Your question about profits - when to take them. As you mention, Option Alpha talks about profits at that 2/3rds level. For myself, I use that 2/3rds level for most positions (more like 90% on really long positions). My thinking is that I can realize those gains, free up the backing for a new position, as well as remove the risk that shares suddenly move drastically against me (which has happened - in post split dollars a >$40 share price move on expiration day).
You mention closing at low IV - generally speaking, closing at low IV is a GOOD thing for you as an option seller.
The questions I ask myself when looking at closing a position:
1) Is there a different position I would rather be in? This is usually focused on a different position with better day to day profit potential. In your example, you've got a $3 option that started at $10 with 2 weeks remaining. You can (upper end) earn $3 more over the next 2 weeks. Is there is a different position you would replace it with right now with a better risk / reward profile?
If yes, then this is easy. Close and open the new position.
And sometimes there isn't! I've ridden out positions like yours to earn that last $3 because there wasn't a 'better' position I wanted to be in. Because heck - $3 is better than nothing
. Just think of the current position as a new position - knowing what you know now, would you open that $3 position today for expiration in 2 weeks?
2) Do I want out of the current position because I see an event coming that could push this against me? You mentioned your view that IV is low right now. In an option selling strategy, any time you can sell at high IV and buy to close at low IV, that is good for you. You'll sell relatively high priced stuff, and then buy it back at relatively low priced.
If I want out for risk management, upcoming event, etc.. - then I vote for ruthless. In this case (getting out to avoid a freight train I foresee arriving soon) then I'm out immediately and cheer for my 2/3rds profit.
3) Close a current position at a good spot, to get ready for a new position 'soon' that you believe will be better. This sounds reasonably close to what you're thinking, in which case how much risk do you want to take on to earn some of that last $3, before closing to be ready for the new position?
BTW - in this situation, I've cheerfully closed at a 50% profit. Either for getting ready for a new position, OR because I've already ID'd a position I would rather be in.
Some other thoughts. You mention that this is your first covered call. An important characteristic I optimize for is my "sleep at night / stomach churn" quotient (stress, or risk). If the position is high stress for you, then close it. I believe that important to this strategy, executed over many trades over time, is that it needs to be something you can readily repeat over many trades over time. Individual trades won't always be low stress, but the more you can make them low stress, the better you'll like it. (Or at least, this is true for me).
Or another way to think about it - if you think you'll be doing this regularly, then optimize for choices that enable you to continue doing this over many trades.
( I think my own bias, given the circumstances you've described, is pretty clear. But I'm not you - hopefully these are some useful things to think about ).