Favorite variation of chess?

No, Losers and Suicide are two different variants. In Losers Chess the normal rules for check and mate apply, you are not allowed to expose your King to capture, and resolving check has priority over making a capture. In Suicide the King is just a normal piece, and you can even promote to it (which is frequently the best choice). There is a subtle difference between Suicide and Giveaway in how they treat stalemate (in one case the stalemated side always wins, in the other case the one with the fewest pieces wins).

Actually it was already mentioned in the pros and cons thread in this forum section. And it is one of the (non-Chess) variants that can be played by the Nebiyu engine under WinBoard:

Fun game, but not a variant of chess.

...it's also a game of chance working with dice, what more similarity do you want?

What?  Chess is not in any way a game of luck.

Of course it has luck.  It is just like poker as the players keep their aces hidden.

No.  Chess is pure strategy.

You're doing it wrong.

Risk also involves diplomacy, which, except for offering and accepting draws, doesn't happen in chess.

I use tarot cards to analyse a chess position.  After that I use my intuitive sense to paint a picture using microsoft paint. 

What does that have to do with Risk being a variant of chess?

It's also a board game, and you can win by following your intuition, and by skill (i.e. reading tarot cards)

Anish Giri said Chess does have a little bit of luck involved: having the luck that your opponent gets distracted/annoyed/has a black out and makes a blunder.

Only if you play sober.

Risk and Chess are two different games.

Not according to Australia.

Laser-eyed shark BilliChess is another one of my favourite chess variants

Bughouse

yes

Dunny Chess