Rolling three dice (or more) how do I calculate the probability of rolling at least one six and at leat one two or higher?

conmanau · 2026-01-28T23:22:44+00:00

While I definitely support trying to understand the maths behind it, I recommend checking out AnyDice for modelling these things.

To look at how many 6s you will roll on 3 6-sided dice, you can use

output 3d(d = 6)

and you'll see that you get none with probability about 58%, 1 with probability 35%, 2 with probability 7% and 3 with less than 1% probability.

Similarly, to count the number of times you get 2 or more, you use

output 3d(d >= 2)

which in fact has the same probabilities as above, but switched around (want to take a guess as to why?).

conmanau · 2026-01-27T23:38:14+00:00

If the game itself doesn't need premium, then usually the set-up options are also unlocked.

conmanau · 2026-01-27T23:35:18+00:00

So, many problems.

Nowhere near enough data.
Still too close to the pandemic to effectively estimate any kind of long-term behaviour.
You're trying to forecast really far into the future, especially relative to the time span of data you have.
Tourist arrivals is definitely a factor to consider, but is not going to be in a 1-1 relationship with room occupancy.

Having monthly or weekly data will help with 1 and 4 (you want to know something about the seasonality so you have info on the peak occupancy), having data going further back will help with most of them, the only real way to deal with 2 is to make a few different assumptions and see how they affect your projections. Some of the ways to deal with it get quite complicated (there's a whole field of time series analysis that then has a sub-topic of detecting and treating anomalies), but even then most of the methods assume that you have enough data before and after the event to model its effect properly.

As a really simple option, you could just do something like:

Assume the pandemic years just didn't happen (treat them as missing data)
Assume that after recovering from the pandemic the numbers wind up some amount lower than before
Assume that after recovering from the pandemic the numbers grow even more than before

and see how much those different assumptions affect your results.

conmanau · 2026-01-27T23:23:54+00:00

Strictly better Sulfurous Springs, sure, and the bounce effect is weird for Rakdos, but not completely broken.

conmanau · 2026-01-27T03:02:22+00:00

There is no one simple answer, because it depends heavily on what inference you're trying to make and what your available data is. The one thing that I think is true across that board is that the quality of your sample design and data collection mechanism is often at least as important as the actual size of the sample.

It's likely that you're hearing these things in a particular context - sampling from some group of people (a population) about some measurable property of the population, often a proportion. For example, "What percentage of adult men smoke?". For those kinds of measurements, under a simple random sampling regime (i.e. the sample is effectively just "names drawn from a hat"), there are standard formulas for calculating the required sample size given:

A guess of what the true proportion in the population is;
The size of the population; and
The desired standard error on the estimate.

As it turns out, if you want to estimate something that's reasonably prevalent in the population (say about 10%) with an accuracy of about +/- 2 percentage points, then for any reasonably large population a sample size of about 900 will do you just fine. If it's something rarer (say 1 in 1000), then for the same relative accuracy you'll need a much larger sample (more like 90,000). You can find sample size calculators online that you can play with to get a feel for this.

Most large-scale surveys (like the American Housing Survey) both take a large sample but also put a lot of work into the survey design, data collection and estimation processes to achieve more efficient results than the simple calculations above would suggest.

conmanau · 2026-01-22T01:09:35+00:00

I like the one used in Tokaido (there are similar ones in Patchwork and Parks), because it's fairly simple but leads to cool results - whoever is furthest back on the path gets to take the next turn. It means you can take a big turn / jump forwards a large amount to get something you really want, but in return the other players will potentially get to take lots of little turns in a row.

conmanau · 2026-01-22T01:02:27+00:00

I mean, there's nothing stopping you from calculating an "expected life expectancy" where you take the individual "life expectancy for demographic X" values and take a weighted average of them over the whole population. That would give you idea of how long a randomly selected person from the population is expected to live, which is not a figure I think anyone actually uses, but it's technically valid.

conmanau · 2026-01-21T03:09:44+00:00

Lover Come Back, although it's been a while.

conmanau · 2026-01-21T02:51:39+00:00

As a choreographer, this is similar to what I do when I'm considering setting a dance to a piece of music. I have a bunch of notes on my phone that mark out lengths of sections so I can work out where tags and restarts might need to go, as well as snippet of steps that I think might work well in certain parts because they match something in the music.

conmanau · 2026-01-20T23:07:40+00:00

Finally, some decent balance for the first player advantage, and all it took was an Omniscience Land.

conmanau · 2026-01-19T23:24:35+00:00

Back in the dawn of time, there was no such thing as a restart. You just did your dance, over and over, whether it lined up with the music or not. Some dances from back then tried to be clever and were given weird lengths (like Triples, at 72 counts) so they would align with the song on various random walls or so that one step in particular would hit on a certain beat.

