# Saheeli or Grindstone Combo: What Are the Odds to Get It In Draft?

In Round 10 at Pro Tour Aether Revolt, during the second Draft portion, I was paired against Jacob Wilson. In our first game, I seemed to have the upper hand, as I deployed a good curve of creatures while Jacob merely played Cogworker’s Puzzleknot, Leave in the Dust, and Reverse Engineer.

And then he untapped, played his sixth land, and showed me these 2 cards:

All right.

After congratulating him on assembling that combo, I looked at my sideboard and realized that green-white is not exactly known for its instant-speed interaction. I boarded in an extra 2-drop with the hope of rushing him, but I didn’t succeed. The second game went much like the first, and Jacob assembled the combo once again on turn 6.

The only thing I could do was laugh and snap a picture to commemorate the occasion.

Bizarrely enough, at the Pro Tour I lost more games to infinite Cats during the Limited rounds than during the Standard rounds.

Afterward, I wondered.

## How likely are you to face this combo in a Draft match?

Well, let’s do the math! There are 60 uncommons in Aether Revolt and 3 different uncommons per booster, so the probability of seeing a booster without a Felidar Guardian is 59/60 * 58/59 * 57/58 = 0.95. (I am disregarding foils for simplicity.) Since there are 16 Aether Revolt boosters per Draft, the probability of seeing a Draft without a Felidar Guardian is 0.95^16=0.440 or 44.0%. Conversely, in 56.0% of the Drafts at least 1 Felidar Guardian is opened.

Now, we could determine the probability that at least one Saheeli Rai is opened in any of the 8 Kaladesh boosters and then multiply the two probabilities together. The resulting number would indicate how often a Draft pool contains at least one copy of each combo piece. But that’s not a satisfactory answer to the question. After all, if a Felidar Guardian is taken by a white-black or white-green drafter, then it seems too unlikely that they can incorporate Saheeli Rai. A white-blue or a white-red drafter could probably make it work, but a double splash goes too far.

To analyze how likely it really is to end up with a Jeskai Copycat deck in Draft, I will make the following simplifying assumptions:

1. There are 3 white drafters per tableâ€”that’s a typical numberâ€”and they pick their second color at random.
2. Any Felidar Guardian that is opened will be handed to one of the 3 white drafters at random (each with probability 1/3).
3. Any W/U or W/R drafter who picked a Felidar Guardian will go all-in on the combo if they see Saheeli Rai in Kaladesh. But W/B or W/G drafters will ignore the planeswalker.

As a result of the first assumption, you will see:

• 0 W/U or W/R players with probability 1/8
• 1 W/U or W/R player with probability 3/8
• 2 W/U or W/R players with probability 3/8
• 3 W/U or W/R players with probability 1/8

To determine the number of W/U or W/R drafters who got at least one Felidar Guardian, we essentially have to convolute the above distribution with various multinomial distributions. I’ll spare you the detailsâ€”the calculations can be found in this Google spreadsheet. The results are as follows:

 Number of W/U or W/R drafters who got at least 1 Felidar Guardian Probability 0 68.59% 1 27.85% 2 3.55% 3 0.01%

Now let’s move to Saheeli Rai. Since there are 15 mythics in Kaladesh and one out of every 8 packs contains a mythic, you’ll open Saheeli Rai in one out of 15*8=120 boosters.

At a regular Draft on Magic Online or your local shop, you can expect that anyone who opens a mythic planeswalker will take it for value. So you’ll never be passed one. In that case, combining the 1/120 ratio with the table above yields the expected number of Copycat players per Draft: 0.0029. This means that on average in the long run, there will be a Copycat player once every 343 casual Drafts.

At the Pro Tour, however, it’s more reasonable to assume that no one takes Saheeli Rai unless they are a W/U or W/R drafter with at least 1 Felidar Guardian. So you’ll always be passed the planeswalker if one is opened. In that case, the expected number of Copycat players per Draft becomes 0.0226. This results in 1 Copycat player per 44 Drafts in expectation.

Since there were approximately 54 Draft pods on Day 1 and 34 Draft pods on Day 2, I shouldn’t even be surprised that someone was able to assemble the combo in Limited at the Pro Tour. It is still quite unusual that I lost two consecutive games to it, but these oddities are what I love about Magic.