Take the first example, a pair of 10's against a 5. If you have that hand at a neutral count for $10 and stand with it, you'll win 84% of the time and lose 16% (counting pushes as a half win and half loss), for a net gain of 68% of your $10. If you split, you'll win on each Ten 63% of the time and lose 37%, netting 26% of $20. Since the first option makes more raw dollars, standing is your proper play.
Now if somebody else has that hand and is toying with the idea of splitting, your two options are either to get half of his split and win it 63% of the time -- or do nothing. Were he to split the hand on his own, he'd have a solid positive EV, albeit a reduced one compared to standing. You would just be getting in on his reduced profit.
It's the same with doubling 8 against a 6, with 9 against a 7, with 11 against and Ace, with splitting 9/9 against a 7 as well as a handful of soft hands that are incorrect basic strategy doubles, such as A/2 against a 4. They all win more often than they lose, although they do even better if played the basic strategy way.
There's a chapter on this in Bluebook II and it's also dealt with in Beyond Counting.
Woops! I'd better hedge on that last sentence. I'm not sure that Beyond Counting addresses improper basic strategy doubles and splits that still yield a positive net EV. Someone else may be able to comment.
