~snip~
It's true in gamblers mindset they're not caring about the money what they are thinking is to place a bet and no matter what will happen they will keep doing it, and repeatedly keep betting their money, on that note, where you mentioned about sports betting, you are right both illegal and legal way of betting, gamblers will support the team that they think will going to win, placing their money in hope that they will be able to make some decent earnings out from the bets that they've made.
The important thing for them is that they can still bet, and lucky are those who have a responsibility in betting because they won't just waste their money and only choose to bet on sports or matches with teams they know. The rest, they won't bet at all rather than lose. Some can restrain themselves from betting on every game and only bet when they know the team. And they are called responsible gamblers because they don't have to bet on many games.
It can be classified as responsible gambling if you are in control of your gambling habit. I mean, if you carefully analyze your bets and assess both your money and time and are still doing a good balance of your time, then yes, it can be called responsible gambling, especially if you are betting on sports that you fully understand and can utilize the chances of winning.
Though there's no accurate outcome or accurate prediction, the chance is good if you know the game and the player or fighter that's playing.