From my perspective I can’t see how adding a 365 or any other number to your domain will affect you in the Google SERPs. It just doesn’t make sense for Google to pick a number and say that this domain isn’t relevant. The way Google works today is that other web sites link to your site and that counts as a vote towards your relevancy. If you have a gambling related site that is a PR6 then you will get good benefit from a gambling related link no matter what your domain. If you get a link from a site about cutting hair that is a PR6 then you will get little to no benefit from that site since it isn’t relevant. Google SERP position is based on a mathematical equation, and to just blanketly say that any domain with a number in it isn’t as relevant as a domain without a number doesn’t make sense.
More importantly is the understanding you need to have when buying a domain. My opinion is that it doesn’t matter what domain you register, it could be abcxyz.com and you would have the same chance of ranking for any given keyword as if you had gambling365.com. You can’t just buy a domain name these days with the word gambling in it and expect to show up in the SERPs. Ranking in the SERPs is all about the on-page factors and the off-page factors (ie: linking) that you have.
My recommendation is to register a domain name that is memorable that you can brand. Keyword optimization can happen for any domain name, you just have to know how to go about it.