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@SouthpawHare The unspoken problem here is that after the initial fall and break, you now have (very likely, anyways) new spikes. Either way, it's a point where the HP mechanics and the story don't really support each other.
Hello Baergren! We recommend that posters wait at least a day before accepting an answer: this site is used and seen by people around the world, and it takes time for people to see new questions and vote on them. A little delayed gratification ends up with better answers, and also helps the whole community help you.
@IronWaffleMan Yup, it's all about knowing what kind of game you're in. Although I am surprised that you accepted an answer so quickly: SE works best when you give it a few days. Oh well! Have fun, and good luck with your "all-talk" build.
@Erik I have made such a campaign (with random encounters) before, but I did not mess with a normal distribution or with a deck of cards. I have had a DM use cards for encounters before, but I never knew if it was on a bell curve or not: I suspect this solution will yield a very similar experience.