Make trials cards reset themselves.
Mercy cards will reset automatically after 2 losses.
Ferocity, Wealth, and Confidence reset themselves after 1 loss.
Count rounds won outside of the card for the purposes of the 50 round wins rewards or whatever it is. (make it to where resetting a card doesn't reset this)
OR move rewards back to bounties and have the bounty turn-in reward you the drop.
Finally, going flawless, Mercy card or otherwise, will lock the card allowing you to continue playing regardless of loss for more rewards in the flawless pool. If you wish to reset, you turn the card in (for another adept chance as is currently) and then buy another card.
Yes, this will cause pain points for people that like playing with losses on their cards. A worthy sacrifice.
EDIT: Dropping the flawless pool and doing nothing else basically puts us in the same system we're in now, in case that's not obvious. The only difference being instead of only having resetters to deal with, you'll have them plus all the people that already play in the flawless pool.
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If I lose my mercy in the first couple of games I reset my card because I don’t want to be going into my 4th, 5th, 6th and 7th match without a mercy and so do a lot of other players. If they do as you propose all that would happen is people would throw their next game. Now this is fine if your in a fireteam and everyone consents to it. But if your running and decide to do it, especially in the solo queue then it will be far more toxic than the current environment. If you want to get rid of card resetting either get rid of the mercy card or the flawless pool. Neither option will please the people complaining about card resetting though.