in it will be a true sample as well. With these numbers, you can build your deck with knowledge of the true average.

Drawing Into It
They are somewhat like Leylines in that we want them in our opening hand but would rather not draw into them. However, drawing into these is much better than drawing into a Leyline; more relevant effect in the lategame and half the mana cost. Still this is not the ideal outcome. The more copies you run, the more likely you are to open with it but you are also more likely to draw into it as the game progresses. When looking at these probabilities keep in mind that these are the odds when all copies are in your deck. So the odds for four copies means you kept a hand without OUT. But if you play four copies and got a free one at the start, you are actually looking at the odds for three copies. The odds of drawing at least one by each draw are as follows:

Four OUTs
One Draw: 7.55%
Two Draws: 14.65%
Three Draws: 21.35%
Four Draws: 27.64%
Five Draws: 33.55%

Three OUTs
One Draw: 5.66%
Two Draws: 11.10%
Three Draws: 16.33%
Four Draws: 21.35%
Five Draws: 26.17%

Two OUTs
One Draw: 3.77%
Two Draws: 7.48%
Three Draws: 11.10%
Four Draws: 14.66%
Five Draws: 18.14%

One OUT
One Draw: 1.89%
Two Draws: 3.78%
Three Draws: 5.66%
Four Draws: 7.55%
Five Draws: 9.43%

So the first thing I notice is that if you run a full set of OUT, the odds of opening with it are greater than odds of drawing it by Turn 6 on the play. The thing is, unlike a Leyline you probably actually want to topdeck an OUT on Turn 6. That is the point in the game where you have the excess mana to hardcast OUT and whatever threat is lurking in your top five cards. So it will usually only be frustrating if you draw it in the first four turns; too late to be free and early enough that you care about the mana cost. However, the cards is not a miracle. You do not have to play it right when you draw it. If you have other action in hand, you can continue to play that until you are flooded enough to want to hardcast the OUT. So when it comes to topdecking OUT we need to keep in mind that it happens less often than free copies do. If you draw it late the mana cost usually is not relevant and if you do draw it early you likely have other action in your hand anyways. Again, remember that the odds above are for all of your copies being in your deck. If you begin the game with a free one, the odds of drawing one will be more like what you see in the “Three OUTs” bracket.

Number of Hits
As a card that digs up lands and creatures, OUT statistically improves as you run more creatures and lands. This had led to some players straight cutting two lands and two creatures to jam a playset. Folks can do as they please but they should know that they are making the card weaker in order to play it; a bit illogical but possibly necessary. This a sample of deck compositions to demonstrate how they impact the power of OUT:

30 Lands + Creatures
Whiff: 2.6%
1 Hit: 15.1%
2 Hits: 32.3%
3 Hits 32.3%
4 Hits: 15.1%
5 Hits: 2.6%
Weighted Average: 2.50

35 Lands + Creatures
Whiff: 0.9%
1 Hit: 15.1%
2 Hits: 25.1%
3 Hits: 35.9%
4 Hits: 23.9%
5 Hits: 5.9%
Weighted Average: 2.91

40 Lands + Creatures
Whiff: 0.3%
1 Hit: 3.5%
2 Hits: 16.3%
3 Hits: 34.4%
4 Hits: 33.5%
5 Hits: 12.0%
Weighted Average: 3.33

45 Lands + Creatures
Whiff: 0.1%
1 Hit: 1.1%
2 Hits: 8.2%
3 Hits: 27.3%
4 Hits: 40.9%
5 Hits: 22.4%
Weighted Average: 3.75

50 Lands + Creatures
Whiff: 0.0%
1 Hit: 0.1%
2 Hits: 2.7%
3 Hits: 16.1%
4 Hits: 42.2%
5 Hits: 38.1%
Weighted Average: 4.13

I assume most decks will play about forty-five hits and an average of 3.75 choices in your top five cards is an awesome number of options to have. Even at thirty, which is quite low, we are looking at half of the cards being options on average. This is a seemingly low number of hits but even here, you are whiffing just 2.6% of the time. The thing about a whiff is, sure you would rather have hit something but you likely just bottomed five cards that you did not want. So your draw steps will be greatly improved going forward.

Number of Lands
The simple fact is that creatures are not lands and vice-versa. When you fire off an OUT, you are usually searching for either a land or a creature depending on what your hand looks like. Your odds of success should be factored into your mulligan decisions then. To help with the land side we have a subset of common land counts to help out.

