1% house edge is the most common nowadays. But there are also a handful of dice sites which offer lower. Crypto-games, as you have mentioned is one. They have 0.5% house edge. I don't have a problem with the site. They even have a clean account here, as compared to other gambling sites that have red tags. Just like crypto-games, safedice is also offering 0.5% house edge. Megadice is also offering lower than 1% house edge. They have 0.9%. And if you are regularly following Bitsler's offers, you might chance upon a 0% house edge offer for a limited period of time.
Afaik Cryptogames has 0.8% House edge. I won't recommend to gamble on safedice although they offered you 0.5% house edge (kinda low from other gambling sites) since they still have problem with their site (admin goes offline since a year ago, their main account also hasn't active on here anymore).
That is the problem of some sites who are offering a lil bit lower house edge than others. They couldn't maintain the operations or let's say, they can't cope up with the competition. Even though they are offering lower house edge, yet, the sustenance is quite hard especially if you have no sufficient bankroll on hand. So I would say, sometimes it is better to play with known sites even if they are offering like 1%, but you know for sure when it comes to payout, you will have no problem at all.