it starts by their history. for example if the service is an old one you can easily look at some feedback on this forum or elsewhere to see what other people's experience with that service has been like. if they scammed any of their users, if they were gotten hacked, leaked any personal information of their users,... and a lot more. with a quick search you can easily figure out how much trust you can put in a certain service.
for instance an exchange service that has been hacked before and has poor customer support deserves a very small trust from traders.

then it is a matter of how much risk you are willing to take. for example the gambling site you mentioned, you can verify their fairness and history and then decide if you want to trust their honesty and for how much.