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Mirreille
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I know recently I saw a discussion in a topic where they explained how to figure out which improvement is better between banks and stadiums. I am at that point now, where I am going to buy one or the other. I went through 16 pages of this subforum, but just could not find it. :(

I have 20% income boosting from my 2 banks, foreign ministry, and a harbor. So I get that a stadium will net me $6 x 1.2 =$7.2 increase to my gross. How do I figure out how much a bank would add? That is the part where my math skills fail me. Little help?

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Well, technically you have 20,897% extra income from your improvements: 1,14 (two banks) * 1,01% (harbor) * 1,05 (foreign ministry) = 1,20897. 1,20897*$6 = $7,25382. So that's the amount of money a stadium will give you.

Wel'll say your population's gross income = x. Then the income increase of a bank would be 1,07*x and that of a stadium would be x+7,25382.

1,07x = x+$7,25382 ==> 0,07x = $7,25382 ==> x = $103,626. So that's the break even point.

In other words, if the gross income is higher than $103,63, you're better of with a bank, if the income is lower than $ 103,63, you're better of with a stadium.

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The principle of choosing improvements after the harbor is simple - what maximizes income (whether by increasing income, by lowering costs or by getting the most value from aid funds).

After a harbor the choice is usually between factories, banks and stadiums. The reason is simple - banks give the highest income increase (+7%), and factories lower infrastructure purchase costs (-8%) and stadiums give +3 happiness (which equates to +$6 income, increased by multipliers such as banks). At the early stages - infra is the primary target as this determines population, which determines income, which determines growth.

Depending on resources, income levels, aid levels and expected spending (as not everything goes on infra) a bank, factory or stadium will usually be the best choice after the harbor - to find out which will be best you need a calculator (ie work it out). Aid levels make a difference as this is not generated by income levels but is simply there to be spent, so maximizing the value for money is important.

The maths: First you should look at your income levels and divide by the multiplier. Since harbors give a 1% boost, if you had one harbor you would have a multiplier of 1.01. If you had one bank, the multiplier would be 1.07 (7%). Having both, it is 1.01 * 1.07 = 1.087.

As previously mentioned, same improvements multipliers stack, so two banks and one harbor gives you 1.14 * 1.01 which gives 1.1514. Now, take your income per day, and divide by your multiplier. Say the income is $130.00 and you have one bank and one harbor. $130 / 1.0807 $120.29. This is your base income. To see how much your income will increase if you buy a bank, multiply your base income by 0.07. In this case, one bank will give you an increase of $8.42. Compare this to a stadium.

One stadium gives you +3 happiness, which equates to +$6 * (multiplier) income. Your multiplier is 1.0807. So, 1.0807 * $6 = $6.48. The bank gives you more income at this time. Buy a bank.

If you have significant aid cash (significant in relation to earnings) then factories may make sense as you are simply going to spend a lot on infra and can benefit enormously from the lower cost.

(MFO Improvement Guide)

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Thank you all for the replies. I hadn't realized you have to do all the individual income multiples seperately. Also I had not figured out to divide the gross by that number to find the base; the base is what I couldn't find.

ArgonV: That's algebra, you lost me right there. I haven't used algebra in decades. :blink:

Boondock: That sounds like a safe plan in any event. What was throwing me was the fact that I have an extra odd multiple in there(foreign ministry) and a an extra happiness toy as well(border wall) confusing the issue.

Edit: Ok, I tried to do this myself. My gross is $124.78, I ended up with a 1.35744 multiplier for my 4 banks, ,and foreign ministry. The Bank number I came up with was $6.4346, and the Stadium number I came up with was $8.1446, the base income number I came up with was $91.923. If all of this is correct...stadium next, right?

Edited by Mirreille
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The maths: First you should look at your income levels and divide by the multiplier. Since harbors give a 1% boost, if you had one harbor you would have a multiplier of 1.01. If you had one bank, the multiplier would be 1.07 (7%). Having both, it is 1.01 * 1.07 = 1.087.

As previously mentioned, same improvements multipliers stack, so two banks and one harbor gives you 1.14 * 1.01 which gives 1.1514. Now, take your income per day, and divide by your multiplier. Say the income is $130.00 and you have one bank and one harbor. $130 / 1.0807 $120.29. This is your base income. To see how much your income will increase if you buy a bank, multiply your base income by 0.07. In this case, one bank will give you an increase of $8.42. Compare this to a stadium.

One stadium gives you +3 happiness, which equates to +$6 * (multiplier) income. Your multiplier is 1.0807. So, 1.0807 * $6 = $6.48. The bank gives you more income at this time. Buy a bank.

