While saving the casino password on the browser maybe risky as someone (probably any family member) can access your computer and then access your account. In some cases, the password may be comprised / hacked, being saved online in the browser but it really depends on how much fund you keep in the gambling site.
For example, I do not keep much funds in the casino wallet and hence i prefer to save my login details in browser. I get the advantage that i don't have to manually type the password each time I login and it saves me time. At back of my mind, i know I don't put too much amount in the gambling site and till now, I haven't faced any bad situation

You can easily save your password offline, somewhere else rather than a web browser. It does not cost you anything while the lazy and favorite pracitce - automatic save password in web browsers - can cost you more. Even you say you don't plan to store big fund in any gambling account, it's still money and losing it is worse than don't lose it.
Remember that if you have this bad practice habit, you might become familiar with it, feel safe with it and in future perhaps you will lose big fund by this bad security practice.
I understand your stance, but perhaps you'd be interested to password managers as mentioned by notocactus? You still get the convenience of not typing manually and don't have to remember the particular website's password from a-to-z, while getting optimal security because many reputed ones are open source and provides better encryption of your data especially locally. They can probably make encrypted backups too.
Remember passwords is impossible if the only way is using a same password for all or many websites. It is another terrible security practice that is not recommended. Using easy memorable and repeated passwords or passwords with similar patterns is bad and need to be avoided as most as possible.