Hell no,
It doesn't run better in any position, Unless you have a first generation problem machine like I do.
Vertical and the one I have to do to make my games work most of the time, Upside down, damage the CDs easier then Horizontal playing.
I've always love the pop open loader on the PS1, And it's sexy that new PS2 model goes back to it.
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I've had my PS2 since launch day and, aside frmo the few times I took it to a friends house, standing up all the time. I have yet to have a problem with my PS2 that was the result of my PS2 and not a faulty (IE rented or preowned) game. I heard everyone saying how their first generation PS2s have DREs or other problems, then I look at Old Faithful sitting there on the floor on my room, under my tv stand, standing upright, and think I must've gotten lucky