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.

Gosh it’s almost like I was joking by coming to a correct conclusion through faulty reasoning

I mean I could have just been a complete dweeb and explain that the outcome of the second roll is unaffected by the outcome of the first, and you are just as likely to roll two ones in a row as you are to roll any two numbers, but then I’d have to find a locker to shove myself in

I have a character that started with 14 12 10 8 4 3. In 2011.

He is my only character that hasn’t been downed, and he is religiously restricted suicidal. He is a Life Cleric and HUGELY beneficial to the party; magically, politically, & financially.

He is a 910 year old dwarf who has a guaranteed place in Elysium*. He just cant die of old age. He’s DESPERATE to die in combat.

*Terms and conditions apply.

And when the Nat 1 shows up, rub your eye because you had sand in it.

That’s very interesting to me (I am a bit mathematically illiterate when it comes to probability). Wouldn’t it still have a lower chance of being a 1 if you said you want your second roll to be the one that counts beforehand? Or would different permutations screw with the odds, say rolling a 12 then a 1, rolling a 15 and a 1, etc, counting towards unfavourable possibilities and bringing it back to 1/20?

Because the outcome of a dice roll is an independent event (ie. the outcome of any given event does not impact subsequent events), it doesn’t matter if you said only your 2nd/3rd/4th etc. roll counted. Every roll has a 1/20 chance of rolling a 1 on a D20 die.

Consider this thought experiment, there are ~60.5m people, each rolling a 6-sided die. Only the people who roll a 6 can continue to the next round, and the game continues until there is only 1 winner.

After the first roll, only ~10m people remain in the game. After the second roll, ~1.7m people remain After the third roll, ~280K After the fourth, ~46.5K 5th, ~7.8K 6th, ~1.3K 7th, ~216 8th, ~36 9th, ~6 After the 10th and final roll, there should only be ~1 player remaining.

So even though initially there is only a 1-in-65m chance of rolling 10 6s back-to-back initially, each attempt still has a 1/6 chance of succeeding. By the time we get down to the final six contestants, they have each rolled a 6 nine times in a row - yet their chances of rolling it another time is still 1/6.

Yeah I think the easiest way of understanding how monty affects the choice is to imagine 100 doors, and after you pick one monty opens 97 other ones. Wouldn’t you want to change after that?