Posted September 24, 2013

I thought I'd clear up some pretty ambiguous information regarding what are probably the most useful hirelings in MM6 and 7: namely, the Factor, who can increase your total gold looted by 10% in exchange for a 5% cut, and the Banker, who can increase your total gold looted by 20%, for 10%.

First things first: the calculation that they use to determine how much money you get is multiplicative, not additive. To give you an example, if you were to loot a pile that would otherwise be worth X gold and you had a Banker in your party, an additive calculation would be X + 20%X - 10%X. (i.e. X + 10%X)

That's not what happens. What happens is that you loot what would otherwise be X gold, and the calculation is X * 120% * 90%.

Since 90% of 120 is 108, this comes down to X * 108% (a 2% decrease from the additive equivalent, but still an 8% profit).

Factors work the same way: X * 110% * 95%, which equals X * 104.5%, yielding a 4.5% profit.

I use the word "profit" here loosely, since it's only really a profit if it recoups the initial investment and then some. For Factors, the initial investment is 500g, and my goal is to show you that it isn't worth it.

To be profitable, a Factor must make a total increase to your loot assets greater than 500 gold. Thus, 4.5% * X > 500. Some simple algebra proves that X in this case must be greater than 11,112 gold; in other words, after hiring a Factor, you won't actually make a return on your investment until you've looted 11,112 gold (before returns) or 11,612 (after returns), and it's a waste of money to dismiss him/her before then.

But Bankers will be available to replace your Factor long before you loot that much gold. Thus, it's better not to hire a Factor at all.

For the sake of completeness, here's how much money you have to loot with a Banker in your party, before you get a return on that investment:

8% * X > 1000

X > 1000 * 100/8

X > 12,500

If you ever hire a Banker, and then dismiss him/her before looting 12,500 gold (before returns) or 13,500 gold (after returns), then you would have been better off not hiring the Banker in the first place.

Study your algebra, kids. It may make your RPGs easier.

First things first: the calculation that they use to determine how much money you get is multiplicative, not additive. To give you an example, if you were to loot a pile that would otherwise be worth X gold and you had a Banker in your party, an additive calculation would be X + 20%X - 10%X. (i.e. X + 10%X)

That's not what happens. What happens is that you loot what would otherwise be X gold, and the calculation is X * 120% * 90%.

Since 90% of 120 is 108, this comes down to X * 108% (a 2% decrease from the additive equivalent, but still an 8% profit).

Factors work the same way: X * 110% * 95%, which equals X * 104.5%, yielding a 4.5% profit.

I use the word "profit" here loosely, since it's only really a profit if it recoups the initial investment and then some. For Factors, the initial investment is 500g, and my goal is to show you that it isn't worth it.

To be profitable, a Factor must make a total increase to your loot assets greater than 500 gold. Thus, 4.5% * X > 500. Some simple algebra proves that X in this case must be greater than 11,112 gold; in other words, after hiring a Factor, you won't actually make a return on your investment until you've looted 11,112 gold (before returns) or 11,612 (after returns), and it's a waste of money to dismiss him/her before then.

But Bankers will be available to replace your Factor long before you loot that much gold. Thus, it's better not to hire a Factor at all.

For the sake of completeness, here's how much money you have to loot with a Banker in your party, before you get a return on that investment:

8% * X > 1000

X > 1000 * 100/8

X > 12,500

If you ever hire a Banker, and then dismiss him/her before looting 12,500 gold (before returns) or 13,500 gold (after returns), then you would have been better off not hiring the Banker in the first place.

Study your algebra, kids. It may make your RPGs easier.