Hi, Im Kaci. I play too much Kingdom Hearts. If you've got questions, I've got answers.

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Which do you think is the better deal: 3 medals for 600 jewels or 10 medals for 3000 jewels? I'm asking cause I'm caught up with the story so for now the only way I can get jewels is through daily login. But I need stronger medals if I actually want to progress through the story without having to use jewels to continue.

This is a great question, and one that I’ve been grappling with for a long time.  The ultimate goal of KHUX in terms of medal pulls is to get guilted Epic and Premium medals.  This means getting seven of the same medal, which can be a real pain.  So figuring out the optimum way of getting epics is paramount.

First and foremost, the strong cards - Premiums - are only available during Epic Medal Carnivals (EMC).  This means you should NEVER spend jewels outside of those times.  EMCs also give guaranteed epics in the 10 pull, which is pretty important.

So let’s get into statistics.

For the 10 pull, you get 10 medals for 3000 jewels.  You are guaranteed two 5* and eight 4* during the EMC.  One of those ten will be an epic, guaranteed.  I believe this can take any of the ten spots.

From here on in, everything is theoretical.  

Fact of the matter is, Square probably has these things weighted against us.  I’ll prove this later.  But the statistics should still hold up because we are using an equivalent measurement of analysis: that is, we are evaluating the different draws based on 3*+, 4*+, and 5*+ meaning the same thing across deals.  There’s a chance that Square changes the draw tables/rates between deals, but I’m hoping they don’t hate us that much.

For the purposes of this analysis, we are going to assume there is an equal chance to acquire any medal in the pool.  Here’s our operational definitions:

3*+ means you can get any three, four, or five star in the medal pool (which right now is 215 medals).

4*+ means you can get any four or five star in the medal pool (which right now is 156 medals).

5*+ means you can get any five star in the medal pool (which right now is 97 medals).

Add all 11 premiums to these definitions because of the EMC.

38 medals are epic.  11 are premiums.  So you have a 49 of 108 (or 45.4%) chance or a 49 of 167 (or 29.3%) chance.  That’s two rolls at 45.4% and eight rolls at 29.3%. (.454*2) + (.293*8) = 3.25 epic medals on average.

But EMC gives a free epic!  That epic, if it takes the place of a 4*+ means you’ll receive (.454*2) + (.293*7) + (1.00*1) = 3.96 epic medals on average, or if it takes the place of a 5*+ you’ll receive (.454*1) + (.293*8) + (1.00*1) = 3.80 epic medals on average.  Since the chance of an epic medal taking the place of a 5*+ is 20% (2/10) then we have (.454*1.8) + (.293*7.2) + (1.00*1) = 3.93 epic medals on average

Remember how I said the draws were weighted against us?  Here’s the math on the Premium medals.  You have 11/167 (6.6%) or 11/108 (10.2%) chance, then 11/49 (22.4%) for the epic roll.  (.066*7.2) + (.102*1.8) + (.224*1) = 0.88 Premium medals on average.  That means you should get one almost every single 10 pull.  But you don’t.  So obviously the rates for Premiums are lower than 1:1.  The rates for Epics could also be lower, which could explain why you don’t get ~4 epics per pull.  But the lower ratio would apply to both the 600 medal pull and the 3k medal pull, so for the purposes of this discussion, it’s irrelevant.

On to the Daily Deal.  You get two 3*+ and one 4*+ for 600 jewels.  This means (after five days) you get ten 3*+ and five 4*+, totaling 15 medals.  Again, 38 epics and 11 premiums.  So you have 49 of 226 (or 21.7%) chance or 49 of 167 (29.3%).  That’s ten rolls at 21.7% and five rolls at 29.3%. (.217*10) + (.293*5) = 3.64 epic medals on average.

There’s no guarantees on Daily Deals so there’s no further calculations.

So it seems like the 10 medal pull is the clear winner!

But!  There’s other deals too.  Let’s take a look at the new Daily Summer Deal.  That’s two 3*+ and a 6*!  We already figured out that 3*+ during EMC has a 21.7% chance at an Epic.  What about that 6*?  Well, there are 108 6* medals in the pool, including premiums.  49 of 108 is 45.4%, or the exact same as a 5*+.  (.217*10) + (.454*5) = 4.44 epic medals on average! So technically that’s the best one right now, though it doesn’t guarantee anything and it’s more of a gamble.  Also, when the EMC ends, Premiums might get removed from the deal, which means that a lot of its worth fades too.

So let’s sum up:

~Only spend jewels during Epic Medal Carnivals!!
~If you’re new or really hurting for some medals, the daily deal has you covered for quantity, but not quality.
~10 medal pulls have a better ratio of Epic medals, which is your long-term goal.
~Often new medals are guaranteed in 10 pulls (see Pooh/Piglet/Owl or Musketeer medals) which can be helpful when going after specific medals.
~Sometimes you are guaranteed TWO epic medals from 10 pulls (see Roxas/Axel/Xion event, where you were guaranteed an Org. member /and/ another epic)
~Nothing is exclusive to 10 pull anymore, even if the odds are slightly in its favor

Good luck and have fun!

tl;dr 10 pull

<3 KCM