It depends on the player's skill and the stakes they're playing in.
Make no mistake, a beginner will leak money because of a lack of skill, so it will definitely cost him money. I would guess a beginner to have a ROI of approximately -25%, so for each game they play it costs them 25% of the buy-in. For cash games the ROI can look a lot worse, I believe.
For instance, if said beginner plays $20 in tournaments a day, it would cost him $5 a day to play poker.
For lot of players with mediocre skills, it might less, but still cost something.
For a player at the top 60-70% of the player pool, it might costs him nothing as he is break-even -- he is essentially just "working" for the poker site, generating rake for them. Poker sites love these types of players.
The good thing is that to learn to play poker well it doesn't have to cost a player any money, as they could start learning with play money, freerolls, and slowly move into the real money micro stakes.
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