Theoretically this is false.
If this were true, there would be no rank climbing. In order to rank climb, you must have a greater than 50% win rate. Why?
Simple, no bonus stars at higher rank, so lets assume no bonus stars at rank 20.
Rank 20, 0/3 stars. Win 1, 1 star. Rank 20 1/3, Win 2, 1 Star, Rank 20 2/3, Win 3 Rank 20 3/3 stars. Win 4, Rank 19 0/3 Stars. Win 5, Rank 19 1/3 Stars. Lose 1, Rank 19 0/3 Stars. Lose 2, Rank 20 3/3 stars, Lose 3, Rank 20 2/3 Stars. Lose 4, Rank 20 1/3 Stars, Lose 5 Rank 20 0/3 stars.
50% win rate.
But what you are trying to say that your deck is going to get a 50% win rate just at different levels.
As in, I start at rank 20, win 20 games get to rank 15, and then at rank 15 I end up with a 50% winrate if i have a "good" deck, therefore I would stay at rank 15. Or move to rank 14 fall to rank 15 over and over based on a 50% win rate.
And then you are saying that if my deck sucks, I would drop to rank 23 (if possible) and stay there beating decks crappier than mine and losing to decks better than mine.
So your saying the bot is only as good as my deck, and my deck determines my rank.
That would be correct if EVERYONE was a bot and played with the same logic. Statistically this is WRONG, but I wont divulge.
Yes, having a 50% win rate is a GOOD rate for a bot, but its not mathematically proven that every deck will eventually fall to a 50% win rate.