Show HN: Wordle-style game for Fermi questions

[danielfetz]

Some months ago @andrewrn tried to create a Wordle-style site for order-of-magnitude thinking. This was a wonderful idea, but the actual site was somewhat over-engineered and confusing. (https://news.ycombinator.com/item?id=43632278)

In the past week, I looked at this idea again and built a very simple site which gives you a new Fermi estimation question every day:

How many new cars were sold in the US in 2024?; How many humans have ever lived (including those currently alive)?; How many chickens are slaughtered for meat every year?

To win, you need a guess within ±20% of the correct answer. For this you have a maximum of 6 tries and after each guess, you can see if your answer was too high or too low.

Fermi questions are, by the way, a wonderful way to build up your own numeracy and sense for order-of-magnitude differences. Douglas Hofstadter proposed using them for exactly this reason in his essay "Number Numbness, or Why Innumeracy May Be Just as Dangerous as Illiteracy" (https://gwern.net/doc/math/1982-hofstadter-2.pdf)

[redfloatplane]

I like the concept but it's basically a bisect / binary search simulator. Guess a reasonable but definitely high number as a high bound, a reasonable but definitely low number as a low bound, guess the average of the two, then the average of that and the high or low bound, etc.

This is especially the case when the question is asking for a bounded number in the first place (eg a percentage). In fact I'm pretty certain you should _always_ succeed within 4 steps given +-10 on a percentage question and nearly always within 3 steps. ChatGPT says it's provably so but I'm not smart enough to verify. Rings true though.

Certainly made easier by knowing whether it's higher or lower, and especially with the yellow arrows if you're not too far off.

One UX change that might be nice is to have a "spoken" version of your guess live-update below the input. I keep having to count zeroes and it would be nicer to see "Eleven billion".

[danielfetz]

I think I found a solution to bring the focus a bit away from the binary search and would greatly appreciate feedback from you.

The game now shows a hint after the second incorrect guess. For example the hint "The US covers 1.87% of the Earth's surface." is displayed for the question about what percentage of the Earth's surface is land.

How does the new information received through the hint impact your guess and assumptions?

[redfloatplane]

Yeah, that's a great idea. I think perhaps after the fourth guess you could also show the guess direction arrows, so the user can know if they're in the ballpark and they won't get too frustrated? But it's hard to keep the simplicity of a wordle-style game!

[danielfetz]

The UX change you propose would be quite an improvement and it is unfortunate that I haven't considered that myself. I'll implement that in the next few days.

[andrewrn]

Hi, I'm the @andrewrn mentioned.

For those interested, I did polish the initial app a lot: https://fermi-game.onrender.com/ (bad news though... I over-engineered it even further I think. It's my first real public project, so I learned my lesson to viciously descope the mvp). Some of the comments here (like scientific notation and sharing) are present in my project. I tried to re-share after polishing but the HN link sharing dynamics have been a bit opaque to me and kept the project buried when posted.

It's clear to me that there is a lane here for a fun brain teaser/exercise. Just getting the answer right on 2 tried on OP's version by guessing ~5% of 330M population buying new car was a nice hit of dopamine. Combining a little math and world-knowledge is pleasing, it would seem.

@danielfetz, any interest in collaborating?

[praash]

I really enjoyed spending a bit of my morning with these two implementations of the concept.

I prefer your idea of treating the question as a proper puzzle with a 1-submission limit. The "calculator" UI took a whole 2 minutes to understand initially, but I really liked seeing the chain instead of having to mush all the factors in my head.

It's really nice to see the correct answer broken down to get a feel about the real numbers!

The current question's answer seems to contain big errors in magnitude in its factors:

"How many kilograms of skin does a human shed in their lifetime?"

    Skin cells shed per day: 5e8 / day
    Mass of one skin cell: 3e-6 g
    Years in a lifetime: 80 yr
    Grams to kilograms conversion: 1 kg / 1000 g

The final "correct" result is displayed as 44 kg, but these values result in 44,000 kg. It's also odd to show a conversion factor for kg/g, but not day/year.

The first two factors correspond to shedding 1.5 kg/day, which is definitely unrealistic!

[andrewrn]

Thanks for trying it and sorry about those errors. All fixed now.

You're very much not alone on the UX friction-- that's what most people have said. My gut says that what is fun about Fermi estimation is chaining the factors, (which OP's clone doesn't have), but it's not a trivial thing to package into an intuitive UI. So I'll have to think about it a bit more. If you've got any more ideas or suggestions, I'm all ears!

[danielfetz]

Hi Andrew, great seeing you here. I'd love to chat with you because I also plan to create some more games around Fermi estimation in the future. I would, if you don't mind, send you an email to the address you've listed in your profile.

[andrewrn]

Please do! This is a fun area that I think has some potential.

A HN moderator actually directed me to this post. I never would have seen it otherwise, so I'm grateful for that.

[plaguna]

User with Spanish keyboard here: when I enter 99999 it formats it as 99.999 and when I submit it, it shows as 99, because it uses the dot as decimal separator that is the way we do over here.

Otherwise the UI and concept looks pretty interesting. But until that is fixed, it is unplayable for me.

(On an iPhone, using Safari)

[danielfetz]

That is very unfortunate and I'll be looking into this. Thanks for surfacing this to me!

[danielfetz]

It should now be fixed.

[Notjoanbaez]

Same issue FR iOS digit keyboard.

[danielfetz]

It should now be fixed. Sorry for the delay!

[littlestymaar]

Same here (with French keyboard).

[danielfetz]

It should now be fixed. Sorry for the inconvenience!

[littlestymaar]

It is, thanks.

