10 vs 10 Double

[Renzey]

You (and Fred) are oversimplifying things. If the dealer gets a low card, he'll draw again and may get a better hand. If you double and get a low card, you can't draw again. There are also some issues related to the dealer peek. You have a different chance of drawing an ace on your 10 than the dealer.

Your inability to take a second hit after you double, and your better chance to catch an Ace than the dealer are just integral "piece-part" components that all add up to the bottom line which says you win 51.3% of the time if you hit and 49.8% of the time if you double (counting pushes as a half win and a half loss). Those are the two numbers that tell you what to do.