I figured out a way to see whether they do 3 nights on the birth year promo. Just go to the flexible dates calendar and try selecting 3 nights. If the hotel will do 3, it'll show up.
On 2 , it's not always a great deal. But for those of us baby boomers, the 3 night option can work out pretty well. If you are a millennial, it's clearly not so good.
And some places only offer it for Thursday through Saturday arrivals.