(MFO Improvement Guide)

I'm sorry, but I don't agree. You have alerted me on a mistake I made in my previous post though, it has to do with improvements stacking instead of multiplying.

Anyway, the mistake is as follows: Say you have a base income of $100,00, 2 banks and a foreign ministry (for simplicity's sake). That would mean each citizen now earns $100*1.14*1.05 = $119,70. If you buy another bank, then, according to your guide, you'd only make $7,00 more. Base income of $100*1,07 = $7. However, if you do the math, you should be getting $100*1,21*1,05 = $127,05. That isn't a $7,00 increase, but a 7,35 increase.

The error here is simple, you're ignoring the foreign ministry. 7,35/7 = 1,05 which is exactly the modifier of the foreign ministry. So if you want to find out if a bank is the a choice than a stadium, you need to divide your income by the modifier of your banks only and check if that number*1.07 is more than the $6*(current modifier) that you'd get from a stadium.

I tried this (on paper, not in game) for multiple other improvements as well, like a harbor and a foreign ministry, and it still flies then. So I think there's an error in your guide.

ArgonV: That's algebra, you lost me right there. I haven't used algebra in decades. :blink:

Edit: Ok, I tried to do this myself. My gross is $124.78, I ended up with a 1.35744 multiplier for my 4 banks, ,and foreign ministry. The Bank number I came up with was $6.4346, and the Stadium number I came up with was $8.1446, the base income number I came up with was $91.923. If all of this is correct...stadium next, right?

Ok, I'll try to leave algebra out of it this time then :P

Let's see. Your total modifier is 1,28 (four banks) * 1,05 (FM) * 1,01 (harbor) = 1,35744 indeed. Your base income is then $124,78/1,35744 = $91,923. Add the modifiers for the FM and harbor again and you'll get a modified base income of $97,484. One bank would add 0,07*$97,484 = $6,823. A stadium would add $6*1,35744 = $8,14464. So yes, a stadium is obviously the better choice for you.

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A rotation is always good between the two. Why?

Because the Stadium increases your base income and the bank is a multiplier of the base income.

If your base is low then you just are multiplying a low number. If your multiplier is low then your base just sits there unboosted.

Essentially, they feed each other. By themselves they are simply good improvements. Working together they are great!

People are always trying to figure out which they should get out of banks, stadiums, and factories next. You could pound out the math and likely find out that an even rotation between the three ends up close to correct for just about every nation. So why go killing yourself? Just alternate between the three. If you are scrimping for every last nickel then go sell some tech! A half dozen tech deals and you'll have vaulted past this bank/stadium question because you will already have 5 of each. ;)

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That would not work for me +Zeke+, I have no tech cost reducers, and the price for 50 is already over $1.5 million for me. What with paying a middleman there is no way I can make that profitable; I'm just not set up for it.

Going back and forth sounds like a safe option in any event. I guess the foreign ministry and border wall I have balance each other out. I was wondering how to account for them in the decision.

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Having the foreign ministry early isn't necessarily a problem, particularly if you receive a lot of aid or are tech dealing, but a border wall is way too early for very little gain. There are far better choices to gain happiness than the border wall which is costing you 2% of your population. Granted, it improves your environment by one, but that only translates to .4 happiness. You should really replace that border wall with a stadium and you'll be making more money than you are currently.

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I'm sorry, but I don't agree. You have alerted me on a mistake I made in my previous post though, it has to do with improvements stacking instead of multiplying.

Anyway, the mistake is as follows: Say you have a base income of $100,00, 2 banks and a foreign ministry (for simplicity's sake). That would mean each citizen now earns $100*1.14*1.05 = $119,70. If you buy another bank, then, according to your guide, you'd only make $7,00 more. Base income of $100*1,07 = $7. However, if you do the math, you should be getting $100*1,21*1,05 = $127,05. That isn't a $7,00 increase, but a 7,35 increase.

The error here is simple, you're ignoring the foreign ministry. 7,35/7 = 1,05 which is exactly the modifier of the foreign ministry. So if you want to find out if a bank is the a choice than a stadium, you need to divide your income by the modifier of your banks only and check if that number*1.07 is more than the $6*(current modifier) that you'd get from a stadium.

I tried this (on paper, not in game) for multiple other improvements as well, like a harbor and a foreign ministry, and it still flies then. So I think there's an error in your guide.

You're right, the wording is incorrect. Thanks. You should be dividing the income by only the modifiers for your banks, THEN multiply by .07.

Compare that to $6*multiplier.

So in the guide example: $130 base income/1.07 (current bank level). Then that value is unmodified by banks, so you can see what an additional seven precent yields.

Thanks for pointing out the mistake ArgonV.

Guide fixed.

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