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.
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".
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.
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.
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!
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.
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.
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.
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?
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.
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.
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.
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.
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).
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%?
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.
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.
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.
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".
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?
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?"
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!
A HN moderator actually directed me to this post. I never would have seen it otherwise, so I'm grateful for that.
Otherwise the UI and concept looks pretty interesting. But until that is fixed, it is unplayable for me.
(On an iPhone, using Safari)
After about ~10 questions though, I started getting the same question every time. Like five times in a row.
So, I any guess above 1 000 is truncated. 1 000 is 1.
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
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.
Then report the average of this metric over time with each game.
I have an idea for a gameplay that I think I would enjoy more:
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.
This is a really cool game. I was so off!
Source for this: https://ourworldindata.org/the-future-is-vast