Oh yeah, also need to mention that I had a guy doing this was conveniently “forgetting” to remove the bonuses from what he changed away from. One week he has Weapons Finesse, the next week Power Attack, but he’s still using the bonuses from Weapons Finesse, that sort of thing.
“How are you still doing fire damage on that hit? You said you switched to a keen sword.”
“Oh, did I? um, ok, um… (scribble scribble) I guess I didn’t do the fire damage then. I may have to switch back.”
You may not want to go this far, but just FYI, there are cryptographic algorithms that allow multiple players to generate random numbers without risk of cheating by one player. This is often referred to as the “Mental Poker” problem.
–Mark
Could you please provide a cite for this?
If I understand you correctly (more than 14 means SUCCESS, and 14 less means FAILURE), the probability of such a streak would be 0.005.
Chronos calculated something different (I’m sure his calculations are correct), but you need to take heed of his comments regarding previous streaks of 20 rolls that weren’t remarquable.
The odds of rolling five consecutive 19’s on d20 is about one in three million. The odds of rolling a 4, 8, 2, 19, and 14 (in any order) is also about one in three million.
As Chronos pointed out, in the second case no one is going to jump up and claim these odds are so remote the roller must be cheating. In first, well, maybe. We would perceive the first case as being unusual, the second case not at all, in spite the odds being exactly the same.
I think the OP is wise to ignore this to a point. The player is only cheating themselves, and if it’s to the benefit to the party then perhaps all involved will be enjoying the adventure more. I’ve never hesitated fudging as a Dungeon Master, if I roll a 20 on d20 and the whole party dies, I’m going to say I rolled a 3 … my priority is always player enjoyment, and who likes to die in a 10d8 damage cone of fuming hydrochloric acid?
That was a fun, little journey down memory lane. Thanks for finding that.
Nitpick: In the second case, there are many different orders the 5 numbers can fall in, and each one would be as likely as 19,19,19,19,19. So call that 120 in 3 million? 
[side note prompted by OP]
Why would anyone want a 30 sided die? And if such an odd duck were to be found, would he be strange and mysterious?
I wanted a 30-sided die because it’s cool. And now that I have one, I’m still trying to figure out what to use it for. But it’s still cool.
And I’m not sure how the OP prompted that-- So far as I can tell, you’re the first person in the thread to mention a d30.
Because then I would have a 30 sided die!
Duh!
Sheesh. You normal folks…
Just saying hi/yanking your chain/seeing what response/and actually wondered after you mentioned it elsewhere in GQ (which I mentioned IRL).
So, maybe I’ll accept “strange and mysterious.” (Some chicks dig that, BTW.) Which is what you’ll remain, by accusation, since you haven’t denied it, and this hijack must end, unless anybody can figure out what to use the 30-die for in this thread.
ETA: Just saw NoelQ. Hah!
IME, though, people like to play in a game world where that (or equivalent calamity) is possible, because it means their playing decisions feel like they have real weight.
True, I should have said in any specific order. So “4, 8, 2, 19, and 14” is the same odds as “4, 2, 14, 19, and 8” etc … which is the same odds as “19, 19, 19, 19, 19”.
I also object to too much fudging, because it kills utility characters. GMs are okay with killing off thieves, who are more likely to be sneaking alone and disarming traps alone, because it creates the right amount of danger and drama. But it wouldn’t be very “realistic” seeming to kill off the tank and then still somehow have the party win the combat without a TPK, so that’s the area that tends to get fudged up more.
Yeah, I was gonna say: it depends on the players. Some might prefer that a game be played completely “fair.” What watchwolf49 describes means that any danger that a whole party would die is purely illusory.
But this gets us out of GQ and into IMHO or The Game Room territory.
Might be interesting for the DM to fudge their dice rolls similarly when dealing with this one character…
There are a number of online die rollers you can use to guard against this sort of thing, if you feel so inclined.
I haven’t actually used either of these sites, so I can’t speak to their specific feature list, but they are both free, so they’re probably worth at least what you pay for them.
To help adjust for this issue it would be useful to know what prompted you to start recording his rolls. If you noticed he seemed to be having a lucky streak and so retrospectively looked back at his last 20 rolls, then as Chronos says, you have to account for selection bias. The probability is low enough that I might still be skeptical, but it may be like being dealt a four of a kind, if you play enough poker eventually it will happen.
However if you started prospectively recording his rolls after you became suspicious, then there is no selection bias and a probability of 2 in 10,000 is very unlikely not to be cheating.
If this data was collected retrospectively, my advice would be to let it go, but periodically (without telling him) collect some rolls and follow Chronos’s calculation. If the number of standard deviations above normal tend to be frequently 2 or higher then you may want to confront him again. After being confronted the first time he may clean up his act, so that even if he was cheating none of the future runs will come up significant, but then that’s what you want anyway.
To check this out I took a look at the Kolmogorov–Smirnov test comparing the observed distribution to what you would get if you took the best of two dice. The result showed that the data was entirely compatible with this hypothesis (p=0.535).
I will point out that quite a few d20s have a bubble or two and thus they are slightly "loaded’. He may have such a “lucky” die and think just that- it’s lucky.
However, to get so few rolls in single digits is indeed, strange and unlikely.