Monday, 4 June 2012

Eggs vs. Beans: Fight!

A recent forum thread asked whether it was better to make beans or eggs.  In particular, the analysis focused on whether it was better to make Fruit Beans or Chicken Eggs.  Some helpful comments on that thread explained the imagination gained for making and donating each and the energy required to make them.  What I'd like to do is convert everything into equivalent units and talk about which is most favorable for the time you spend making them.

So what are my common units?  I've used these conversions before.  Energy is worth 0.8 currants because you can pretty easily buy food at auction for 80% of it's list value.  Imagination is worth 1.07 currants because you are choosing to donate rather than sell things, which means you are choosing to get 0.72 times their list value in imagination rather than 0.75 times their list value in currants - but also to get the imagination you need to use shrine powder, so I discounted it to 0.7 as an approximation.

Buying Garlic
Most of the comments on the thread were comparing beans to eggs while assuming you were grinding your own garlic.  So first let's do a little comparison of grinding versus buying garlic.

First, buy garlic at a produce vendor, not a grocery vendor.  Produce vendors mark up 11% while grocery vendors mark up 13%.  That doesn't sound like a big difference but there is rounding.  Garlic is worth 4, so 4.44 rounds to 4 while 4.52 rounds to 5.  Thus garlic at a grocery vendor is actually 25% more expensive.

Thus you can either use 10 allspice, 20 energy and 3.2 seconds get 10 garlic plus 12 imagination or you can use 40 currants to get the garlic and get no imagination.  If the 20 energy is worth 16 currants and the 12 imagination is worth 13 currants then the question is, would you sell 10 allspice and 3.2 seconds of your time for 37 currants.  Since you can currently sell that allspice at auction for 6 currants each (less a 7% listing fee) you could turn the 10 allspice into 55.8 currants.  So I think buying is the clear winner.

Bean vs. Egg Profits
If you aren't going to grind garlic then you get 3 imagination per white gas and 15 per chicken egg you make.  With 20% bonus from high mood that's 3.6 and 18.  A post in the thread incorrectly says you get 4 imagination from making white gas; you'll get 4 if you make only one with full mood, but making one a time is going to be terribly inefficient, and making 40 at a time will get you 144 imagination - 3.6 each.  You also get 144 imagination for each egg donated.  That's a total of 165.6 imagination per egg.  Doing that requires 30 energy, 8 gas, 1 egg, 40 currants and 2.625 seconds spent crafting.

For the fruit tree beans you don't have the option of buying ingredients from vendors so you have to make them all.  Grinding cardamom and making laughing gas gives 1 imagination each, so a total of 6 with full mood for large quantities.  The fruit bean itself is worth 50, or 60 will full mood.  You get 108 imagination for donating it.  That's a total of 174 imagination per bean.  Doing that require 39 energy, 6 gas, 9 allspice, 1 bean and 4.2 seconds spent crafting.

Let's convert all of that to currants.  Using Ecurnomics I'm valuing General Vapour at 7, Allspice at 6, Eggs at 5 and Beans at 6 (beans being more valuable than eggs is strange but true).

So the cost of making an egg is:
24 currants (30 energy)
56 currants (8 gas)
5 currants (1 egg)
40 currants (40 currants)
= 125 currants

And you gain 165.6 imagination which is worth 177.2 currants.  That's a profit of 52.2 currants which is 19.89 currants per second.

The cost of making a bean is:
31.2 currants (39 energy)
42 currants (6 gas)
54 currants (9 allspice)
6 currants (1 bean)
= 133.2 currants

And you gain 174 imagination which is worth 186.2 currants.  That's a profit  of 53 currants which is 12.62 currants per second.

Eggs win!

Is that Too Simple?
You probably would have a point if you said that reducing everything to currant value is not an accurate representation of the worth of things.  Suppose you gather the ingredients yourself instead of buying them at auction?

First of all, let's look at gathering the ingredients yourself.  The egg takes a total of 9 tree ingredients while the bean takes 16.  Gathering tree ingredients takes 3 seconds to get 12 ingredients with a 10% chance of getting 36 more for a total of 15.6 ingredients.  Of course there is a lot of walking in between.  To get an idea of how long it took to actually get the ingredients I took a 15 minute walk on the gas route to see what I'd get.  I managed 168 harvest which should average 2620.8 gas.  That's one gas generated every 0.347 seconds.

