The only characters who don't come out of random are Zero Suit Samus and Sheik (though you get Samus and Zelda and can switch). It's seriously random otherwise (notice how no one here seems to observe the same patterns?). The number of trials to prove reasonably that the odds are uniform (or close enough to uniform) is a bit daunting so I'm not going to do trials, but it seems obvious that it is actually random.