[riidom]

I found the arrows misleading. Interpreted them as "should my next guess be higher or lower" and not as "current guess as too high/low". I'd prefer it written out "that was too high" or similar.

[danielfetz]

One of the main downsides of the game so far was the focus on doing somewhat trivial binary search if one did not succeed in getting within ±20% of the correct answer with the first guess.

I think I did find a solution to bring the focus a bit away from the binary search and would greatly appreciate feedback from all of you.

The game now shows a hint after the second incorrect guess. For example the hint "The US covers 1.87% of the Earth's surface." is displayed for the question about what percentage of the Earth's surface is land.

I hope that this brings into the game a whole new dimension where you have a second moment after the initial Fermi estimation to really think through your guess and the assumptions you have made. How does the new information received through the hint impact your model?

I think those things put together now make the game a very compelling training ground for getting better at Fermi estimation and updating your beliefs in light of new information without over or under-reacting.

[estomagordo]

This was really fun.

After about ~10 questions though, I started getting the same question every time. Like five times in a row.

[danielfetz]

I'm sorry for that, I should put up a different screen when all questions are answered. The archive doesn't go back any further than that as of now.

[danielfetz]

This is fixed now and you can't play questions on repeat.

[mike-the-mikado]

An interesting game, if you can come up with enough good questions. (At least it isn't telling me which digits are right, but in the wrong place).

With a target of 20% accuracy, it won't make much difference, but I think that symmetrical error bounds are appropriate in this case - the factor by which the answer is wrong. so 2 times too big, is as good as 2 times too small.

[_ache_]

Can't play the game. My local use space ' ' as a hundred separator.

So, I any guess above 1 000 is truncated. 1 000 is 1.

[danielfetz]

It should now be fixed. Sorry for the inconvenience! If there is any issue remaining, please let me know!

[_ache_]

Thank you. No other errors. It works. Nice game. :D

[dave333]

The classic question of this type from high school physics/chem class is "How many molecules from Caesar's dying breath are in a persons lungs now?"

[gabagool]

Do you think you could support typing answers in scientific notation? So 8e9 for 8,000,000,000. It would make typing in answers easier considering my guesses always end in a bunch of zeroes!

Does the orange mean your answer is within 25% of the absolute value? Or that your logarithm value is within 25% of the logarithm value of the true answer?

Thanks for making this, this is awesome

[danielfetz]

I'll definitely support scientific notations going forward. But it might take one or two days before I have that implemented.

The orange means your answer is within 50% of the absolute value. I might change it at some point away from a linear scale to a logarithmic scale, but I'm not quite sure yet.

[lorenzohess]

Would be nice to show users their % off between their first guess and the answer. If I'm close but get unlucky and it still takes me 3+ guesses, at least I can see that my initial guess wasn't too far off.

Then report the average of this metric over time with each game.

[danielfetz]

That sounds good! Would you also say that the win criteria should be loosened up a bit? More like ±25%?

[hereonout2]

No, if anything I was disappointed to read within 20% was correct! (I played it before reading your post!)

[danielfetz]

Initially the win criteria was within ±10% of the correct answer, but 15 minutes ago I changed it to ±20%. My rationale here is that the goal of the game is to get within the ballpark of the correct answer. And a guess of 80 billion when the correct answer is 100 billion seems quite good and indeed should probably win the game.

[munch117]

Thank you for making this.

I have an idea for a gameplay that I think I would enjoy more:

  - If the first guess is within a factor of sqrt(10), then you win.
  - If not, you are given two choices for the second guess: Up or down.
  - Up and down are 10x higher and lower guesses (making them adjacent ranges to the first guess).
  - If the second guess is wrong, you lose. No more guesses.

The point is that the second guess makes you rethink the original question once more, to figure out what it was that you missed. Which is more fun that doing bisection.

I wrote 10x and sqrt(10) to make a game literally about orders of magnitude, but you could of course you smaller numbers, like 4x and sqrt(4), to make it harder.

[danielfetz]

I greatly appreciate your suggestions, munch. I really like it, but I worry that the game loses some of its mainstream appeal through that. I don't know, I have to look into this in more detail.

However, I did find a solution to bring the focus a bit away from the binary search/bisection.

Namely, the game now shows a hint after the second incorrect guess. For example the hint "The US covers 1.87% of the Earth's surface." is displayed for the question about what percentage of the Earth's surface is land.

This of course lets you, just as you wanted, rethink the original question once more now in light of new information.

text: I think I found a solution to bring the focus a bit away from the binary search and would greatly appreciate feedback from you.

The game now shows a hint after the second incorrect guess. For example the hint "The US covers 1.87% of the Earth's surface." is displayed for the question about what percentage of the Earth's surface is land.

How does the new information received through the hint impact your guess and assumptions? help

[d--b]

Geez, I seem to be particularly good at this. Made my day!

[ishita159]

117B people have lived on the planet!?!?!?!

This is a really cool game. I was so off!

[danielfetz]

It's quite extraordinary that so many people have come before us, and it gets quite sad when one understands that half of those died before they turned 15 years old. The human graveyard is full of children, and we shall never forget where we came from and how much progress we have since made.

Source for this: https://ourworldindata.org/the-future-is-vast

[mondobe]

Very neat! I'd love a feature where I can share my score with a link to the website (although it's possible there already is one and I just missed it).

[danielfetz]

No, you didn't miss it. I will implement that either today or tomorrow. If you don't mind to answer: do you have any other feedback? Is the win criteria of ±10% good? Or should it be loosened up to ±25%?

[mondobe]

I think the win criteria is good. I would think about automatically showing the "How to Play" screen on a user's first visit so that they are aware of the criteria.

[danielfetz]

I have now implemented a share function, thanks for the suggestion once more!