I'd love to read an expanded explanation of the rule changes and peoples experience (positive or negative) with them.
Okay, I finally found the link to the website with the original A&A Chess rules. To be honest I didn't play this variant much, but it seemed apropos to the original post about luckless games so I mentioned it. From my limited experience I can concur with the inventor's comments: although it looks identical to normal A&A they really are very different games.
A&A Chess is about deciding how to position units to make them the most versatile: most able to contribute in an effective way on multiple fronts. It's about hiding your true attacking power by attacking with units based in multiple territories (i.e. using units your opponent didn't realize could reach) or by fainting one attack while intending all the while to make another (Calais v. Normandy?). In this way, the base strategies of Chess and A&A Chess are similar, although the mechanics have nothing in common except a board.
I've found that there are two main reasons why people don't end up liking A&A Chess:
My preferred answer to both issues is also suggested on the site and goes by the name Low-Luck Axis and Allies. This variant still grants a hit for every six attack or defense points, but allows players to roll a single dice against their remainders. In statistical terms, LL A&A tightens up the variance around the expected result (i.e. reduces the potential influence of the random dice rolls). For mathematical reasons best explained on another stack exchange site, LL's effects are most noticeable in small battles, where a couple bad rolls can make a huge difference.
My advice is that if you're frustrated with bad dice rolling and just want to smooth out chance, go for LL A&A. If you're looking for a complicated and well-nigh impossible to optimize luckless war game then go with A&A Chess.