18 Lands
Whiff: 15.6%
1 Land: 36.9%
2 Lands: 32.3%
3 Lands: 15.4%
4 Lands: 2.4%
5 Lands: 0.1%
Weighted Average: 1.58

20 Lands
Whiff: 12.1%
1 Land: 33.5%
2 Lands: 34.4%
3 Lands: 16.3%
4 Lands: 3.5%
5 Lands: 0.3%
Weighted Average: 1.67

22 Lands
Whiff: 9.2%
1 Land: 29.7%
2 Lands: 35.7%
3 Lands: 19.8%
4 Lands: 5.1%
5 Lands: 0.4%
Weighted Average: 1.83

24 Lands
Whiff: 6.9%
1 Land: 25.9%
2 Lands: 36.1%
3 Lands: 23.3%
4 Lands: 7.0%
5 Lands: 0.7%
Weighted Average: 2.00

26 Lands
Whiff: 5.1%
1 Land: 22.1%
2 Lands: 35.6%
3 Lands: 26.7%
4 Lands: 9.3%
5 Lands: 1.2%
Weighted Average: 2.17

The great news is that even at just eighteen lands, you are usually going to hit a land. Admittedly, these odds get even better if you keep a no-land hand but you almost certainly should not. But they do tell us that one-land hands are relatively safe. Even at eighteen lands, there is an 84.4% chance that you are going to rip a land on average. Even if you whiff, you are now five cards closer to finding one with your draw step.

Number of Creatures
While lands are neat, you should still be building your deck to have a proper number of them. Many of your opening hands will have the proper numbers of lands and that means you will fire off OUT in search of a creature. To help you figure out your odds of success we have a subset of common creature counts.

10 Creatures
Whiff: 38.3%
1 Creature: 42.2%
2 Creature: 16.1%
3 Creature: 2.7%
4 Creature: 0.2%
5 Creature: 0.0%
Weighted Average: 0.83

15 Creatures
Whiff: 22.4%
1 Creature: 40.9%
2 Creature: 27.3%
3 Creature: 8.3%
4 Creature: 1.1%
5 Creature: 0.1%
Weighted Average: 1.25

20 Creatures
Whiff: 12.0%
1 Creature: 33.5%
2 Creature: 34.4%
3 Creature: 16.3%
4 Creature: 3.5%
5 Creature: 0.3%
Weighted Average: 1.67

25 Creatures
Whiff: 5.9%
1 Creature: 23.9%
2 Creature: 35.9%
3 Creature: 25.0%
4 Creature: 8.1%
5 Creature: 0.9%
Weighted Average: 2.08

30 Creatures
Whiff: 2.6%
1 Creature: 15.1%
2 Creature: 32.3%
3 Creature: 32.3%
4 Creature: 15.1%
5 Creature: 2.6%
Weighted Average: 2.50

These probabilities tell me quite a lot. I have seen OUT recommended for threat-light decks that would like to see those threats in their opening hand more often. But looking at the 10 and 15 creature brackets, I cannot recommend it. The odds of whiffing are just too high. You really want to hit at least one most of the time but it can be beneficial to to hit more on average. Simply put, the more creatures you run, the more options you will have on average when you fire off an OUT.

Key Takeaways
-The more OUTs you run, the more free OUTs you get
-The fewer OUTs you run, the fewer OUTs you draw into
-You are more likely to open with OUT than to draw it in the first five turns
-It makes for a solid topdeck in the lategame when mana is abundant
-Most decks that run it are looking at 3-4 choices per OUT
-Even an 18 land deck will OUT into a land about 85% of the time
-Even a 20 creature deck will OUT into a creature about 90% of the time

Wrap-Up
That was intense but I think we have covered all of the general relevant statistics. It is an interesting case in that the effect is simple but gauging its power level is complicated. To be honest though, I am not sure how to feel about the results. I have already cried from the rooftops that the card is very powerful. Now I have gone through the calculations and I am even more impressed. How do you feel about it though? Is it being forced into too many decks? Please share your thoughts with us in our discussion group. Or if you would like to take a swing at writing content for the site you can contact us directly here. We will be back tomorrow with another article for you to enjoy. Until then my friends.

 

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