The most improbable set of dice rolls I ever saw, that I'll think was legitimate, was a 15th level character getting one-shot-killed in a Star Wars (d20 Original Core Rules) game by a Stormtrooper before they could take any action.
The party opened the door, where a couple of Stormtroopers were standing on the other side.
Initiative.
The Stormtroopers roll a natural 20. That had them going before any of the PC's.
First Stormtrooper attacks, and rolls a Natural 20, and then confirms that as a critical hit (I think it was an 18 or a 19 on the die), and with as heavily armored and defended as those PC's were, that's about what it would have taken. In that system a critical hit would go to wound points. Then does enough damage with their 3d8 blaster rifle to chew through his 15 or 16 Wound Points (CON score plus bonuses from feats like Toughness)
. . .thanks to high-level characters with high CON scores and feats like Great Fortitude, this was a "don't roll a 1" moment. He rolled a one for his Fort save.
The stormtrooper managed to get a lucky shot, shoot a 15th level PC in the face and kill him outright in one shot. Needless to say, the other 5 PC's promptly eradicated the Stormie and his seconds later in the same round, but dead was dead.
As for dice rolls that I think were definitely NOT legitimate. . .
One particularly odious player who hung around our college gaming group for a while back in the late '90s had this idea that somehow, for some reason, all D&D games were open to anyone who just showed up to them, that he could just invite himself to a game and the DM would HAVE to let him in. Also, he thought that ALL official manuals and products could be used to build a character, and that he could roll and write up his character himself.
He showed up with (in 2nd edition AD&D). . .
A Lawful Evil (because he said all other alignments are "too restrictive") Elven Fighter/Mage/Thief (and I think he had some overpowered kit I'd never heard of too), who claims he rolled straight 18's for his ability scores (resulting in a 17 CON and an 19 DEX, and of course he had 18/00 for his Exceptional Strength as a Fighter with an 18 STR). . .and on top of that (of course), a Psionic Wild Talent that was the most amazing set of powers possible (I think it was two Sciences and a handful of Devotions). . .he showed up uninvited at a game, insisted on being let in, said he had even rolled up his character, the DM took the time out of raw curiosity to look at the sheet and see this, before telling him to GTFO as he was uninvited and he'd clearly cherry picked his numbers and even if he did invite him into the game he made players create their characters with him, and his setting had no psionics at all and no elf PC's. . .after much whining, he was finally berated into leaving.
. . .and a time my character was killed in a game and I'm about 99.9% sure it was some fudged rolls as a way for him to kick me out of the campaign and say it was just the dice. . .
The DM had said that because the session was the climax of a huge plot arc, if any characters died in that adventure, their players would NOT be welcome to create another character, they were out of the game.
Well, my Cleric was doing well the WHOLE game. Managed to make it to the epilogue after the adventure when the DM goes "Roll a Fortitude saving throw"
I roll a 19, with my bonuses that was somewhere around 23 or 24.
Not good enough apparently, the DC was high enough to be "needs a Natural 20 to save". to me.
At that point the DM flashes back to a scene earlier in the adventure when I was handed something. . .that was apparently covered in poison. . .and he said he rolled a save for me when I initially touched it, and rolled a Natural 20, and this poison had a delay of 1 day (instead of the rules-standard 1 minute) and now I had to roll again, I didn't make it on the 20, and it's CON damage poison, and he already rolled the 2d6 and it was doing maximum damage of 12 points of CON. . .and I've got a 12 CON, so it's dropped me to 0 CON and my character drops dead and I'm now out of the campaign.
Yeah, that was the DM kicking me out and saying it was the dice, which would have to be very unlikely rolls to be legitimate (a natural 20 for when I first touched it to not be affected, then maximum CON damage on the secondary damage later).
