"double dip" refers to getting points and airmiles on the same stay -
In your calculation you can get either the 500 "bonus points" or airline miles.

Also, just to get you started out right... Don't forget the.------

"AMEX CO BRAND ONLINE BOOKING BONUS" - Book your hotel at hhonors.com, using your amex, and pay with the same amex, and get another 500 points...

Also, when you get to "Gold" or "Diamond" status, you'll get another 25 or 50% of your BASE points added on top...

I can break out a recent $103 hampton inn stay to show you...

1035 base points
250 myway preferences points ( instead of water or chips)
517 diamond vip points
500 online booking bonus points
and possibly Another 500 double-dip points, or in my case 1/2 a southwest airlines credit...

2302 points AND 1/2 credit on Southwest total for me...

You could actually get 2802 points if you gave up the airline credit.

Parking could go either way, but most times it's counted towards points for me.

And at the end of the month you'll get another bonus for spending on the AMEX.. in this case
500 more points...

The only time you have to worry about room rate is if it's a "convention rate" - you still get points if you use
AAA or AARP discounts...
FYI: if you just got the AMEX read the fine print - it's not very well publicized, but if you stay at Hilton properties 4 times in the first 90 days of having the card they bump you to Gold status....

$20k in spending in the first year will also get you gold...