So let's look at that again.  The cost of making an egg is now only 64.9 currants because we aren't paying for the gas but we are paying energy to harvest it.  That makes the profit 112.3 but the time to make it is now 5.75 seconds, so it's 19.53 currants per second.

The cost of making a bean is not only 32.8 currants because we aren't paying for anything but the energy.  So the profit is 153.4 but the time to make the bean has increased to 9.74 second so that's only 15.73 currants per second.

It's closer but the egg still wins by a wide margin.

But what if you argued that spending currants on garlic for the eggs was beyond your means.  You make beans because there is no currant input!

It turns out that in this case that doesn't help the case of beans at all.  Suppose instead of donating all the eggs you just sold 4 out of every 15 you made.  That would mean you get 600 currants per 15 eggs so the cost of eggs in currants would go to zero.  On the flip side you'd only get 11/15 of the 144 imagination you are supposed to get from donating each egg, so you'd lose out on 38.4 imagination which is 41 currants.  That means it only drops the profit of eggs by 1 currant and even then that's only because of the way I've rounded things - if I didn't round at all it would be dead even.

Finally, what if you don't value energy at 0.8 currants but instead you value it at nothing because you  don't play for long stretches of time, you meditate and use no-no powder and otherwise never actually have to spend real energy that you paid for.

That reduces the cost eggs by 24 currants but reduces the cost of beans by 31.2 currants (slightly more in the gathering scenario).  That leaves eggs at 29 currants per second if you buy ingredients and 23.7 currants if you harvest; but beans only make it up to 20.3 currants per second if you buy ingredients and 19.11 if you harvest.  Eggs still win.

Aren't We Getting Favor Too?
We sure are, and that just makes things look better for eggs.  With eggs you get 60 favor per egg but with beans you only get 45 favor per bean.  Since eggs take less time to make than beans, eggs are far better for favor.

Why Do People Make Beans?
It turns out people make beans for imagination rather than eggs are not all crazy or misguided.  Some of them are doing exactly the right thing.  But how could this be.

Every day you can only earn so much imagination from donating - 10% of what your current level costs.  That cap will range from very small at low levels to over 100k at high levels.

Suppose every day you make enough eggs or beans to exactly reach that cap, or you don't make enough to reach the cap.  Then the analysis above is correct and eggs are better.  However, suppose each day you made gathered and crafted and made so many eggs and/or beans that you could reach that cap and exceed it?

With eggs you get 87% of the imagination you earn from the donation, the rest is from crafting.  With beans you get only 62% of the imagination you earn from the donation, a full 38% comes from crafting.

So suppose you are crafting eggs and your donation cap is 50k.  You are gathering ingredients.  In order to make enough eggs to reach your cap you will need 347.2 of them each day.  That will take about 1997 seconds or just over 33 minutes.  In that 33 minutes you'll earn 50k from donations plus almost 7.5k in crafting imagination and 1.2k from gathering from trees.

But you don't play for just 33 minutes.  What if you decided to earn your 50k from donations by donating beans instead?  You'd need to donate 462.9 of them, and that would take you almost 68 minutes to harvest and create.  You'd get your 50k from donations plus 30.6k from crafting and 2.8k from gathering.

In the first example you spend 30 minutes earning 58.7k imagination and in the second you spend 75 minutes earning 83.4k imagination.  The eggs scenario is way better imagination per second (29.4 vs. 18.5), but the question is, how much imagination can you earn per second with those 42 minutes that you aren't harvesting gas and crafting eggs?

If the answer is that you can earn more than 10 per second than you should just make eggs and use that second best activity during the non-donating time.  But 10 per second is actually a really large amount.  If you played for two hours in a day 10 per second would be 72,000 imagination, a full day would be 144,000.  Do you earn imagination at that rate when you don't take donations into account?  Most of us do not and the rare cases where someone does it's usually by seasoning a large number of beans!

What Should You Do?
If you are actually producing what you can donate and your chief motivator is imagination then you should be making beans rather than eggs. Keep in mind that this is kind of a tall order.  As I noted above harvesting and making beans to keep up with 50k imagination in donations would require about 75 minutes of play per game day devoted just to that.  If you are getting into the higher levels your daily donation limit might expand well beyond 50k.

If you are currently level 47 or above and you play aggressively to make imagination for more than two hours each game day then beans are probably the ticket.  If you are not that high level or you don't play that much it probably means you are not nearly as crazy as you have to be to actually make beans better than eggs.

Here's a good use for all of that imagination you'll earn: Put 15 gas trees on your street and join the gas route.  More chicken eggs for all!


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