Dice Rolls, Entropy, and SeedSigner | Keith Mukai SLP766

**Stephan Livera** (0:00)
Hi, everyone, welcome back to Stephan Livera Podcast. Today, we're going to be chatting about dice rolling, entropy, and the SeedSigner. And joining me today is Keith Mukai, as lead developer of SeedSigner. Welcome to the show, Keith.

**Keith Mukai** (0:12)
Hey, thanks for having me.

**Stephan Livera** (0:14)
So Keith, I saw you had some recent research or findings that you put out on dice rolling, because you were trying to, let's say, correct some misconceptions around that. So, you know, why don't you start us off there? What was some of the key learnings from that?

**Keith Mukai** (0:30)
Yeah. So, I mean, in the wake of the cold card exploit, right? Like, everyone is understandably terrified about entropy. Like, and what this whole episode revealed was just so many people just don't even understand any of it, right? So, obviously, they were the people that got horribly wrecked by trusting the onboard RNG code on the cold card. But even the people that did the dice rolls and they were safe, once the exploit was fully explained, even days later, people are like, I did the dice rolls. Am I okay?
Like, come on, you know, the explanation is out there, right? The exploit has been described, and people just still didn't have any core understanding of what the dice rolls provided them. Whereas like, if they really understood, and I don't want this to sound like insulting or condescending. Like, I totally understand like the terror, the panic, the confusion of that time.
But like, if you can understand the core principles behind dice rolls, then you can sleep easy, you know, through this. So I just wanted to at least explain, you know, what the dice rolls are, how it works, you know, what the basic principles are. But then of course, any time you talk about dice rolls, then all of the folklore, all of the superstition comes out. You have to use casino gray dice. You've got to fill a cup of water with salt and then float your dice and poke at them and make sure that a different face pops up each time. You've got to do 150 rolls.

**Stephan Livera** (2:23)
And of course, the truth is not that, right? No, no.

**Keith Mukai** (2:29)
So now in the write up that I published, I listed all of my sources and methods. And so the idea is that if I got anything wrong, like you can see exactly like what I was pointing to and you can correct me or you can find better research.
And I used Claude, right? So as far as I know, Claude didn't hallucinate any of these findings, but double check the work, right? So the two biggest studies that we could find in terms of dice roll fairness, like how bad is a cheap pair of board game dice, both studies were kind of shocking. They only found a 1.4% variance from fair. And that's with like the cheapest dice that they tested. And this is over like hundreds of thousands of test rolls.
I was expecting worse numbers than that. And they verified that casino grade dice really are as fair as they purport to be, like within the range of, you know, accuracy of their measurements. But so if like, if you open your Monopoly game and take dice out of that, and they're accurate to within 1.4%, you know, when I had Claude run the numbers and the simulations, for a 12-word seed, you're expecting 128 bits of entropy from your dice rolls. And even if we inflate the inaccuracy, and let's say your dice are 2% inaccurate, you know, it doesn't sound like much, but it's way more than 1.4%, then over your 128 bits, you lose 0.2 of a bit. And that's if you're only rolling with one die that is 2% unfair. So, like, yeah, if it makes you feel better, you can buy casino-grade dice, but I just kind of want to stop people from saying like, you're screwed unless you do this, right? It's not necessary. Like, you know, I was looking at Amazon, like, there's some really cool looking casino-grade dice. You know, I want an orange transparent set of casino-grade dice.

**Stephan Livera** (4:50)
Right, just for fun, right? Yeah, exactly. Cool, go ahead.

**Keith Mukai** (4:53)
It's 13 bucks, you know, it's fine, you know, whatever. Like, your whole seed rolling ceremony should have a sense of fun and coolness and prestige about it. No problem, but just like, don't scare people unnecessarily.

**Stephan Livera** (5:09)
Yeah, yeah, it's an interesting point. It's a good point. And so as you said, like kind of the rule of thumb is sort of 50 rolls for 128 bit for 12 words. And then if you're doing a 24-word seed, then that's where 99 rolls is typically the rule of thumb. And then, so I guess the key points really are, even if you use cheap dice, that's okay. It doesn't have to be a casino roll, a casino level.