I had a site based around horse racing and sports men and women that cheated - all true and proven in court.

However around a month ago after 1 and half years of operating they switched off teh adsense to the site.

So go careful.

better ask AS team

I always found this rule hard to understand, because there are plenty of gambling, casino, and betting ads on Google's SERPs. You can obviously use AdWords to advertise gambling sites, but only on Google and not on publishers' sites (unless I'm missing something).

That games are just for fun.
Players don't earn money or something.They just spend some time playing online.

And this rule is for whole site or just for pages with casino related content?

Ask adsense, and save the response. Nothing anyone says here matters one little bit.

As to why they allow ads for certain categories, but don't allow us to have that sort of content, I assume that it is because advertisers in sectors NOT related to that content might object to having their ads associated with certain kinds of content.

Here is a detailed explanation about content policy for adwords.:
[adwords.google.com...]

At Gambling section it say:

Gambling
Advertising is not permitted for online casinos, sports books, bingo, and affiliates with the primary purpose of driving traffic to online gambling sites.

My pimary purpose is fun.
I don't send any trafic to nobody.

What do you think?

That's for AdWords, not AdSense. It's saying that you can advertise casinos etc..., which it strange because there are plenty of casino ads on the SERPs.

What do you think?

First of all, that is from the AdWords TOS and not the AdSense TOS, which has different guidelines.

Secondly, even if you do put the code on your page it will probably trigger a filter which will only display PSA's.

Finally, you should take BigDave's advice and ask Google directly.

My personal opinion, there is no way they are going to allow it.