While the two principal German nations Prussia and Austria are by themselves no means weak, when either one of them meets the right conditions, they can form Germany. Under certain conditions note If Prussia has already formed Germany, then to form Greater Germany, an independent Hungary must exist and Austria must lose its Great Power status before Germany adds it to the German sphere of influence. As for Austria, they must either directly control or have in their sphere of influence all German territory., they can then form Greater Germany. The bonuses and advantages of Greater Germany are so numerous that they can basically overwhelm and easily beat even the other great powers of the game.
The brokeness is amplified with Austria, as by forming Greater Germany, North German becomes an accepted culture in Austria. However, this also means fighting a rival which has more advanced technology.
Save, reload the game, let 2 days pass, save, reload, let 2 days pass... keep this cycle going until you start receiving notes about national bankruptcies. Due to a fault in a code, if you reload, the factories are listed as empty and all pops have their needs listed as empty, too. On the end date, the two conflicting informations will happen: the already present goods will qualify to fulfill the needs of pops and industrial production, while new batch, whenever possible, will be bought from the market, to fill "empty" slots. As a result, the market gets drained from goods, creating a temporal price spike, while national budgets get empty, since everyone was trying to restock. Not a big deal for larger nations, especially those with industrial base, but lethal for uncivilised and minor countries. And how this is a game-breaker? Once you go bankrupt, you gain massive prestige hit - and in Vicky 2, countries that loaned you money will gain "Repay Debt" casus belli against bankrupt. Every time a country goes into negative prestige, you can declare war on them without dropping your own prestige, which is crucial for building colonial empire via conquest or when you plan to expand your borders in Europe without becoming an international pariah. As an added benefit, if you already have industrial base set, you will be able to sell your finished goods for obscene prices for first month or so due to related price spike, easily recovering your economy and gaining extra profit.
The United States can become ungodly powerful with a decent player, since it's the only Great Power that starts with extensive political freedoms, has a decent military and industrial base, and a weak and backward Mexico as neighbour, from which to pick territory off from. With enough preparation, you can seize Canada from the UK and can gain cores on Cuba through a decision. After this and the end of the Civil War, there's really nothing stopping you from sweeping through the Americas unopposed since any nation that can challenge the US militarily is an ocean away and the Latin American nations can easily be curb stomped.
Victoria 1
In the first game, the USA has an extra layer of brokeness to it from the fact it, well, is the USA. A hard-coded modifier in the game adds a special, insanely high bonus to assimilation and immigrant magnet to the country that bears the USA tag. This means it can, while still with slavery, assimilate pops to Yankee and Dixie cultures at the same rate as any other country with the most liberal policies set - and sometimes even faster. Vicky 2 significantly nerfed the conditions and removed the hard-coded bit, since in the first game it was just too powerful, but by late 19th century, the USA still has a massive advantage in immigrant attraction.
There is an exploit related with turning your colonies into states very early into your game. It was an expensive one to pull, but the more backward your country was, the easier it was to do. Namely, delete all your factories except for a single state (and if you only have them in a single state, even better). Then keep converting pops all across the country into craftsmen. Since there are factories in just one state, pops will move there... to be turned back into labourers and farmers and overspill the local RGOs. Since there is now high unemployment in a single state, the resulting population will try to find jobs and thus move to colonies, which are more attractive than any other destination within your borders. As the population of state culture rises into the colonies, they can both start assimilating locals and grant statehood, allowing to build factories there... so you can get craftsmen migrating directly. This allows situations like Spain turning its colonies in Cuba and the Philippines into states by mid-1850s, or even before Springtime of Nations, but you can also do this as the Dutch, French or even Great Britain. Keep in mind this is an expensive thing to pull and you might just as likely trap your nation in a death spiral of bankrupcies if things won't work out.
Related with above is a further exploit. Since you now have a colonial land turned into state and it's located outside of Europe, you can use local ratings for assimilation, so you can start converting pops of unaccepted cultures into craftsmen, close all but non-European factories and they will start migrate outside the home territory, then get easily assimilated into your state culture, which is already dominant in the oversees state.
