Bankers can be useful. That much I just found out.
Yesterday - in my eternal quest for a perfect Castille/WC game - I decided to pick a couple of bankers for advisors. There weren't any investment-advisors or diplomats available anyway. So I (quite quickly) end up with two 3* and one 4* advisor. And that's just in 1400.
The idea? Such a collection of advisors has indeed an opportunity cost. Not picking investors means I'll lag slighty behind other players. Not picking diplomats or the traditional master of mint means I'll have slower expansion and/or inflation. On the other hand, they might allow me to take loans at acceptable interest-rates, therebye funding conquest in the very early game. The latter turned out to be overwhelming.
Bankers turned out to be the perfect weapon against inflation. In addition they allowed me to do some pretty nice stuff in the early game. So upon two or three months in the game I decided that my starting cash was insufficient for my army. I took a loan (209 ducats for 0.2 interests monthly... lol), build two ships and some forces. I'd go out with these forces, win some war, extort cash, conquer and forcevassalize... and by the time I'd have to repay that loan I'd have the option to extend that loan against the same ridiculous 1% interests or to repay it. It turned out that bankers could be abused as a source of funding. I was quite often running around with two or three loans (four being the maximum so far ), and doing whatever I could think of. Cash was unlimited.
It's 1411 now, and my Castille has already paid off at least 6 loans, has currently two more loans, found the cash to become Defender of the Faith (350 ducats? 400 ducats?), found some more cash to pay for the Gilded Iconography (240 ducats), has an army close to it's forcelimits (40/42 regiments) and a navy greater than it's forcelimits (30/27 or so ships, out of which 18 carracks). I forcevassalized Sicily and Napoli. Conquered all of Granada, grabbed Morea from the Byzantines, conquered five provinces against the Ottomans and two from the Mammeluks (including Judea). I also took four provinces from Aragon. I'm converting all these provinces as fast as I'm gaining missionaries. In the meantime I got lucky enough into a Personal Union with Portugal. My inflation? A 0.02%. And half of that is the result from a goldrush. The DotF-title was mostly there to guarantee constant warfare and wartaxes without skyrocketing warexhaustian. Due to missions my BB is only at 8 points. I think the financial gains are - for the most part - thanks to the war taxes more than the extortions, and thanks to a big army allowing me to crush anyone on my path rather than having to fight pitched battles against even minor countries.
Granted, Castille is quite a suitable country for any blitz-approach. But this start got me hugely surprised. 12 years of play so far. Imagine what the other 400 will add to that.
Bankers rock. Give them a try.
Some maths to convince the reader:
Quite a few players correctly realized that the interest payments on loans killed all possible investment opportunities. (Apart from the Byzantine player, who just needs to survive. But I do not exactly intent to copy that style.) Even one percent of interest would kill most investment opportunities. If you were to take a loan to build something (let's say an old fashioned workshop in a cored province in HTTT, 50 ducats and 8% return or it's equivalent in DW), after five years you'd only have 4 years of return (4*8%=32%), but you haven't regained your initial cash. Lending en masse to pay for workshops would in the end either force you to mint or to extend loans, paying higher interests and... well to mint. Which makes one wonder why one wouldn't just mint and forego the difficulties of lending altogether.
However. Suppose we build the same workshop (8% return per year, one year construction time) with a loan that we could extend as much as we want to against 1% of interest. (In pretty much the same setup as explained above.) After one year, you'd just extend the loan, until the workshop has paid back the loan and it's interests. That equals following equation:
0,01*x = 0,08*x - 1
with x being the needed years for the workshop to pay for itself. The left-hand-side of the equation is the cost of the loan in years. The right-hand-side is the return of the 8%-investment, substracted by 1 as you need to have the original cash returned as well. This equation has a solution for x = 14.2.
Or: if you were to sit around with loans for 14.2 years, you could spam as many workshops in your cored provinces (the 8% return) at day one, and still get away with it. The only 'cost' to this approach is the fact that you need to have bankers for advisors in the first place. Imagine what a 500-province-empire could do with this knowledge, or someone who intends to spam manufactories. (I know, DW cuts these kind of plans down, but hey... I'm still at HTTT, and there may be opportunities to copy this style to DW as well.)