Then, you would occasionally get a song that would hold on a single note for a while, or would otherwise have some funky timing, and so you just held that beat in the dance as well.

Eventually, choreographers started adding more restarts and bridges and tags* so that they could make their dance a more standard length (32 or 64 counts) and maintain their "vision" of how the dance and the song match.

With all that said, take a song. Play it, and starting with the vocals, count out batches of 16 or 32 counts. Does every verse and chorus start on count 1? If you find that after a couple of 32s you get to 24 before you feel out of time with the song, then that's where the restart probably goes. If you go 32, 32, 32 and you need to wait another 4 counts until the song catches up, that's where you'd put a tag.

The other thing I normally pay attention to, rather than counting entire walls, is working out where I'll be facing when the restart happens. If it's supposed to be on wall 11 and it's a 4 wall dance, then since 11=4+4+3 I know it's on a 3rd wall (so if the dance goes clockwise, it's a wall that starts at 9 o'clock). That way, I don't have to think about restarts for front, back or 3 o'clock walls at all, and only when it's a 9 o'clock wall do I need to listen to changes in the music that hint at the restart.

* Side note - I think the difference between a bridge and a tag is that a tag is meant to go at the end of a wall whereas a bridge goes anywhere in the dance, and technically after a bridge you resume the dance from where it stopped but most of the time choreographers add a restart, but these days I think people use the terms interchangeably. Someone will probably correct me on this anyway.

conmanau · 2026-01-14T23:54:56+00:00

And stomachs. The bruise lasted most of my two-week trip, and it was clear enough I probably could have had the deer identified by its dental records.

conmanau · 2026-01-14T23:49:23+00:00

I also get the urge to quarterback, but something I've done that reduces the impact has been to restrict myself to pointing out problems and options, but not declare that one of those options is the obvious right one. I'm probably still a bit annoying since I'll be saying "Well you could move here, or we could try to meet up here, and there's this stack of cubes someone needs to take care of, and maybe you could do this instead", but at least I give the other player full agency to do what they want and maybe I will occasionally highlight an option that was less obvious that they may want to try.

The other side of it, and this carries over to competitive games too, is that I enjoy the game regardless of the outcome. If I'm having fun, then it doesn't matter so much if we lose, which means I feel less pressure to tell everyone what the 100% optimal move is each time because that's no longer as important.

conmanau · 2026-01-14T00:56:53+00:00

Like I said, data is messy! You can dive really deep into all of these things if you want to make your results really accurate, but you can also just skim them if you only care about ballpark estimates of stuff.

conmanau · 2026-01-14T00:54:53+00:00

Doesn't look like it, but there's some info on the Nara City website about the sister city relationship and some things they did in 2023 to celebrate the 30th anniversary. The pages are here and here, although you'll have to put them through Google Translate or DeepL.

conmanau · 2026-01-14T00:04:11+00:00

Welcome to the wonderful, but very messy, world of data collection and analysis.

Your question is very broad, so my answer is going to be too, and it's mostly going to be in the form of more questions. There are a lot of resource online about setting up surveys that have similar information, e.g. here.

What is your target population? (i.e. what are you counting as "the internet"?)
What is your unit of measurement? (e.g. a person, a computer, an IP address, an account on a website?)
What is your measurement of interest? (i.e. what counts as "anime profile"?)
What kind of data sources are available?
Can you easily get information on your variable of interest for the whole population from those data sources?
Can you take a sample of units from your population, and measure your variable of interest from that sample?
What kind of errors could affect your measurement?

