Show HN: Fermi – A Wordle-style game for order-of-magnitude thinking

I echo what the others say about the current interface.

I think there is an opportunity for "normal" and "hard mode" like Wordle. In normal you are given the names of the factors but have to enter the expressions for their value (no default values given). In hard you have to come up with your own factor names as well as the values (the name is purely aesthetic for the user to keep track of their ideas). The win condition is the same (be within an order of magnitude of the answer) but maybe there is a special "super" win for being within 10% (log scaled, so lower bound n^0.9 and upper bound n^1.1).

A few thoughts, I tried this on mobile but got a bit confused by the initial "How to play" dialog (besides that it was too large to fit on screen). The dialog says:

  How to play. String together factors to answer the question.

... but the dialog doesn't pose a question! It just shows two factors with sliders, and the calculated answer, but no reason why we're sliding these two elements from left to right. I would skip the initial dialog for now, and perhaps make the "How to play" dialog very easy to reach to give a general description of the game, what is asked of the player, and how they could think about answering the question, instead of trying to explain the interface.

For the question I got ("How many people are flying in airplanes right now?"), the influencing four factors were nicely chosen, although I would refrain from guiding the player too much with (too) narrow "x - y" bands. We're looking for orders of magnitude, so you could think about sliders that also suggest thinking in orders of magnitude, say "1, 10, 100, 1000" (e.g. number of passengers on a plane), and "10 minutes, 30 minutes, 1 hours, 2 hours, 8 hours" (e.g. flight duration).

(Another angle here could be: how many flights and/or passengers does the nearest airport handle during a year, or how many flights/passengers do the global top 10 airports handle during a year, and how does that account for the total amount of flights in a year?). In other words: I don't think you want your players to do exact guesses using these rather precise sliders and narrow bandwidth, but hint them into also thinking in orders of magnitude.

I would skip the clicking on factors (I saw in another comment that you thought about arbitrarily mixing addition and multiplication, and their order in an earlier version, but that seems too difficult), and just give the player a few sliders and their proposed answer directly. Perhaps you can show the proposed answer directly beneath the question, start with 0, and have all sliders set to 0 (instead of the current random values) as well.

Another idea, perhaps even more intuitive, could be to give the player one (easy), two (intermediate) or three sliders (expert), without giving them hints for individual contributing factors:

- (slider 1) 1, 10, 100, 1000, ... for the rough orders of magnitude (e.g. "100")

- (slider 2) 1-9 multiplier for the chosen order of magnitude to give the player a way to say "it's more in the order of 500 than 100"

- (slider 3) 0-9 multiplier for one order of magnitude lower, to give the player a way to say "it's more 550 than 500"

Then the answer is calulated as (1) * (2) + (3). You can then tell the player if their chosen orders of magnitude were correct ("within the chosen order of magnitude"), slightly off (one order of magnitude too high or low), or too far off. Let the player decide if they want to be rather precise (with three sliders), or not.

Or even combine these ideas! Let the player choose a strategy ("guided" as you've already implemented with a couple of factors already given, or "non-guided", for lack of a better term, for those looking for an extra challenge).

Closing nit: "Share results" contains a non-existing domain.

If you need inspiration for future questions, have a look at this recent discussion [0] and linked website [1].

[0] https://news.ycombinator.com/item?id=43389455

[1] https://taylor.town/napkin-math

A kid/younger audience version of this would be great!

If I were doing something vaguely similar, I might emphasize:

- Bounds rather than point estimates. Hard bounds (definitely more/less than this) and soft bounds (likely). With associated payoffs/penalties. A point estimate too, but bounds first. Like error bars in a plot.

Perhaps even "bet your certainty" custom hardness. Perhaps an advanced "draw your payoff curve", so one might draw a hard step-function low bound with some soft slope on the high bound. So one might draw a big-payoff pointy spike, at the risk of missing entirely. A pretty UI might even multiply the curves for you. Perhaps one gets points for each component estimate, not just the final result - though might need an LLM to cope with the variety of possible steps in reasoning.

- Order of magnitude. That's "is it more like 1/10, 1, 10, 100, 1000" etc. One can do "high/middle/low order 10^n". But oom estimation a different mindset than linear. Exponential not linear. Linear slider as UX smell.

- Permit multiple chains of reasoning. An argument that nicely establishes a hard lower bound may be of no help in firming up a high bound. And a bound may need to be hammered with multiple chains of reasoning to tighten it up.

Fermi estimation can be the aggregation of exponential-rough-quantitative reasoning with attention to confidence/uncertainty.

In a group setting, one might have: "Ok everyone, how many cats live on this block? Is it more like 1, 10, 100, 1000, etc? Can anyone suggest a bound?" "I saw one in the window this morning - so hard lower bound of 1." "Unless it's been taken to a vet." "The town human population is 10^6, so it seems unlikely the block has that many cats..." "What does everyone think?" "How confident?" "Can anyone suggest another chain of reasoning? Can we tighten up the bounds?" "Could we do a stepping stone problem, the number of households on the block?"

Perhaps a "bet coins" on the answer before grading? One advantage of bounds vs more-common point-estimates is it pulls up the handling of confidence where it can be seen and improved. So anything which encourages reflection and self-evaluation, like betting, might help with that. Another advantage of bounding is it makes each attempt at narrowing bounds, on each component, into it's own little fractal estimation problem. So an initial estimation question proliferates many others. I wonder how a UI might emphasize that...?

But all that riffs on the Fermi estimation aspect, not the Wordle aspect.

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