Which house is the best investment to build up money?

Solution 1:

To answer this question, let's first look at the basic values associated with each building:

In the table, we have the following values:

• Name
  The name given to the building in the game.

• Cost
  The amount of money you have to pay to buy the building.

• Tax Time (m)
  The amount of minutes you have to wait between payout cycles.

• Tax Amount $
  The amount of money you earn each payout cycle.

• Tax Amount XP
  The amount of XP you earn each payout cycle. This data point is only included for informational value and will be ignored for any further value assessments.

The first question that needs to be answered is, how many payout cycles does it need to pay off the initial investment for building the house (Return Of Investment)?

New values in this table are:

• ROI after(t)
  The amount of taps (or payout cycles) required to earn back what you initially invested in the building.

• ROI after(m)
  The amount of minutes that will have passed for these payout cycles to happen.

Visualizing this value in a bar chart paints a clear picture:

Obviously, the Brown House is the clear winner. It pays off the fastest and from there on everything goes right into the bank, right?

Not so fast! While it might pay off the fastest, other houses might have the potential to be more lucrative since they pay out more money. So, given enough time, the total earnings may be higher for them compared to the Brown House. Let's check!

We're now introducing a new value:

• Earnings per minute
  The amount of money you earn each minute by having built the given house.

Okay, so, obviously, the Brown House is the best investment. It has the best ROI and it also pays off the most amount per minute. Right?

Well, in theory, yes. But to make use of this money fountain, you would have to make sure to hit every payout cycle within the 24 hour window and tap on the house every 5 minutes.

This is unrealistic in 2 regards:

1. You won't be able to play the game 24 hours a day every day.
2. You won't watch the game all the time to tap the house every 5 minutes.

So, let's look at the table again.

We now have another 2 values:

• Taps/day
  The theoretical total amount of payout cycles in a day.

• Real taps/day
  A value that takes into account 8 hours of sleep time and assumes a delay between payout cycles. This delay drastically reduces the amount of realistic payout cycles for the Brown House.

The results show that the realistic payout for the high-frequency houses is much lower than initially assumed, while the low-frequency houses pay out close to their theoretical limit. They still pay out generally lower because the overlap between your sleep cycle and the payout cycle will vary.

So, given these results, let's revisit the ROI again.

Again, we have 2 new values:

• ROI after (d)
  The same as ROI after (m) we had earlier, but converted to days.

• ROI real (d)
  The ROI in days, using our Real taps/day as a basis for calculation.

• Earnings/minute real
  How much we would actually be earning per minute, given that we don't play 24/7 every minute of the day.

Okay! So, that didn't change much. Even if I only hit 50% of the projected payout cycles, the ROI for the Brown House is still superior to any other house! And I earn money the quickest!

Not so fast Timmy! We're still assuming 96 payouts per day for the Brown House. A bit much if you ask me. The ROI for the Brown House will always be the best, but once you drop the number of payouts per day below 67, the White House will earn at a faster rate. And if you drop the number of payouts even further, the Purple House and Blue House will earn faster as well.

So the Brown House is only the best long-term investment if you're able to keep your number of payout cycles high.

But this isn't even the end of the story.

The lot you place a house on costs money as well. And you can only fit a limited amount of houses into each lot. So the size of the house is relevant as well.

Our new metrics:

• Size
  The number of individual squares the house takes up.

• ROI/square
  When each of the squares will have paid itself off (in days).

• Earnings/square
  How much money you will make off of each square in a day.

Hey, now the White House doesn't look too bad all of a sudden, does it? And this is still with the assumed 97 payouts per day for the Brown House.

So it looks like the White House might overall be a better long-term investment.

So there is one question left to answer. Given the long ROI time for the White House, how long does it take until it becomes a better investment than the Brown House?

Let's take a lot of 16x16 as the base for our calculation (we assume every house fits perfectly into this space, which is, of course, not entirely correct).

Here's the projection for the first year. Looking at those lines, it seems obvious that it'll take a couple more years for the White House to take over. Mind you, this is still with 97 payouts per day for the Brown House.

How would the same look with something like 32 payouts per day for the Brown House?

The point where the White House takes over is after 29 days. It is the best, realistic, investment given cost per square and realistic payout cycles per day.

But I already hear you screaming, "What about the delay for the first payout cycle to kick in?!" Yes, you're right, it's not like every house instantly starts paying out. It takes a while to build. While the White House takes a day to build, the Brown House could already have paid out up to 287 times!
These earnings would only make up for 1 day difference in the projection pictured above. Thus, they were ignored.

References:

• http://simpsonswiki.com/wiki/The_Simpsons:_Tapped_Out_homes
• http://simpsonstappedout.wikia.com/wiki/Land_Expansion