I wish to make a math model for predicting users clicking on context advertising.
Math definition: Let $X$ be the set of users, and $Y$ be the set of adverts. We make a mapping $F: X×Y→P$ that should map a concrete user and concrete advert to the probability that this user will click this advert.
Note: User has only one advert per page and s/he can click or not click. This means that the probability that user clicks the advert is $\frac12$ and there is nothing to predict. But my model will use a lot of information to predict a click. Should I use the term "probability"? Maybe I should say that $F$ maps to $[0;1]$?
Thanks
"User has only one adv. per page and he can click or don't click. This mean that probability, that user click adv. is 1/2"
No, the user is less likely to click on the advert than to not do - they aren't equally likely which is your suggestion.
Anyway to make any kind of prediction you need stats and to further make a prediction based on a particular user you need a lot of stats. If you think "F" is just something I can tell you I think you're out of your depth