Even though the Blessed keyword has been out since the Divine Order set was introduced, there isn't a lot of information about it. Most people simply regard it as an RNG-fest and are unlikely to give playing a Blessed creature or spell too much thought. Today, I'll bring in cold hard statistics to see how Blessed can actually affect the game. Let's go!

I'll be using @motpanda 's article here as the reference for the Blessing cards - he has compiled a list of all 24 possible blessings available to be selected: All 24 Blessing Cards in One image. Thanks a lot!

Summary

When you play a Blessed card:

• Probability of seeing any specific Blessing: 12.5%
• Probability of replacing the Sanctum cards: 23.9%
• Probability of getting 6 or more favor (under some circumstances): 72.3%

Basic Probability

This article will use a number of concepts in the realm of statistics, and I believe that it'd be useful to introduce some basic concepts here first.

• P(event): This represents the probability of event happening.
• P(X and Y) = P(X) + P(Y) if and only if events X and Y are independent. All calculations in this post rely on this concept of independent events; if not they wouldn't be valid.

Disclaimer: I'm no professional statistician, so there might be mistakes. I'll still try to do them to the best of my ability.

Probability of seeing a Zombie's Blessing

Let's begin with a simple issue. Let's find out what's the probability of drawing any one single Blessing when we play a Blessed card. We need to make the key assumption that:

• We assume that each card has an equal probability of being drawn. This may or may not be true, but for the sake of discussion, let's assume it is.

Let's say we are looking to see what's the probability of getting a Zombie's Blessing from playing a Blessed card.

Notation: ZXX means the event that a Zombie's Blessing shows up as the first card, 2 remaining cards can be any other blessing.

P(Zombie's Blessing shows up) = P(ZXX) + P(XZX) + P(XXZ)
                              = (1/24 x 23/23 x 22/22) + (23/24 x 1/23 x 22/22) + (23/24 x 22/23 x 1/22)
                              = 3(1/24 x 23/23 x 22/22)
                              = 3/24 = 12.5%

The probability of getting a Zombie's Blessing to show up whenever a Blessed card is played is 12.5%. This is true for any other specific Blessing that you are hoping to draw. We can also further verify this result by finding the probability of not seeing the Zombie's Blessing.

P(Zombie's Blessing does not show up) = P(XXX)
                                      = 23/24 x 22/23 x 21/22
                                      = 7/8 = 87.5%

Probability of getting 6 or more favor

Now, let's tune up the difficulty a little. Let's assume these conditions:

• Opponent has no creatures on the field
• You have 4 cards in your hand, including the Blessed card
• You have 3 unlocked mana gems

What is the probability of gaining 6 or more favor from playing the Blessed card?

Here are all the blessings that can give you 6 or more favor given the current conditions.

Notation: Notation: AXX means the event that one of these 8 cards shows up as the first card, 2 remaining cards can be any other blessing excluding the other 7 blessings. E is the event that at least one of these 8 cards shows up.

P(E) = P(AXX) + P(XAX) + P(XXA) + P(AAX) + P(AXA) + P(XAA) + P(AAA)
     = 3(8/24 x 16/23 x 15/22) + 3(8/24 x 7/23 x 16/22) + (8/24 x 7/23 x 6/22)
     = 183/253 = 72.3%

There's a 72.3% chance of drawing any one of these cards. For the sake of simplification, let's assume that selecting Unpredictable Blessing will always result in an action that gives us 6 or more favor. This also lets us know that there's a 27.7% chance that we won't be able to obtain 6 or more favor whenever we play a Blessed card under these conditions.

Similarly, let us verify this result by finding the probability that it does not happen.

P(XXX) = 16/24 x 15/23 x 14/22
       = 70/253 = 27.7%

Probability of replacing the Sanctum cards

Let's do one last calculation: what's the probability of getting a Blessing option that allows us to replace the Sanctum cards? Only two blessings can do this, the Rat's Blessing and the Gamekeeper's Blessing.

Notation: AXX means the event that one of these 2 cards shows up as the first card, 2 remaining cards can be any other blessing excluding the other blessing. E is the event that at least one of these 2 cards shows up.

P(E) = P(AXX) + P(XAX) + P(XXA) + P(AAX) + P(AXA) + P(XAA)
     = 3(2/24 x 22/23 x 21/22) + 3(2/24 x 1/23 x 22/22)
     = 11/46 = 23.9%

There is approximately a 23.9% chance to see either of these cards - not too shabby when you want to prevent your opponent from getting that pesky Vow of Power!

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I've always wanted to do something like this especially since there isn't a lot of data out on Blessed cards. Even though this information might not be immediately useful, perhaps it'll be able to stir up some statistically-inclined community members to do more deep statistical analysis on other parts of the game. Cheers!