I recall playing "Stacker" for a little while in the 2000's. It used an LED dot display for gameplay, which was a simple timing game where you "built" a tower by stacking up the blocks, with it getting faster at each level.
What it did was exactly as you describe: it had a minor reward level that you could always win, and then a few levels above that where the game would cheat and instantly warp the block ahead to make you lose. I did get a win out of it once(and got an iPod mini), so I think I did come out ahead, but that was it.
Overall, it's better to be good at pinball(replay scores) or DDR(adoration of strangers).