Megachess

Megachess plays instantly in the browser, which makes it an easy game to try and (fair warning) an easy one to lose an hour to. It's the good kind of stuck: the answer is always derivable, and the click of getting it is the whole reward.

Grab your keyboard and mouse and you're set; there's no settings maze to fight through first. It works on phones and tablets too, so the couch counts as a gaming setup. Fullscreen mode is there when a browser tab starts feeling too small for the occasion. Nothing to lose but the next half hour.