As Prussia, you could increase mobilisation pool, then mobilise your army before even unpausing the game. In the month before mobilisation takes place, relocate your standing army to favourable spots. Once your conscripts are ready, find any of the German countries that has an "except Prussia" in their alliances and declare war against it. Congratulations, you are now fighting against all the German states, except for Austrian Empire, and you have your army already mobilised - before they will raise theirs, most of them will be already overrun and the hold-outs are nothing you can't deal with. This way, grand majority of Germany can be united by force by late 1836, the starting year, with all the benefits it brings. Be warned, as southern German countries start with large mobilisation pools, so once they join mobilisation, you should be already be done with your conquest by then (or extensively focus on conquering them, which might or might not work in time). The kicker is that despite conquering a whole bunch of countries, you don't gain a single bad boy point for it, since they all have your cores. If everything goes smooth, Prussia can turn into North German Federation around 1842, easily beating Denmark and Hanover and getting all the needed land. And if southern states were conquered prior, instantly turn into Germany proper, some 30 years ahead of schedule. And as a by-product, you gain insane amount of prestige via such conquest.
Keep in mind that Hanover is not only outside of the whole Germanic system, but starts the game as ally of Great Britain. Wait them out until the event makes freshly crowned queen Victoria unable to inherit the title of queen of Hanover due to semi-Salic law of the kingdom and get medieval on Hanover, too.
Another aspect of this is the massive cut-down number of countries in the game. Instead of 20+ countries fighting over resources on the market (and majority of them being unable to compete), there are 1-4 within the exact same space. This in turns allows pops, both yours and globally, easier access to goods, as there is simply smaller competition. This means less discontent, less immigration toward the USA and generally a far more stable global economy, achieved years in advance. For this very reason, it's usually in everyone's best interest to get unified Italy and Germany as soon as possible.
When playing as an uncivilised nation, any land you own or conquer is considered to be a state. Even including any overseas possessions you can get. This means you should be conquering as much land as only feasible prior to Westernization, right down to gaining at least a foothold in Africa if you plan to later participate in colonisation.
Japan can gain obscene economical advantage if conquering Korea and/or bits of China prior to Westernization.
The whole "conquer first, Westernise later" is especially important if planning to unify India as any of the still independent countries from what's today Pakistan. It's even more potent if you first venture into Afghanistan and the steppes of Central Asia, that you would otherwise never manage to turn into states.
Tech-trading is one of the most busted aspects of the game. If you exchange tech with other nation, each technology gained this way doesn't have to be researched, but it still instantly subtracts its price in research points from your current pool - which usually means sending you into negative. However, by promoting sufficient number of [POPs] into clerks, you not only bolster your economy (they increase efficiency of factories by a huge margin), but, more importantly, can generate surplus research points than you need on your own technologies. In about a decade, you can clear this way all possible technologies for current time period via extensive exchange with other countries and in the same time, stall their further technology progress, since they will be in -50 or even -100 research due to the technologies you gave them to seal the deal. And even if they couldn't get new technologies on their own for next couple of years due to going into "research debt", they still could benefit from the effects of granted technologies, increasing output of resources to the market and offering steady inputs for economy (particularly important for such countries like AI-controlled Russia, the Ottoman empire or China). This was such a powerful tool for player dominance, second game simply removed tech trading entirely.
Victoria 2
Westernized China has Memetic Mutation status as Game-Breaker. 1/5 of whole population at the game start is under China's control and in final years of game it's still about 1/6. Good resource base. Mostly pathetically weak neighbours. We Have Reserves after the military starts to use modern equipment turns every single war into series of Curb-Stomp Battles, where Chinese will simply overwhelm their enemies with absurdly large armies without much effort. If everything goes smooth, China can westernise as fast as late 1860's (the game starts in 1836), giving you plenty time to heavily industrialise, research the most vital technologies and easily participate in Scramble for Africa, which can turn into painting it whole in yellow. As of Heart of Darkness, it's still possible to modernize quite fast through conquering, but receiving the best of all the techs that have been researched when Westernizing no longer happens.
Related to above, in Victoria 2, conscription is just flat percentage of your total population, rather than a pool that has to be steadily increased over the years. Do the math with Chinese population. Sure, conscript units are literal Cannon Fodder... but in case of China you reallyhave reserves and with such numerical superiority, you can easily squash professional armies by sheer numbers alone. This also saves money on maintenance and supplies, since there are no units to supply until you call troops to arms. The downside is that conscription pool, no matter how big, provides you with zero military rating and AI takes that into account when considering whether or not to attack you.
Also related to the above, a Russia who chooses not to tangle with Europe à la the Crimean War, but instead focus on grabbing land from uncivilized countries can reap big profits. The Black Sea is less valuable when Russia can grab ports around the Arabian Sea and from there, progress to Africa.
