This has happened to me a few times. One I remember was the game Alchemist, where I just sat there confused as hell for 4 and a half hours while three guys were all talking about strategies. Tonight it was Terraforming Mars, where I was told it would be a 3 hour game, but by hour 4 we were halfway done. This time I said "it's 11pm, I have work in the morning, this will be my last hand" and the host got very passive aggressive with me. I just don't know what to do in these situations.
^Also is there a word for this? My girlfriend said I was "held game hostage" but I don't see that used in my searches.^
Update:
I sent an apology for leaving early, and he wasn't too frustrated about it and understood my frustration which was nice. I told him I didn't think it was my cup of tea since it was so dense, but he kept trying to sell me on the game.
I just gotta learn how to decline with this guy, he is a bit of a "won't take no for an answer" person, but I'm still learning to be firm with boundaries.
I'm really a 45 minute or less person, and prefer games with like... 5 rules. I have communicated that before, but he really wants me to play the games he loves which I take as a compliment.
He did have me playing Dominion for a while, and that was a time when I just would suck it up and play for his sake since he was going through a divorce. We literally had the parks and rec sketch where I said "I don't really like Dominion" and he said "what do you mean? You've played all the games!"
He housed me when I was homeless, so it's hard for me to decline things with him since he showed me that huge kindness.
So the people teaching the game with you should make sure everyone is aware of the game time and expectations, first of all. I love board games, but would be a bit irritated if someone expected me to play Terra Mystica at a moments notice. The only exception that comes to mind is if they're cool with ending it early because I wouldn't be able to play the whole time.
Since your friends don't seem very responsible, you have to do more legwork. I would ask which game is being played, and what the expected game time is. In addition, let them know your time limitations and that you'll have to leave by a specific time whether your finished or not. This may lead to less invitations ("lets start a game of Twilight Imperium 3 at 830 Pm on a Tuesday night! but lets not invite Meep_Launcher because he'll leave the game early") but at least everyone will be aware of the situation before hand.
Ideally, your friends will work around the person with the most restrictive schedule, "only 2 hours? lets play some love letter, DND Inn fighting game, and Port Royale". If they really want to play Monopoly, you can suggest a better time when you would be interested in playing where you'd have sufficient time to finish the game.