Now, what happens when we decide to 'wait' constructing the workshops. Suppose that we're a minor country that isn't too eager to mint, and that's too poor/unwilling to visit a banker. Waiting a year to construct it would have an opportunity cost of 8% - 1% = 7%. 8% because of the loss in return, 1% substracted because that smallish country wouldn't be paying loans. If we assume small (non-massive trading) countries have an income of about 25 ducats/province, then minting in order to get the money needed for a workshop would equal 2% of inflation and two years of not investing. All in all, I have a pretty hard time to see how minting is the optimal choice given that you can spend advisors on interest-reduction of course.
Another quick example. Suppose you were to have only one banker (DW). This banker has 6 stars, loans cost 3% of interests, and we're lending money for our 8%-investment. The alternative is minting for a grand total of 2% of inflation. (25 ducats income per province, 50-ducats of investment, 8% or 4 ducats in return)
The lending-approach would yield a profit (for 14.2 years) of 8%-3% = 5% initially for the first 14.2 years. After that phase, the interests are paid for and the loans are cancelled, meaning you'd have a return from that point onwards of 8% on your investment.
Minting gives you 2% of inflation but 8% in return immediately. Or 6% return for the rest of the game.
The equation then becomes:
14.2*x + 8*x = 6 (x+14.2)
with x being the amount of years left in the game. This equation has a solution for x = 7.1 Or: if there's still 14.2+7.1 = 21.3 years left in the game, lending cash is superior over minting given the constraints above.
Veteran players will remark that inflation because of minting doesn't matter too much. Hiring a master of mint could easily deal with that. We make the calculations for the minting approach (with a hired master of mint) and the lending approach (with a hired banker). Both advisors are six-star advisors, giving -0.12 inflation reduction and -6% interests on a base interest of 7% (equalling +1 stability and no loans).
Minting gives you 2% of inflation, gradually reduced by -0.12% a year, for an investment of 8% for the rest of the game. Lending gives you 14.2 years 1% of interests to pay for, after which you have 8% return on investment. The inflation from minting could be brought to zero after 16.6 years. Paying back the interests on the loan is done at 14.2 years. All in all, lending is - in this setup - superior. Even for interest rates of 2%, or for an income/province of 50 ducats and thus only 1% of inflation due to minting, the above holds (given a rate of return of 8% on your investment). If your banker wants 3% however, you should probably put him on some stake.
kind regards,
Andy
Yesterday - in my eternal quest for a perfect Castille/WC game - I decided to pick a couple of bankers for advisors. There weren't any investment-advisors or diplomats available anyway. So I (quite quickly) end up with two 3* and one 4* advisor. And that's just in 1400.
The idea? Such a collection of advisors has indeed an opportunity cost. Not picking investors means I'll lag slighty behind other players. Not picking diplomats or the traditional master of mint means I'll have slower expansion and/or inflation. On the other hand, they might allow me to take loans at acceptable interest-rates, therebye funding conquest in the very early game. The latter turned out to be overwhelming.
Bankers turned out to be the perfect weapon against inflation. In addition they allowed me to do some pretty nice stuff in the early game. So upon two or three months in the game I decided that my starting cash was insufficient for my army. I took a loan (209 ducats for 0.2 interests monthly... lol), build two ships and some forces. I'd go out with these forces, win some war, extort cash, conquer and forcevassalize... and by the time I'd have to repay that loan I'd have the option to extend that loan against the same ridiculous 1% interests or to repay it. It turned out that bankers could be abused as a source of funding. I was quite often running around with two or three loans (four being the maximum so far
), and doing whatever I could think of. Cash was unlimited.It's 1411 now, and my Castille has already paid off at least 6 loans, has currently two more loans, found the cash to become Defender of the Faith (350 ducats? 400 ducats?), found some more cash to pay for the Gilded Iconography (240 ducats), has an army close to it's forcelimits (40/42 regiments) and a navy greater than it's forcelimits (30/27 or so ships, out of which 18 carracks). I forcevassalized Sicily and Napoli. Conquered all of Granada, grabbed Morea from the Byzantines, conquered five provinces against the Ottomans and two from the Mammeluks (including Judea). I also took four provinces from Aragon. I'm converting all these provinces as fast as I'm gaining missionaries. In the meantime I got lucky enough into a Personal Union with Portugal. My inflation? A 0.02%. And half of that is the result from a goldrush. The DotF-title was mostly there to guarantee constant warfare and wartaxes without skyrocketing warexhaustian. Due to missions my BB is only at 8 points. I think the financial gains are - for the most part - thanks to the war taxes more than the extortions, and thanks to a big army allowing me to crush anyone on my path rather than having to fight pitched battles against even minor countries.
