I'm pretty sure the AI in Pokemon actually cheats. I came to that conclusion when Whitney's Miltank smashed me with the Stomp attack eight times in a row.
Cheat is a harsh word for it though, I guess you could call it a home field advantage. Something that makes the gym leaders seem tougher.
I did the math to see how this would pan out, you know, in case anyone is wondering, which you probably aren't. But the chance of being fully paralyzed 6 times in a row (25% chance each time) is a chance of 100(.25^6) = 0,024% while hitting 6 times in a row is a 100(.75^6) = 17.8% chance.
I recently replayed SoulSilver and it was my Ampharos vs Lt. Surge's Electrode
And yup, it wasn't long before both of us were paralyzed. (yeah Gen 4 rules, electric types getting paralyzed)
It got to attack me six times in a row, while I was unable to move all six times.
I mean, yeah, I won because Ampharos can take a punch like a champ, but you get a bit frustrated when you keep getting paralyzed. Paralysis has a 25% chance of not attacking so you really loose any steam that you might have built up until that point. So while possible it would be like flipping two coins and having them both come up heads six times in a row while your opponent never has that happen to them.
For comparisons sake, the chance of encountering a shiny in SoulSilver was 1 in 8192 = 0.0122% without raising the probability by chaining or using the Masuda method. Looking at the odds I think that my point is clear, this is not a case of bad luck, but of AI that is programmed with too much favor being placed on it. Now I wouldn't call it a example of cheating AI, but having fair odds would look a lot different.
And may not be as fun.