Any country that has a decision to reform into a different nation and in the same time can release subject nations can cheese this up for easy infamy reduction. Simply release new subject nations, which drops significant amounts of infamy, then instantly reform into the new state, swallowing the puppet back - your economy and military aren't affected in the slightest and you regain control of those lands instantly. Examples include, but aren't limited to Prussia before forming North German Federation, NGF before forming Germany and Sweden before forming Scandinavia. Since infamy is a very bad thing to have, this exploit goes around one of the hardest stops on conquest. Extra gamey if you conquer a province or two just to qualify for the nation-changing decision, release said province as a subject, then implement the decision, making the war-gained infamy disappear the second it was gained.
This concept can be extended indefinitely by any country that is designated as a cultural union (e.g Germany, Italy, India), due to a special mechanic that applies to those countries: If a cultural union becomes a great power and puts a minor nation belonging to their culture group into their sphere, an event will soon trigger where that minor nation petitions to become integrated into the union. There is no limit to how many times the same minor can be integrated this way, so the union country can just release the minor to lose 5 infamy, then reintegrate them, then release them again, then reintegrate them again, and so on. The only caveat is that the integration event takes on average 1 year to trigger and can only trigger while you're at peace. Because of that, while any cultural union can make use of this to some extent, it's especially useful for unions like Germany and India that have a ton of minor countries that can be released and reintegrated, so you're not as restricted by the event delay.
As powerful as the above exploit is, there is in fact yet another infamy exploit that is even stronger: If you release a country that has cores on your capital province, you'll always retain control of that one province even if the rest of the provinces are granted to your vassal. So what happens if you try to release a vassal that only has a core on your capital province? The answer is that the game acts as if you released the vassal, including lowering your infamy, but you still retain control over your capital, which means the vassal doesn't actually receive any territory. Since they have no territory, the game then acts as if they don't exist at all, which means you can "release" them again, for another infamy reduction. Unlike the above exploit with cultural unions, this infamy exploit has no cooldown whatsoever, so you can eliminate any amount of infamy without passing a single in-game day. The problem is that it only works in these very particular circumstances that don't appear very often. The only country that can make use of this exploit right from the start is Krakow: Being an OPM, the only province they own is their capital which also happens to be a core of Poland. So Krakow can "release" Poland without actually releasing them as many times as they like.
Columbia and Chile. They start as democraciesnote meaning they get four times bigger immigrant attraction than non-democracies in Latin America, get passable resource base (and Chile also an RGO producing precious metalsnote another big magnet for immigration and source of cash). Other than that, it's the same situation as the USA, where any country that can do anything to them is an ocean or at least a continent away, so you can start carving your neighbours for resources and land with impunity. Bonus points for the fact Chile looks like nothing at a first glance, yet in player hands it can reliably become a secondary power by the end of the opening decade and a great power by 1850 mark. Meanwhile, Columbia can reform into Gran Colombia (which includes Ecuador and Venezuela) and will retain the strategic Panama canal within its borders.
Victoria 3
In this installment, Greater Germany becomes even more broken when it expands into the Italian peninsula. Austria starts with some Italian minors as custom union members. Convert these members into dominions or puppets and then continue expanding. Expanding into the peninsula helps Germany with its naval prowess. Once the required states are in hand, this humongous entity can then form Central Europe, making all Central European cultures its primary cultures.
Not to be outdone, once France completes France's Natural Borders, they too can try their hand at forming Central Europe if they choose the option to add some central European cultures as primary cultures.
China continues its string of being completely broken in terms of economy. Due to the sheer size of its population, it can completely ignore all the efficiency-increasing technologies (and especially automation line, which exist only to decrease the workforce's required size) and simply keep increasing the size of its factories, which is far cheaper and doesn't require any extra research. Since China starts as a technological backwater, this allows it to easily overcome its supposed ceiling of growth. On top of that, since each level of factory adds a bonus due to effects of scale, the eventual multi-level factory will provide additional goods, while still being able to operate using nothing but unskilled labourers.
