Theres a thing about probability in math where you can compute how much probability you can have to win or posibly win in a lotto and I'd say you will not even reach 1% because there a lot of people who play lotto and also there millions of conjination or winning combination so even you could think of the possible combination in order to win lotto you will take a lot of tries and you may not even bet on all of it, so quit dreaming about winning a lotto with pure math equations or what, if you are the lucky one then you will most likely won a huge amount but if not then dont hope too much as there are millions of people that is also dreaming about winning a lotto in order to change their lives. It's okay to enjoy and play lotto as much as you want, but don't be too delusional and hopeful that you could win someday; it will only hurt you.
Probability as you said can be squared as odds, this is like in other words, odds tell us how possible it is for us to win a game, and how impossible it is as well, like we all know that the higher an odd is, the higher the risk of losing our money in that game, and the lower an odd is, the higher our chances of winning the game.
But still, probability does not remove the fact that winning and losing in gambling is remains that 50/50 chances, though are usually some factors that when considered and put into calculations, our chances of winning greatly reduces, and one of such factors is same as I have mentioned : odds.
But on the other hand, you are right and I agree with all that you have said; in general terms though.
Winning in lotto is not enough as it seems or appears, it's one of the simplest games to play in gambling (just guessing some numbers), but it's also one of the hardest to win.