"Make it legal but very annoying" is an underrated policy option. And banning advertisement is the first resort in this line of regulation.

If there are no ads to tell you, you have to, first, be informed that sports gambling is a thing people do, then decide that it's a thing you want participate in, and then obtain information on how it's done. This adds friction. Friction reduces participation. But if you really want to gamble? You still can.

Taxing they daylights out of the advertising is another option.

That should push the shadier operators out of the limelight, though it would likely leave large-pot gaming (sports, Powerball, etc.) standing, at least for a while.

(I'd very much like to hear criticisms of this approach.)

So this is sort of a gotcha question, but I don't mean it that way.

Is it advertising when the announcer for a game talks about gambling? There's statements that obviously would be advertising, so the interesting thing is where and how to draw the line.

Not that hard at all. Is the message from the announcer paid for directly or is the casino a sponsor? Its an ad.

If an announcer just wants to talk about gambling, fine, I guess, but I really doubt that there are any announcers that would do much of that.

I mean, are they being compensated for saying so? The sports gambling industry did not invent advertising; there are already clear laws that govern this.

Agree. Gambling, smoking, drugs, and possibly weed should be legal, but just barely more preferable to obtain legally than illegally.