Right at the game's start, any of the unrecognised countries can instantly win a diplomatic play to get international recognition by bullying the USA. Normally, the entire play is about declaring war against a great power and coming out victorious, to simulate Russo-Japanese War. However, at the game's start, the USA is both a great power and has barely any militarynote It only has 12 regiments, which is about the amount a random tribe in Africa can brandish, making it a Paper Tiger. As such, just about any country with 40-50 regiments can instantly put their interest in the US East Coast and start the recognition play. The AI behind the US will recognise the disparity of power, but not the fact it's protected by the ocean, making it simply fold in the negotiations, and due to the geopolitics, nobody in the area can really join the play, as nobody has put their focus there yet. Qing is the obvious candidate for this (starting with one of the strongest armies in 1836), but there is also Japan, Korea, Dai Viet, Persia, Sikh Empire (which for added brokeness is land-locked, but still has a spare interest point)... the list really goes on. And in the case of the USA somehow not folding in the negotiations, the actual war can be instantly capitulated, without any losses or need to fight (save for a 5 year truce).
Standards of living can be artificially boosted within days, especially for lower stratas. All it takes is a sufficiently large chemical plant (providing a large amount of cheap fertilizer), one of the early game technologies and bunch of grain-producing farms. If the farms switch to intense fertilization, this will soak up all the cheap fertilizer (making the factory very profitable), while tripling the grain output. The now ultra-cheap grain will flood the market at pocket change. However, since farms can be cheaply subsidized, at minimal expense from the budget, the bottom price of grain can be maintained, becoming more than affordable for the masses. The profit made by chemical plants needed to pull this off will pay for the nation-wide farm subsidies by itself. As a result, the standard of living will quickly soar, attracting immigrants and preventing any sort of radicalism or discontent.
The Spiffing Brit broke the game before it even came out. When offered the trial copy for marketing gig, he decided to turn Jan Mayen, a barren rock in the Arctic, into the 10th economy in the world. All it took was becoming a subject of a bigger nation, the more backward, the better. As a result, preferential trade deals for raw resources could be made, then turned into finished products to resell back to the same market for massive profitsnote In this particular example, the added factor was the near non-existing starting population of Jan Mayen, meaning all produced goods could be exported, since nobody was buying locally. Since the partner nations are considered to be part of the internal market of the leading country, this doesn't even affect tariffs nor can be in any way stopped by the leader. While the example was deliberately extreme, the basic scheme of "tap into some big market and abuse your preferential position" remains true even in more standard scenarios, like an Italian minor cornering Austro-Hungarian market.
Treaty ports offer a duty-free access to specific markets, depending on which country they have been taken from. There is no limit whatsoever to who can be the target of establishing a treaty port. That's already broken all by itself, but certain locations start as a treaty port for a specific market, rather than just a splinter state. The most prominent ones are Pondicherry and Goa in India. They allow France and Portugal access to the East India Company market... which is part of the British market, which allows them to tap into, without any extra payment, the biggest market on the planet and one that only grows bigger, along with selling readily their own products. France not making any steam engines? They can just buy them at a discount from Brits. Oh, and it doesn't even require convoys for trade itself, since it is treated as overland trade via those ports. Due to the resulting volume of trade, both ports can easily run out of people to operate their trade hubs, despite starting with half a million potential workers each. This was later changed so that the owner of the treaty port must be of a higher rank than the leader of the market it is trying to access (Thus, Goa and Pondicherry become inactive unless there's a drastic change in rank for the powers involved.)
The Sikh Empire went from "plucky little country that can try fighting against the British encroachment and maybe dream about uniting India" to "steamroller that can easily crush the East India Company". Starting political, economical and technological situation means that Sikhs have more soldiers than the Company and of comparable quality, while having stronger economy, allowing to fight the war until EIC folds. The trick is to declare war to any of the other independent Indian minors right off the bat, so EIC will try to join the resulting conflict - and only EIC, without getting either Great Britain or the Princely States that are EIC's puppets involved. Done right, the Sikh Empire can gain both the sea access (and thus allowing wide export of opium and dyes, providing money for industrialisation) and, more importantly, any given state that's controlled by EIC, which will provide huge manpower surplus for the military build-up. Then it's just a matter of waiting for the truce to phase out and repeating the whole process. By the 3rd such war circa 1860, it's entirely possible to reduce British presence in the Indian sub-continent to some rump state, while controlling enough land and population to reliably fight against potential direct Great Britain involvement... which in turn can be used to gain recognised power status.
