Exponential Idle

After my last post turned into a bit of a tirade about the creep of huge, exponential numbers in the current crop of idle games in the Google Play store, this one turns all that on its head.

Exponential Idle just shows an equation and lets you tweak the variables.

It starts with this unassuming blurb:

From there you get the main screen, showing the exponential equation that drives the whole game.  This was such a pleasant contrast from the games with thousands of graphical things bouncing around.  And I have always been fascinated with mathematics.  You should only need algebra to understand what's going on here.  Each tick (10 times per second), the app takes the current number and multiplies it by e to the power of b times x times dt.  f(t+dt) -- which means the current time plus the next tick -- equals the current value f(t) times e^(bxdt).  Perfect.  It shows these numbers at the top of the screen and they tick upwards as you make adjustments.

The point of the game is to reach the biggest number you can reach.  Which in this case, is exactly as advertised, no sugar coating.  And back to my point of the creep of big numbers in modern apps, this guy went all out with "you want big numbers, I will GIVE you big numbers."  

You may know about scientific notation.  It oddly pops up in games all the time these days.  Computers write 1.1e6 for 1.1x10^6, 1.1 times ten to the sixth power, which is 1.1 times a million, or 1.1 million.  So, while other idle games may hit you with an e24 or e30 from time to time, that's chicken scratch in this one.  (I am using lowercase "e" to match the game's style.)

For fun, our best estimate of the number of particles in the universe is about e80.

After a few prestige resets, you can spend 9e150 (9*x10^150) like it was nothing.  You can watch your output reach 9.9e9999, but then what?  We need a newer, shorter form for super-huge number, so welcome the "ee" notation.  The next number is ee4.  And that would be an excellent mid-level test on a math exam.  What would that even mean?  Rounded to one decimal place, the next number after 9.9*10^9999 would be 10^10,000 or 10^(10^4), which is what ee4 means. That's a one followed by 10,000 zeroes. And ee4.4 is 10^(10^4.4), and so on.  Truly insane numbers.

The author says that, within the bounds of the "story", the highest practical number is ee200, so let's call that infinity.

As for the interface, on the left column you can choose Variables or Upgrades.  On the right side you can choose x1, x10, x25, x100 or x(max) which would be the maximum amount you can currently afford.  Your on-hand cash is the f(t) number at the top, the current value of your function.  Under Variables, you can add to the variables, and under Upgrades you get to add to the coefficients in front of those variables.  Long-press the "i" button in the middle to see what the result will be.

A note about the costs of these boosts.  Since this is an exponential game, your cash f(t) is DIVIDED by the cost of a variable change or upgrade, but spending meta-currency is subtracted.

Basically, the x value is going to be some number times y plus a constant, y is some number times z plus a constant, and you can earn stars and spend then on more levels of variables.  Right now, I have

u = 2x11

s = 3u + 2x13

z = 8s + 2^2x26

y = 10z + 2^2x35

x = 25y + 0, which gives 213,500.

So, that huge number times b (currently 10416) times dt (4.33) is the power of e (roughly 2.71828) that is multiplied to my total every tenth of a second.  Until I tap some more and make it bigger.

When db passes 100 you can hit the first of the bottom icons to Prestige, which clears all your variables but gives you a new meta-currency called mu, which you can spend on huge Upgrades, and b gets a big boost, so you start again with a steeper curve.  I had never had reason to consider how the math of these big numbers would actually look.  But if you have ee10 and divide by ee7, it barely makes a dent on the third decimal point.  10^(10^10)/10^(10^7) = 10^(10^10-10^7) = pretty much still ee10, maybe ee9.999.  Now I have fresh math problems to work out in my head at night.  Cool.

That's it.  No graphics at all.  You earn stars and can spend them on upgrades or unlocking the three mini-games for 10, 75 and 150 stars.  You can buy a Buy All button for 30 stars, which will spend as much as you can afford when you hit it.  There are over 100 achievements that pop up when you hit certain milestones.  There is supposed to be an even higher tier of Prestige when you hit infinity: when you choose a Supremacy, it will reset all variables and upgrades and even set b back to a measly 0.001, but it gives a meta-meta-currency called psi for buying even more awesome boosts.

The Instructions page mentions another level beyond that: Graduation, which involves hiring students to do more work, and branching out with different equations and theories.

This is certainly not for everyone, but big points to the developer for being different, not holding back on the information density, and trusting that there is some audience with brain power.  Although the overall strategy ends up being: just Buy All until you can Prestige, rinse and repeat.  I look forward to seeing what the next level of meta is like.

1/12 update: after toying with it here and there, I have hit Prestige 25 times, my b is up to 1.45e6 and the highest total I've had so far is $ee15.2.  It's amazing that, even multiplying by e to the million+ power thousands of times, on the ee scale the numbers still tick up slowly.  The two mini games are both the kind of "slide the tiles to put the numbers in order" puzzles that I have always disliked.

1/16 update: without spending too much time staring at it, I am up to $ee34, and got my first teasers for Supremacy, but it told me to come back when my d(psi)>1.5.  I don't see a delta for psi, but psi itself is up to 1.11.  I added two new variables and the Accelerate button, which you hold down to have the multiplier go up (asymptotically leveling off, of course).  Will see where it goes form here.  I still don't see any reason why this equation should ever converge.

1/17: up to $ee48, and psi=1.41, so I'm getting close to that first Supremacy.  Somehow, I had 703 stars, so I bumped up a few variables and bought alpha for 150.