You need a group that plays games like Pandemic, where the whole table is working together - although some games in that genre do include saboteurs.
I got to the point with my friends where I'd refuse to play some games like you describe, very long games where you can get screwed over early on and never have a hope of recovery.
My current favorite is Terraforming Mars, where everyone is cooperatively terraforming the planet but also trying to outperform the other corporations. It's less about actively attacking each other and more taking advantage of opponents weaknesses and missteps.