It might be useful to see how the Collatz sequence differs from a coin toss. Coin tossing can run forever and eventually will result in a constant number of heads. Also the odds of heads and tails is even.
To capture the difference, starting at one for heads multiply by 1.5 and tails divide by two. Collatz is also not infinite and terminates when the result is less than one. This model corresponds to the linear case showing that Collatz will eventually always terminate.
The Seed value in a Collatz run has the ability to juice the run length. Certain runs have more odd than even steps depending on the Seed. I’ve not thought about how to model this, but it seems to be a relevant missing piece. With the right model it would be easier to simulate the sequence on a computer rather than running the actual sequence.