Granted, Castille is quite a suitable country for any blitz-approach. But this start got me hugely surprised. 12 years of play so far. Imagine what the other 400 will add to that.
Bankers rock. Give them a try.
Some maths to convince the reader:
Quite a few players correctly realized that the interest payments on loans killed all possible investment opportunities. (Apart from the Byzantine player, who just needs to survive. But I do not exactly intent to copy that style.) Even one percent of interest would kill most investment opportunities. If you were to take a loan to build something (let's say an old fashioned workshop in a cored province in HTTT, 50 ducats and 8% return or it's equivalent in DW), after five years you'd only have 4 years of return (4*8%=32%), but you haven't regained your initial cash. Lending en masse to pay for workshops would in the end either force you to mint or to extend loans, paying higher interests and... well to mint. Which makes one wonder why one wouldn't just mint and forego the difficulties of lending altogether.
However. Suppose we build the same workshop (8% return per year, one year construction time) with a loan that we could extend as much as we want to against 1% of interest. (In pretty much the same setup as explained above.) After one year, you'd just extend the loan, until the workshop has paid back the loan and it's interests. That equals following equation:
0,01*x = 0,08*x - 1
with x being the needed years for the workshop to pay for itself. The left-hand-side of the equation is the cost of the loan in years. The right-hand-side is the return of the 8%-investment, substracted by 1 as you need to have the original cash returned as well. This equation has a solution for x = 14.2.
Or: if you were to sit around with loans for 14.2 years, you could spam as many workshops in your cored provinces (the 8% return) at day one, and still get away with it. The only 'cost' to this approach is the fact that you need to have bankers for advisors in the first place. Imagine what a 500-province-empire could do with this knowledge, or someone who intends to spam manufactories. (I know, DW cuts these kind of plans down, but hey... I'm still at HTTT, and there may be opportunities to copy this style to DW as well.)
Now, what happens when we decide to 'wait' constructing the workshops. Suppose that we're a minor country that isn't too eager to mint, and that's too poor/unwilling to visit a banker. Waiting a year to construct it would have an opportunity cost of 8% - 1% = 7%. 8% because of the loss in return, 1% substracted because that smallish country wouldn't be paying loans. If we assume small (non-massive trading) countries have an income of about 25 ducats/province, then minting in order to get the money needed for a workshop would equal 2% of inflation and two years of not investing. All in all, I have a pretty hard time to see how minting is the optimal choice given that you can spend advisors on interest-reduction of course.
Another quick example. Suppose you were to have only one banker (DW). This banker has 6 stars, loans cost 3% of interests, and we're lending money for our 8%-investment. The alternative is minting for a grand total of 2% of inflation. (25 ducats income per province, 50-ducats of investment, 8% or 4 ducats in return)
The lending-approach would yield a profit (for 14.2 years) of 8%-3% = 5% initially for the first 14.2 years. After that phase, the interests are paid for and the loans are cancelled, meaning you'd have a return from that point onwards of 8% on your investment.
Minting gives you 2% of inflation but 8% in return immediately. Or 6% return for the rest of the game.
The equation then becomes:
14.2*x + 8*x = 6 (x+14.2)
with x being the amount of years left in the game. This equation has a solution for x = 7.1 Or: if there's still 14.2+7.1 = 21.3 years left in the game, lending cash is superior over minting given the constraints above.
Veteran players will remark that inflation because of minting doesn't matter too much. Hiring a master of mint could easily deal with that. We make the calculations for the minting approach (with a hired master of mint) and the lending approach (with a hired banker). Both advisors are six-star advisors, giving -0.12 inflation reduction and -6% interests on a base interest of 7% (equalling +1 stability and no loans).
Minting gives you 2% of inflation, gradually reduced by -0.12% a year, for an investment of 8% for the rest of the game. Lending gives you 14.2 years 1% of interests to pay for, after which you have 8% return on investment. The inflation from minting could be brought to zero after 16.6 years. Paying back the interests on the loan is done at 14.2 years. All in all, lending is - in this setup - superior. Even for interest rates of 2%, or for an income/province of 50 ducats and thus only 1% of inflation due to minting, the above holds (given a rate of return of 8% on your investment). If your banker wants 3% however, you should probably put him on some stake.
kind regards,
Andy
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