This can be exploited a step further if timed right and Great Britain is busy somewhere else. Should EIC be liberated from its subject status, it will instantly balkanize into a group of petty Indian kingdoms in 4 out of 5 cases. This allows to both push the Brits out of the subcontinent and make any future conquests even easier, since the Sikhs will now face a bunch of small, backward kingdoms that aren't in any sort of alliance, union or defensive net - and thus each can be fought separately and have separate truces. And should EIC remain in power rather than balkanizing, it will face such monumental unrest caused by radicals, it will collapse on its own into a whole series of revolutions.
Not to be outdone, the EIC itself can go about annexing its puppets either via war or by invoking the doctrine of lapse. Once all its puppets has been subsumed, the EIC can declare a war of independence against Great Britain. With proper preparation beforehand, Britain will be forced to give up its crown jewel. After independence, the EIC will be forced to divide up its vast territories among its puppets and left with only Bengal (or form India if Pan-nationalism is researched). But, if there are no puppets to divide the land with, Bengal will inherit everything, making it a Great Power right off the bat.
Thanks to how the secession prior to the American Civil War is handled (state has to have land owners as the dominant voters bloc) it is entirely possible to create a situation where in every single state except something tiny, like Delaware, there will be no land owners majority, making the resulting Confederacy a complete joke to be squeezed within two weeks. Best part? It can be achieved unintentionally, since your goal is to industrialise, building everything but farms that increase the number of land owners. At the very least, it is possible to simply destroy all the farms in states with barracks in them, then wait a month. This way, the entire standing army will be on the Union side, allowing the Union to quickly overwhelm the Confederacy, which will now take over 13 months to get a competent standing army, because newly recruited troops (from barracks that must first be built) have a 360 day long power debuff.
Or just destroy the barracks in the disloyal states prior to the secession (it's on a timer once things start going downhill) to prevent the Confederacy from having any army at all. Sure, you might not have it yourself, but that's the least important part, as overwhelming AI even with fresh recruits is very easy.
It is possible to prevent secession entirely, by first introducing debt slavery. While it increases the absolute number of slaves if passed, it reduces the political power of the landowners. More importantly, it gives them something to be happy about. Couple this with the opinion bonus from the "Manifest Destiny" missions, it is possible to merely displease the landowners when debating to end slavery, rather than outright angering them.
After fighting the Civil War, if the US accepts Afro-American culture (by passing Cultural Exclusion or Multiculturalism), the culture will become a US primary culture. This means incorporating states which are homelands of pops with African Heritage within 5 years instead of 20.
The Ottoman Empire starts the game with three negative modifiers and a timed journal entry Sick Man of Europe. While it is possible to remove these by achieving reform objectives, players can also remove these by triggering a civil war, switch over to the other side and then winning the civil war. While this will cause the player to miss out on several claims on Egyptian territory, it also removes the sword of Damocles hanging over the Ottoman Empire, allowing it to reform (or not) at its own pace. And by getting the right people behind the revolution in the first place, it might be even faster to do it this way around than the supposed course of action. Patch 1.3 changed it such that journal entries and claims on Egyptian territory are inherited, but this just means easier reforms as the negative modifiers are still removed. The patch actually makes it easier for the revolution to succeed as there are events allowing you to push certain interest groups to join the rebels. In patch 1.5x, this path is made even easier with the introduction of the "reduce autonomy" mechanic for subjects; after the civil war, the rebellious European protectorates are likely to accept reduction in autonomy to become dominions.
Patch 1.5 reworked the military system, reversing the previous trend. Now the more commanders on a single front, handling smallest possible units, the easier it is to overwhelm the other side. This is especially useful against AI's tendency to make huge stacks under a single commander, which means few breakthroughs vs. just one. Interestingly, technological disparity isn't as severe as it used to be, because while a single stack of units under a single commander will be getting their teeth kicked in while defending, and the other will be getting their teeth kicked in when assaulting, every other stack will be left barely opposed, thus easily gaining ground in the all-around offensive, taking land all around the frontline, as every stack that isn't countered by a stack from the other side simply grabs land, rather than starting (or joining a pre-existing) new battle. Even if it's just a handful of irregulars. This also has the completely unintended potential to completely switch the clout of various Interest Groups, as each commander will be providing a 5% modifier to his group - and you can always just keep fishing for people from a specific IG, while fielding loads and loads of low-ranking generals.
, but you can also do this as the Dutch, French or even Great Britain. Keep in mind this is an expensive thing to pull and you might just as likely trap your nation in a death spiral of bankrupcies if things won't work out.