I don’t know but if you rub my lucky clover you’ll get a little squirt of luck.

Maybe the real Cthulhu was the impossibly mind-breaking irrational thought experiments we subjected ourselves to along the way!

Short version, two coin flips. There are 4 options:

HH, HT, TH, TT

So there’s two chances to get one Tails and one Heads, out of 4, so 2/4 = 1/2, half the tosses. Then 1/4 on each of HH and TT.

So rolling one Tails is more likely than rolling two.

But once you’ve flipped the first coin, it’s “locked in”. If it was Heads, the only options left to you are HT and HH. The fact that there could have been a T that, if flipped first, would land us in TH is irrelevant fantasy. We’ve got the H, and all that’s left is HT or HH, even odds.

Dice are the same. What makes a double 1 rare is that you have to roll 1 specifically and only two times to get there, whereas a single 1 can be first or second, and the other number can be any of the other 19 other numbers. It’s the duplication of different results we consider “the same” that make one thing more likely. But once you’ve already rolled a 1, none of that matters anymore. Now it’s just 20 numbers, each equally likely. We’re locked in.

Roll my number, roll my number, roll my number, I’m not afraid…

I think the problem is that people forget Monty Hall has information that the contestant does not. The naive assumption is that he’s just picking a door and you’re just picking a door. The unsophisticated viewer never really stops to think about why Monty Hall never points to a door and reveals a prize by mistake.

One way I’ve had success explaining it is to expand the problem to more than three doors. Assume 100 doors. Monty Hall then says “Open 98 doors” and fails to reveal a prize behind any of them. Now its a bit more clear that he knows something you don’t.

The same logic applies to a nat 20 though

Maybe? I don’t think that was my issue. I think I was overthinking it and using the second “choice” as an event with separate odds.

And of course the traditional sentence for dice which misbehave one too many times.

The thing you’re getting by switching is the benefit of the information provided by the person who revealed an empty door.

Before a door is open, you have a 1/3 chance of selecting correctly.

After you select a door, the host picks from the other two doors. This provides extra information you didn’t have during your initial selection. The host points to a door they know is a dud and asks for it to open. So now you’re left with the question “Did I pick the correct door on the first go? Or did the host skip the door that had the prize?” There’s a 1/3 chance you picked the right door initially and a 2/3 chance the host had to avoid the prize-door.

Where did they get an AI that managed to mess up “roll” as “role” twice in the same page? Humans do it because they sound the same, but AI doesn’t know how they sound. The AI knows that sometimes people say “role” instead of “roll”, but they’re generally set to raise the probability of a token to some power, and since most people spell “roll” right, they’re even more likely to. And they also generally have a post-training step where they’re trained to spell stuff right and that sort of thing. And they don’t even need to be trained on that specifically, since some people spell better than others, so they can understand the general concept of good vs bad spelling.

That’s stupid. But obviously how the dice strikes the table impacts its balance and therefore the probability of rolling specific numbers. So we must figure out what side need to strike the table first to decrease the probability of getting an undesirable roll. Boom, I out physicsed you’re probabilities.

The funny thing is that this logic assumes the rolls are independent (so you can just multiply probabilities), but the definition of independence is that past rolls can’t affect future ones. So basically it’s saying that past rolls can’t affect future ones and therefore they must.

Me every time I think about this.

The math checks out, but the problem is the danger of rolling a nat 20 on your practice roll. The odds of getting two nat 20s in a row are almost as low as the odds of getting two nat 1s, so you may be screwing yourself out of a crit

Weirdly enough, it’s just the way probability works.

Once something stops being a possibility, and becomes a fact (ie. dice are rolled, numbers known) - future probability is no longer affected (assuming independent events like die rolls).

e.g. you have a 1/400 chance of rolling two 1s on a D20 back-to-back. But if your first roll is a 1, you’re back down to the standard 1/20 chance of doing it again - because one of the conditions has already been met.

Besides, everyone knows you play the long game of training your dice by always resting them with the high value up.

It probably does nothing, but maybe the atoms shift over time and it warps just a bit and rolls better.

After like three 20s I can’t roll over 10 I need better dice. Or better luck.

I thought that was the d8. At least the 4 is flared at the base

Jesse, that’s not how probability fucking works.

Yes, it is more like a sleigh of hand or a magic trick. When the presenter discards an option, they are acting as a hand of god that skews the probability.

It is much easier to understand with a hundred doors. You choose one and then the presenter discards 98 doors, now you decide whether to keep yours or to choose the other one.

Here it is more obvious the role of the presenter discarding negatives.