winning percentage

[Mr. Ratface]

Lets assume we are in a six handed game playing holdem except there is no betting on any streets, the cards are dealt face up and all 5 cards are flipped right away with all six players in the hand. If this were the case it would be accurate to say that you should expect to in, on average, 1 out of six hands.

My question is if we were playing in a six handed game of limit holdem, but the standard betting applies and players may choose to call the big blind as they please, is it still correct to say that I should win 1 out of every six hands? I suspect this may be hard to calculate as there are too many uncertain variables but please enlighten me.
Also what are the odds of only winnign 1 in 40 hands or 1 in 60 hands in a six handed table?