I got thinking about profit and variance in Texas hold'em and pot-limit Omaha.
In hold'em I recorded results using hold'em manager. What I noticed, and others have reported this, is that all of the profit in hold'em was from Aces and Kings. I broke even on the rest of the hands combined.
I don't have HEM for Omaha so I have to speculate some. Suppose that for a winning player all of your Omaha profit comes from AA hands.
Now the AA hands don't win as often as they do in Omaha as hold'em. But there's a positive side. You'll be dealt AA again soon enough so you'll get more frequent shots to make your profit.
In hold'em you are dealt Aces 1 time in 221. Same for Kings. So you grind and expect to break even on 219/221 hands (99.1%) and all your profit is on 2/221 (0.9%). Losing with AA-KK is a disaster as they are so infrequent. It would seem then that hold'em results in a way could take longer to converge, as the profit hands are so infrequent.
In Omaha you get AA 1 time in 40 (2.5%). So you may break even on 97.5% of Omaha hands and get ahead on 2.5%. Losing with AA isn't so bad as you only have to expect to wait 39 hands for your next shot, instead of 99 hands in hold'em. So in that sense although there may be more deviations and swings along the way, results should in a way converge sooner in Omaha than in hold'em.
