Full monopoly problem

[stnikolauswagne]

I guess the problem is simple mass. There are probably lots upon lots of opms in the HRE, some of which have good sliders. You will probably have 5 merchants trying to compete in your cot every month (which is even a bit conservative i think). The AI is stubborn, so you will eventually lose your monopoly, upon which point the cot quickly fills up. If you wanna go for a really sucesful mercantile empire take either china, japan or india. For one thing they have easy access to the ridiculously strong east indian trade route modifier. For another thing their markets are not open to anyone of importance until someone beats you in a war.

 

[n0thin]

(a) formula for determining probability of a binary choice over x attempts is (possibility of desired outcome)^x. So in this case we want to know at what point it becomes more likely for a merchant to compete you out of the COT than not. Thus the point of comparison is your compete chance, which is .99. Next, since we want to know that point, we set it equal to that point. Hence it becomes .99^x = .5.

.99^x = .5
x log .99 = log .5
x = log .5 / log .99
x = 68.96756 = 69

Hence, ~70.

(b) I follow your logic here, but I'm simply observing my own data, which is suggesting that I can't seem to hold a full monopoly with 99% compete against everyone for more than a few months at a time. There's a discrepancy between your logic (which from all appearances is solid, I agree with you fully on it) and my results.

Well, your formula is just not right in this place. We don't want to find out when it becomes more likely for a foreign merchant to beat yours, that doesn't matter at all in this consideration. We just want to find out at which mean value your merchant with 99% compete chance (against EVERYONE) will lose against another merchant. And that is as simple as it looks: 99% chance => statistically the 100th foreign merchant will compete you out.

Probably the most important point to take into consideration is that you will NOT have the 99% compete chance against everyone. The usual Free Trade Countries (usually also with low infamy) like Holland, Navarra, Mecklenburg, Bar, Lorraine etc. are likely to have more than a 1% compete chance against you, if you are full Free Trade (as you said somewhere) and especially if you are trading in a lot of CoTs as the number of placed merchants slowly kills your compete chance . There is not that much you can do against that folk. The probably easiest ways besides moving towards Mercantilism (which is plain stupid if you are already full Free Trade) is either embargoing or conquering those countries. However, if you are able to hold full monopolies all over the place while being a FT country, Mercantilism is even worse than it is already, so this may be just as it is thought be PI.
One point to notice here is that in this case it is not recommend to free too much of the French minors if you win a war against France. Countries like Armagnac, Provence or Champagne have a really high Free Trade slider making them very annoying.

 

[Slym]

That isn't the way probability works.

 

[brifbates]

Well, your formula is just not right in this place. We don't want to find out when it becomes more likely for a foreign merchant to beat yours, that doesn't matter at all in this consideration. We just want to find out at which mean value your merchant with 99% compete chance (against EVERYONE) will lose against another merchant. And that is as simple as it looks: 99% chance => statistically the 100th foreign merchant will compete you out.

No. Statistically one of every 100, not #s 100, 200, 300, etc... And the simple fact is your coastal, high value, CoT is pretty likely to get hit with 100 traders a year or more once the province is known to the latin tech group. The a.i. traders focus on high value CoTs as having the greatest potential return. That 1% chance can turn their 2-3 ducat cost into 8+/month in a CoT worth 1800. Since it can easily take you 2-3 months to get merchants there to kick them back out one success can easily pay for 5+ failures.

If you want to dominate a CoT the best way is to put it somewhere out of trade range and hidden from Europe. The best locations are inland as coastal provinces are too easily reachable.

As a free trader you can completely monopolize a number of CoTs, but to do so you will have to limit the number of CoTs you trade in as well as other maluses like uncored CoTs. I have been able to maintain up to 20 13 empty chair monopolies by only trading in those CoTs and predominantly trading in distant overseas markets most of Europe couldn't reach and/or didn't know about (slow map spread ftw). Having a massive trade tech lead and eliminating most of the free traders helps too.

While the ability of free traders to dominate more CoTs is a problem, you have to consider that in general it requires a much greater investment to do so. Most nations start heavily mercantalist and full blown free trading pretty much requires SCP as well as NTP. You also lose some pretty nice trade income modifiers/decisions. IMO the compete chance malus for number of placed merchants needs to somehow consider open seats in your monopolies and it should also be an escalating, not flat, penalty. It is somewhat infuriating to be unable to maintain more than a couple full monopolies of 100% owned CoTs as a full merc nation because of the malus for placed merchants when you are only trading in owned CoTs. Perhaps removing that penalty in owned CoTs?

 

[unmerged(499943)]

. And that is as simple as it looks: 99% chance => statistically the 100th foreign merchant will compete you out.

Correct: One out of hundred merchants will (on average) compete you out.
Incorrect: Statistically the 100th foreign merchant will compete you out.

 

[midget_roxx]

Quite possibly it could be an event. I know there is a free market event that will put a merchant into a CoT while evicting the owner's automatically

 

[Pewt]

Well, your formula is just not right in this place. We don't want to find out when it becomes more likely for a foreign merchant to beat yours, that doesn't matter at all in this consideration. We just want to find out at which mean value your merchant with 99% compete chance (against EVERYONE) will lose against another merchant. And that is as simple as it looks: 99% chance => statistically the 100th foreign merchant will compete you out.

That's not how probability works; you'd do well to take a stats course.

 

[n0thin]

Correct: One out of hundred merchants will (on average) compete you out.
Incorrect: Statistically the 100th foreign merchant will compete you out.

Well, I might have explained bad what I meant. If you have a monopoly you can estimate that it will on average last against 100 tries from foreign merchants. It will (in most cases) of course not last exactly 100.

Back2topic: It is probably easier to hold full monopolies in CoTs that are not one of the worlds richest. So if you have a 1800 or more CoT somewhere, it might be easier to break it apart in 2-3 CoTs. The AI won't attack your full monopoly in a CoT worth 900 as fiercely as it will attack the world's biggest CoT. If you don't have an escalating problem with the number of placed merchants yet, it might be even easier to get 2 full monopolies at 900 CoTs then at one 1800 CoT. Many heavy mercantilistic countries are only trying to trade in big CoTs or in the ones they are part of.
It might still be the best option to conquer or embargo the typical Free Trade countries as they are not unlikely to have more than a 1% chance against you.

That's not how probability works; you'd do well to take a stats course.

I do right at moment at my university and I had a stochastics course (which is what we are really talking about) 3 years ago when I was still at school. However, you'd do well to don't get too personal.

 

[Manchester.bw]

So I have this COT in the Dominican Republic, New Amsterdam, which is worth 1800 ducats. I own a nominal monopoly and have a 99% chance to compete out anyone in the COT and have done so to every merchant repeatedly.

...then, out of the blue, someone else who I have a 99% chance against magically appears in the COT. I don't lose my monopoly, so they clearly did not compete me out to get in. They just start magically bypassing the monopoly altogether. What gives?

it's a bug, you can never oust them from the last slot. you're playing a paradox game, what do you expect

fortunately the change in income is not very great. with say a 2200 value cot and 60 TE you will make ~1240 annually. if you could gain control of that bugged slot you would hypothetically make ~1310 (~8 more wealth per month) - nothing that breaks mercantilism's value really.

of course, you do have to send each merchant manually as a mercantilist. but everyone knows you should be doing that already