Depends on what we are playing.
I am horrible at video games.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
It depends on the quality of the program. Some 'against the computer' games allow you to set the skill level. Some games are definitely 'winnable' if you know the trick. eg. NIM if you go first.