If he's up all night on the computer, I would put a keylogger on the computer he's using. That'll tell you soon enough.
WARNING, however -- what you might see is NOT for the faint of heart. Mine turned up "older woman younger men sexual positions" one night, and when I got the email report in my inbox, I had an anxiety attack. Literally couldn't breathe!
Maybe you could have the email report sent a trusted 3rd party? I dunno, just a thought. Most here will tell you "no snooping!" but I think you may need to protect yourself, even if it's "just" a gambling problem. Wiring funds to Mexico and finding Viagra wrappers are pretty big warning signs.