http://www.wizardofodds.com/blackjack - See "Bad Strategies"
Look at that and it NEARLY answers this situation.
With out doubling or splitting there's a 5.48%
Intuitivly you would think your idea would give you better than 50-50 odds. The MAIN reason that I know of that this is NOT the case is that the dealer takes his turn last in play order.
Therefore:
- If you bust the dealer wins
- If the dealer busts you win
- If you BOTH BUST, the DEALER WINS!!!
I would imaginine doubling and splitting correctly will eat up about 1/2 of that 5.48 percent but to even the odds as much as possible you still have to play the rest of the basic strategy table correctly.