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I thought that the extent of one's edge and the va****** are inveresely correlated.
Not really. Variance and one's style of play have a strong connection, but some of the best players play a very high variance style. Some marginal winners play a very low variance style. In certain games a strong player might also play a very low variance style (like a live 1/2 nit). If you are taking a lot of aggro lines, building big pots, triple barreling off some of the time, there is the potential for things to go very, very bad and the potential for things to go very, very well. Wheras if you just nut peddle and trap, you will probably lose a ton of blinds, lose a ton of small pots, lose a few big pots and win lots of big pots. So it will be a very low variance style.
There is a stronger connection between winrate and probability of not being stuck after x hands, but that is not the same thing as variance.
Omaha is higher variance because there are a lot of multiway allins and multiway pots, and because your opponent tends to have more equity when you get the money in. Even if you cooler someone they will usually have an extra 5-10% from backdoors, and then there are all the flips like big draw vs strong made hand. The games also play much deeper, exasperating the feast or famine effect.