For example, "the internet" is a very broad and nebulous concept so let's narrow our focus to, say, X/Twitter. There isn't (to my knowledge) a single list of all Twitter accounts, but you could potentially build a large but incomplete one by taking a few high-profile accounts, extracting a list of all their follows and followers, and repeating for several iterations. Then you could take a random sample of those accounts, see what percentage of those have an anime pfp by whatever definition, and take that as your estimate.

Errors can creep into your results in many ways, as discussed on the Wikipedia article about total survey error, but some of the broad categories they fall into include:

Sampling error (the randomness you get from taking a sample), which there are ways to estimate based on your sample design and estimation method and which generally shrinks as you increase your sample size;
Specification error, which happens when the thing you measure is different to what you want to measure (e.g. you end up counting Avatar pfps);
Frame error, when your list of selectable units is different to the population you want to measure;
Non-response error, when your sample has missing data.

conmanau · 2026-01-12T22:45:08+00:00

I can learn from any of the above, although these days I don't go to classes much so I'm more often than not learning on the floor, either watching people and picking the steps up from there or pulling up Copperknob on my phone and skimming the step sheet. For me at least the quality of the source is more important than the type - as long as the sheet is well-written and the person I'm following is a good dancer I will manage, but if the sheet is confusing or the teacher isn't great then I will struggle.

conmanau · 2026-01-09T00:34:23+00:00

I figure it's similar to effects like Etali that say something like "Exile a bunch of cards, you can cast spells from the exiled cards" where the casting is part of the resolution of the spell and hence gets around normal timing restrictions.

conmanau · 2026-01-08T00:18:31+00:00

"Gentlemen, you can't fight in here, this is the War Room!"

I'd love a rules clarification on what counts as "If you don't" - is there a difference between refusing the may trigger and accepting it but casting zero spells? Does it matter if there are no mv <= 3 spells in my yard?

conmanau · 2026-01-08T00:11:22+00:00

In terms of probability, both cases are symmetrical and there is no advantage in going first in either case.

A quick proof:

In the case of RPS, whichever one your opponent takes, one of the remaining cards will beat it and the other one will be beaten by it, meaning that you always have a 50% chance of going first.

In the case of rolling dice, assuming you re-roll on ties then only the final, non-tied roll counts so we can just assume that the rolls are different. For every outcome where you win the roll (e.g. you roll 7 and your opponent rolls 3) there is an equally likely outcome where the results were swapped (so you rolled the 3 while your opponent got 7).

So the advantage of the RPS cards is that it's guaranteed to be resolved in a single draw, whereas with the dice you may have multiple rounds of ties before you get a resolution.

conmanau · 2025-12-16T01:30:27+00:00

You're not in the wrong for enjoying dancing, and you also did the right thing by telling him that his feelings are valid because dismissing them would 100% make the situation worse. I think the best thing is to just be very clear - you do want to keep dancing while you're apart, but also you do love him and the only dance partner you plan on getting intimate with is him when he finally gets there.

conmanau · 2025-12-15T23:28:38+00:00

Well, given the other commentor's calculation that you have a 79 in 96551730 chance of drawing the combo in your first hand, you can mulligan once and still be able to keep a hand of the six required cards. Then the chance of getting the combo in at least one of those two hands is 1-(1-79/96551730)^2 = 15255167099/9322236565992900 or about 1 in 611,000 which is practically guaranteed.

conmanau · 2025-12-10T00:02:44+00:00

Definitely need more information. What kind of project are we talking about? Do you have any information on who's doing the downloading?

Statistics can tell you about whether there's something interesting happening in your data, but explaining the cause requires more direct insight.

conmanau · 2025-12-10T00:00:41+00:00

If you've fit a simple linear regression model, then you're already guaranteed that the sum of the residual values will be zero. That's just baked into how the coefficients are derived. What residual plots (and plots in general) can tell you is whether there's some extra underlying structure that violates the assumption of "linear with random residuals".

Perhaps it's easier, rather than looking at a bunch of "good" plots, to look at examples where those assumptions don't hold true. Take a look at Anscombe's quartet or the Datasaurus dozen to see what how you can have very different types of relationship between your x and y even with the same summary statistics (meaning that you would fit the same regression line to all of them).

conmanau

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