Do the chess bots on here change their strength?

I have been playing these bots on registered accounts logged in as well as being completely logged out. I noticed that the bots seem to play stronger when logged out, but when I log in I am having much more success. Specifically, offline Isabel 1600 gives me so much trouble I have to resign to end it and then I look at the moves with an engine. When I log in and play Isabel I might make a stupid move (between move 10-15 usually) take back, and then it's easy after that. Isabel will make 3 mistakes or one of them will be a blunder, and then it goes into self-destruct move. As long as I am careful at that point stalemate attempts don't work.

Other ideas include:

1. It adjusts future moves if you take back, maybe notching down to the second or third best move.

2. It gives a challenge relative to your accoount when logged in. Likewise, if you are 2000 not logged in, it doesn't know this from say a 1200 player.

3. Marketing ploy to get you to pay for membership. If you can beat the 4th highest in some rating range, you might pony up the money to get other higher rated bots. This makes sense because when you start an account you can get a higher rating easily than you are. Then you start losing.

4. It takes your game history into account, and like number 1, it will ratchet down if you take back.

I also noticed