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Most likely students are getting their allowance from their parents and if that was the case, then they are not allowed to use the money that is entrusted to them because it's not really appropriate for children to waste their money just because they are getting it freely from their parents. They don't understand how hard was it to earn such an amount of money and they are just wasting it overnight and in the morning they ask for more. That's why they shouldn't be allowed teenagers to play and they should be strict with it.
In the OP's story, this teenager is gambling with his savings. plus, the weekly money he gets from his family. In fact, this teenager is only 18+ and doesn't understand many things about life. even at his age, gambling was legalized. however, ideally he would be better off doing other activities. In the end, this teenager relied on the weekly money he received, with the alibi that he had savings.
I don't want to judge someone by their gambling, but at an age that is still very vulnerable and unstable, the side effects will be very bad for their development. At this age, it will be difficult for us to know whether this boy is truly responsible with his gambling. let alone those who are still teenagers, we as adults have quite a hard time dealing with issues of responsibility. in particular, those dealing with gambling. which in the end, as you said. this teenager has the potential to squander the money he gets from his weekly allotment. they have the potential to spend money in one night on gambling, at a very young age, self-control, understanding and responsibility, unlike what mature men understand. So, in OP's story, it's only natural that parents feel worried about their children.