The handicap in Go [1] works amazingly well. I have had enjoyable games with dan-level players despite being at best conversant at the game.
That said, I've also enjoyed such games immensely with no handicap, despite no prospect of winning at all. In most games you can have some partial success and psychological reward despite losing the game.
The thing that makes go fun for me even while losing is that if you lose the whole game you've still got a lot of smaller skirmishes that you've either won or learned from. Losing a skirmish in go makes it very easy to go "Well what should I have done differently here?" and come up with a good answer.
It's different from a game like risk in that way. If you lose a skirmish in risk there's basically nothing you can learn from that since the amount of random involved just obscures any influence you have yourself. At the end of a game of risk I'm sat there having no idea what I did wrong, and no idea how to do better next time.
That said, I've also enjoyed such games immensely with no handicap, despite no prospect of winning at all. In most games you can have some partial success and psychological reward despite losing the game.
[1] https://en.m.wikipedia.org/wiki/Handicap_(go)