If you want a suggestion, since I'm a huge fan of user choice wherever possible, give users a setting with 3 options, where they can choose what the cards should do with the antibot
- reduce frequency
- no change
- increase frequency

If you want a fancy suggestion, leave it as it is, but let the cards add to the antibot reward, you know, pay 1 card per % from the cards more or pay some other extra in antibot reward.

..... and let us know when you're done with that, because most users will rarely check their account settings.