Spin, you're spoiling the fun!
I know the answer, and you know the answer, but I was hoping the original poster (OP) would respond.
Anyway.....
To elaborate on what you said, the more ITM a call is, the higher the delta, and delta is a way of calculating how much the call will move relative to a $1 move in the underlying stock or index. A delta of 0.80 would mean that, (all things being relatively equal, and they won't be exactly) that the option will increase in value $0.80 when the stock moves $1.00.
Now in real life, the reality is that options never exactly track the underlying as the delta predicts, but they will more or less follow as predicted.
Playing deep-in-the-money calls has one drawback which is the wide bid-ask spread that you will be exposed to. DITM options are often thinly traded, as well, which is also tied to this. On the other hand, if you have a comfortable feeling about a particular stock, you can use them for moderate leverage. DITM are not suited to short term holding unless the stock moves rapidly upward because you will have to pay up to get in and pay out to get out.
On the other hand time decay is less of a factor with DITM calls, so holding them for a reasonable period of time is not going to slowly bleed you down. You'll only lose significantly if the stock goes down, which is the same risk that stock holders face, too. In fact, if the stock drops dramatically, you will definitely lose less, because the deltas will decline as the stock price drops down toward your strike price. It is still losing, however..
Hopefully, this is helpful to the OP.
Merry Christmas, Spin, and everyone!