what games give the skilled player the greatest edge?

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No Limit Hold 'Em.

Duh.

But remember, long term, not short term.

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The OP specified limit games with community cards (why, I don't know).

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My local card room occasionally spreads a 6/12 fixed limit game that is 10 handed. You can't play 10 handed TDL or Razz, etc. I'm trying to figure out what game is best to pick, and also just some of the dynamics of different poker games.

Omaha High is widely played at this room, fwiw.

[SweetLuckyMe]

I'd say 7stud/8, then FL08

[AncientPC]

Stud 8/b or O8 give a greater edge to good players vs bad players, but very little edge with great players vs good players.

OTOH, HE gives a bigger edge for great players vs good players, and a smaller edge for good players vs bad players.