How to make both Trading and Flair worthwhile

TL;DR: You can make a fair and vibrant late-game economy by only allowing cards to be traded if they are of the same rarity and have flair (and the flair is lost in the transaction).(Warning: Math Below)The Problem
The issue isn't the trading, it's that what is being draded is obtained for free so the only value is scarcity, and not just from the rarity. The issue is this:

• You have a 2.611% chance of getting a 2-star card in a given pack. But that's ANY 2-Star.
• Your odds of getting a particular 2-star card in a pack is 0.261%
  • (except for Mewtwo packs which only have nine 2-stars, so your odds are 0.290%, which already makes them slightly less valuable, all things equal).

This is why trading cards of equal rarity (all the way up) would kill the game economy: If I can trade my random 2-star for the 2-star I want, the ease of getting the one I want just got divided by 10. Let's account a little for some being more popular than others and say there's only half a chance I can make such a trade (when I have the more desirable card in general but not the one I want), that's still cutting the effort down 5 times.

• Instead of it taking 266 packs to have a 50.117% chance of getting that 2-star you want,
• it would now take a 53 packs to get a 50.169% chance of getting a card you could likely trade for it.

Assuming an average of 3 packs a day, that's a 71 day difference. And that's just for the median of luck. When you consider how long it would take to definitely get one, it's a much bigger deal.

• It currently takes 1,146 packs to have a 95.003% chance of getting the specific 2-star you want,
• it would only take 228 packs to have the same odds (with the same trading assumptions above).

That's a difference of 306 days. This is why trading is such a tricky issue.There are multiple solutions to this, but the simplest is to just tax trading. By making you pay a finite resource to trade, it offers flexibility while balancing the game economy. The most mathematically useful resource to tax would be cards themselves, directly linking to the probability of drawing. In other words: to trade your 2-star card, you'd need to also burn a number of 2-star cards. Of course, the problem here is how unfair it feels to give up multiple cards, not to the person you're trading with, but as a tax.The Solution
The game already has an elegant solution baked in: only allow people to trade cards they have a Flaired version of (along with the flair) and then lose the flair when traded.

Psychologically, the person is only trading one card for one card and all they are losing in the trade is something that has no mechanical value in the game (the flair).

Mathematically, this would require 4 copies of a 2-star card and require trading 2 of them to get 1 card in return. Let's break that down:

• You need 2 identical cards before you can obtain flair, then you have to sacrifice a 3rd; to keep the minimum of 2 left, that would require a 4th to trade.
  • It takes 580 (of the same) packs to have a 50.140% chance of getting 4 of any 2-star card, more than twice what you'd need to just pull one, so it makes a pretty big barrier to entry, but look at what it does on the tail of the curve.
  • It takes only 987 packs to have a 95.005% chance of getting 4 copies of a 2-star card, notably less than the 1,146 needed to have similar odds of pulling a given one on your own.
• While that may seem too far off at first, it rewards the push for late-game progression because you only expended 2 of those duplicate cards (1 for the flair and the other for the trade).
• Let's assume your first four 2-star cards were somehow all duplicates and you trade one off for one from a different set/subset. Just for having 2 of the same card in one subset means that:
  • You only need 453 packs to have a 50.143% chance of pulling either 4 of a single, new 2-star or 2 of the 2-star you already have 2 of.
  • You only need 865 packs to have a 95.014% chance of being able to trade again.
• If you end up with 4 identical copies of 2 cards, those odds beat the odds of naturally pulling the single card you want, even at the median:
  • 265 packs giving you a 50.163% chance of getting a tradeable 2-star.
  • 605 packs giving you a 95.037% chance of a tradeable 2-star.
• And these are all very conservative estimates, not factoring the other 2-stars you would accumulate while trying to get your desired 2-star or a tradeable one.
• This also doesn't factor in cards people wouldn't want to trade with, but that's intentional, as I'll explain now.

Maybe the greatest benefit of this is to the game economy. If cards are only traded to either use or complete collections, there will always be cards almost no one wants to trade because of their superior value and cards no one wants to trade for because of their low value. That leaves the trading market only dealing with those in the middle, leaving for a lack-luster experience and disappointment when you get a "junk rare." Even if everyone were trying to complete their collections (which is far from the case), this would incentivise so many cards evenly as to have little effect in the highest tiers of rarity where most players are missing a lot of cards. But if you give cards the secondary value of tradability only with certain quantities, this changes things significantly.

• People will have far fewer tradeable rare cards (that is, cards they already have at least 4 copies of) than those they need for their collection, and those are the most valuable for them to draw because they can be traded for a number of other cards.
  • At the same time, its value to trade is much higher than its value to spend as an extra flair or to hold onto, so players are incentivized to trade even the best cards if they're lucky enough to have duplicates.
  • On the other hand, while pulling a "junk rare" would be even less valuable if it's your 2nd copy of it (not completing your collection or tradable, yet), it would be MORE valuable to trade for because every rare card you collect 3 copies of, the 4th is tradeable.
• In other words, this method subtly raises the incentives for trading more desirable cards for less desirable ones or the same rarity.
  • This also has a cascading effect because just that fact makes pushing for 3 of every high rarity you can a worthwhile goal and thus makes even those junk cards more valuable. It's like creating a post-game dex.

Emotionally, this even creates a feedback loop because if not all cards are equally tradeable, but all increase the tradability/value, no card is ever complete junk, and yet you still need more, keeping the luck aspect that is so exciting.  It's the kind of tricks that make gambling addictive but applied to the free part of the game.

Finally, the elegance of this system even works down to the single diamond level as you can collapse that market pretty easily as well (though it's far less of a loss, given that you get most of the cards you need there pretty early and the Exchange system helps with the others). That's because you'd need 6 1-diamond cards to trade for another due to higher flair costs (which the community is already used to). If you really wanted to, you could also make it necessary to trade the last available flair for a card, which is available on the 1st flair for 4-diamond and star cards but you have to buy many flares to get to for lower tiers.

Please Note: My math here is a bit simplified (for instance, I treated the odds of pulling a card from a pack as a single number rather than looking at the odds of pulling from each card individually). Where possible, I tried to estimate on the side that didn't support my point, just to me illustrative.