There is someone at my table that uses one of those dice rolling towers, and for probably 4 sessions straight he rolled 15 pluses for combat encounters. It felt like he never missed once, but then it started evening out. I agree to notate every roll, but it could take several sessions for a balance to be established. Don't notate one session and use that as your basis to approach him until you have more data!

+1 for the first half, -1 for the second. If you're going to ignore it/forget it there's no point in checking in the first place. That said, I value my time, and you should too. If someone is cheating they may not be losing you money, but they are cheapening the experience and possibly wasting your and your party's time. Further if someone is willing to cheat in a game with no stakes, there's no telling where else they're willing to cut corners.

The stuff about the likelihood he is cheating is valid (though you ignore the possibility that the dice are unfair but the guy doesn't know that.) However, money has nothing to do with it. People don't want to play games with cheaters. They may not even want to be friends with them. I wouldn't. Someone who cheats at a game is someone who is hard to trust in general. They'll lie and scheme in other situations. Being able to trust someone is vital in a friendship. Integrity matters.

You make good points in this answer, but I'm not a fan of how you strongly assume the OP is wrong and doesn't know about confirmation bias. You claim you're "99.9% sure his dice are perfectly fine", but you have absolutely no basis for that claim, which comes across as a bit condescending.

@PierreCathé you mean apart from having taught statistics to post-graduates?

@DaleM So you're applying your own bias of "people don't know about confirmation bias" to the situation ? You could simply warn OP about confirmation bias without telling them the dice are definitely fine, which you don't know.

Casinos have standards for dice quality that are ridiculously high by typical RPG player standards. Meeting those standards is meaningfully expensive to achieve, and dice that are that good will generally have it as a prominent selling point - and they still won't stay that good for long if they're rolled a lot. I would be surprised if there's even a single die "good enough that a casino would use" among the entire group of players.

@PierreCathé I will recommend that you take this disagreement with Dale to chat. We get cautions with some frequency form the mods to "not argue in comments" -

You have abused statistics in a way that reminds me of the "on average, each human has 1 teste and 1 breast" joke. Weighted dice are a thing and people buy them. Some use them to cheat. It seems more likely that if they are weighted then the owner probably knows and bought them for that reason. It seems unreasonable to assume 0.1% odds of knowing. Your stated odds suggest less than 1 in 1000000 people cheat with weighted dice, a shocking assessment. Otherwise good/funny answer +1, especially the "more likely to be a murderer", but I suggest you improve your answer's statistical analysis.

Never assume to malice What can be attributed to random chance.

-1. I don't agree with the "99.9%" chance that someone isn't cheating bit. They literally sell sets of weighted 4d6 called character builders, what makes you think that people won't cheat if you're easy on them?

Plus you want to screw with his lucky dice and everyone knows that if you do stuff like that, Lady Luck screws back! Are you suggesting, that valuing others people's superstitions is more constructive than emperical testing?

@AndrewSavinykh absolutely- people are more important than pure rationality. I’m an engineer and a scientist and I know rationally that dice are not “lucky” - that doesn’t mean that my emotions about dice and luck follow my rationality.

Absolutely agree with this answer. D20s "fixed" effectively enough to have any statistically significant deviation will either behave or look extremely obvious. They'll visibly roll very very weirdly due to weighting, magnetism or stickiness, or will have the high numbers visible in a cluster (ie, 18 and 19 next to 20, missing numbers, etc). Even reliably-weighted D6s roll funny, and they have a lot less work to do to act weighted! Realistic-looking weighted D20s that affect the outcome enough to be noticed, simply don't exist.

@DewiMorgan I completely disagree. It might be weighted incorrectly from the factory and the player might know (or doesn't want to confirm) that. Or they might have put a lot of work into doing it neatly and don't want to give up the fruits of their labor. It could also be a different style of cheat die.