Um, well, I have to say honestly, I would not put up with that for a minute. My EX-husband got very involved in online gaming- to the point where he got us thousands of dollars into debt, ignored me and our son and would stay up until 2 or 3 AM gaming, crash out on the sofa and go into work late because of his gaming obsession.
To me, anything OUTSIDE of real life should not be more important than your ACTUAL FAMILY. There is a difference between a hobby for enjoyment, like watching Sunday afternoon football or your college alma mater's games- and obsessively belonging to THREE fantasy leagues and betting on them?? I mean, come on, why three?
But the big warning sign to me is that he is putting this activity above spending time with you and your baby. Sure, a lot of men are immature and don't realize before having a baby how much time they take!
But- a lot of men GROW UP and grow out of their college-age obsessions! I'm sorry, but the person below who says 'you married him, he is not going to change' is wrong. Lots of people change when they have a child- they become more responsible and stop putting their own entertainment FIRST on the list of 'needs'. Your family should come first for him- or he shouldn't have a family and he could just keeping being bachelor guy!
I would sit down and have a serious meeting with him. Use specific examples of times when he has blown you and your daughter off for football or fantasy league activities. Tell him that all things are fine- in moderation. Ask him if he would consider going down to just one favorite league and also schedule SPECIFIC 'family time' during the week and weekend, when he will focus on his REAL LIFE and family- no checking scores, no tv or radio on, etc.
If he get belligerent about this I would tell him you want him to see an addiction counselor. Seriously, this kind of addicition, especially if he is actually gambling money, is just like an addiction to alcohol or smoking or anything else- don't kid yourself!
My first marriage is like a cautionary tale of how that kind of thing can ruin a family and relationship because the person who is addicted won't admit it and refuses to change his behavior- even after his wife left him and it ruined our finances!
Good luck- a lot of people will tell you this is no big deal. I know better- talk to him, get him to go to some counseling if he won't change his ways!!