Keep playing the same game again and again also can be addictive so keep changing the games and also the bet amount to make ourself refresh and not get addicted to that.
When you are addicted, your bet amount is way higher than what you can afford to lose, and how often you gamble doesn't count anymore as you can loss a big amount of money in just one bet, especially in sports gambling.
Addicted gambler usually focus on one gambling game which they think they can win, and because it's really challenging, they also challenge themselves putting an amount that would put much excitement that could affect their financial status in life.
You are right, addictive people will not bother much about how much they are losing, they will bet the higher amount for higher rewards but there focus will be on one game. Because they already know when to exit from the game they desired.