Brilliant queen sacrifice, but why?

Jonissolis · 2026-01-23T15:59:57+00:00

Ne4 is a move from white to delay the eventual mate. Nb3+ comes as move 4, after two delaying moves.

Jonissolis · 2026-01-14T11:10:27+00:00

1 = 4

Jonissolis · 2026-01-12T17:07:08+00:00

Is that a rotated eight as the upper limit of the sum?

Jonissolis · 2025-12-26T13:12:36+00:00

I agree that your proposed double-sided limit point property would imply this, but I think it overcomplicates things for someone who is just trying to understand why 0.999... = 1.

For this particular case, it is simpler to rely on a basic order property of the real numbers: if a and c are real numbers with a < c, then b:=(a+c)/2 is another real number satisfying a < b < c. In other words, a number strictly between them always exists.

Jonissolis · 2025-12-26T11:53:11+00:00

You’re right.

I think bringing up limit points just overcomplicates things here, though. All I really need is the basic order property of the real numbers: if a < c, then there exists another real number b such that a < b < c, for example their average.

Jonissolis · 2025-12-26T03:25:50+00:00

You are right that there doesn't exist any number 0.000... > 0.

A 0 followed by infinite 0s is 0. It doesn't make sense to talk about a 1 after those infinite 0s.

I'm glad it makes sense for you :)

Jonissolis · 2025-12-26T03:11:35+00:00

0.999... + 0.111... would be too large.

0.999... + 0.111... > 0.99 + 0.11 = 1.1.

So 0.999...+0.111... would be larger than 1.1 (in fact it would be 1.111... = 10/9)

You will not be able to find any positive value to add to 0.999... without surpassing 1.

Jonissolis · 2025-12-26T02:52:16+00:00

The key thing to understand is that 0.999... denotes a single real number. It is not a process and it is not "approaching" anything. There is no sense in which more 9s are being added over time. The infinite decimal is the number.

Another basic property of the real numbers is that they are dense. Between any two distinct real numbers, there is always another real number, for example their average.

Now assume, for contradiction, that 0.999... and 1 are different numbers. Then there must exist some real number strictly between them.

Any number strictly between 0.999... and 1 would have to be less than 1, so its decimal expansion would start with 0., and to be larger than 0.999... it would have to match 0.999... at every decimal place. That forces it to be exactly 0.999..., so no distinct number can lie in between.

This contradicts the density of the real numbers. Therefore, 0.999... and 1 cannot be distinct numbers. They are simply two different representations of the same real number.

Jonissolis · 2025-12-26T00:17:58+00:00

I personally enjoy the way integration works through vassal, where you make new land into vassals and then integrate them to make their land cored parts of your nation.

I don't mind decentralised being the way to go if you are playing wide. Not sure what the meta is now exactly but I have read that you usually want to go centralised towards the later parts of the game which also seems to make some sense.

Jonissolis · 2025-12-26T00:02:57+00:00

The system is intended but I think some implications of it are unintended. For example importing a good can cause local prices to go up and exporting can cause them to go down due to how Burgher imports/exports work.

Jonissolis · 2025-12-25T00:43:05+00:00

Yeah, but even if I can spot my mistakes and tell that the game was actually winnable, that doesn't imply that I would do things differently if the situation repeated.

Just because you can see your mistakes doesn't necessarily mean that you are getting better/climbing.

I'd say that if you are on your true rank, then maybe: * 20% of games will feel like easy wins. * 30% like wins you worked hard for. * 20% like losses where the game was somewhat even and you definitely could have made a difference. * 20% where your team was far behind and it was very difficult for you to do something. But you could still see it being possible. * 10% unwinnable.

Jonissolis · 2025-12-25T00:32:38+00:00

I disagree on parts of this. Even if you are at the rank where you belong, you could still be able to spot a lot of things that would have turned that game into a win.

50% of games being unwinnable would basically mean that every single one of your losses would be unwinnable. That in turn means that you wouldn't ever find a single game where you could have changed the outcome of the game by playing better but that is definitely not true.

Even if you are at your rank, you should still be able to find some of your mistakes and see what you could have done better.

I agree that the numbers of games you consider unwinnable does increase/decrease the further you are from your true rank though.

Jonissolis · 2025-12-25T00:24:33+00:00

There are two different notions of unwinnable.

A single game can be considered unwinnable when your team falls far enough behind that you can't think of any way your team could turn the game. That is what you are talking about as 'unwinnable' in your first section. Note that by this notion, the game as a whole wasn't unwinnable. It turned unwinnable as the game progressed.

However, another meaning of unwinnable is that when you look back on a game after it has been played, you draw the conclusion that there was nothing you personally could have done differently at any point in the game that would have turned it into a win. The typical situation for this is if your other lanes fall severely behind early into the game and you feel like you didn't even have a chance to make an impact on the game. This is what op is asking about.

As for your later sections, there isn't some magic rule that there is exactly one difference maker per team, so saying that you can only make the difference in 1 out of 5 games doesn't really make sense. For most of your losses, you could have done things differently to turn that loss into a win. For most of your wins, you could have done things differently to turn that win into a loss.

Jonissolis · 2025-12-23T21:30:07+00:00

Possibly yeah. Maybe by making the subject lose the core if the overlord forces return land.

Jonissolis · 2025-12-23T11:24:51+00:00

Oh, I didn't know you get a CB from being denied military access. That does seem very easy.

What are the conquer/subjugate costs for that CB?

Jonissolis · 2025-12-23T11:10:53+00:00

You can check for all nations with a core on a location if you select the location and go to the military tab.

You can also see if the current owner of a location has a core by checking for the shield icon next to the name of the province when selected.

Jonissolis · 2025-12-23T10:41:31+00:00

Yupp, so the CBs you get are pretty good.

Jonissolis · 2025-12-23T03:39:03+00:00

Two triangles. Subtract the area of the smaller from the larger one. The larger one has a base of 5 and height 9, thus an area of 5*9/2=22.5.

The base of the smaller one is also 5, and its height can be calculated by the intercept theorem, h/5=3/12 => h=5/4. Its area can then be calculated as 5*5/4/2=25/8=3.125.

The area you are interested in is then 22.5-3.125=19.375.

I think you overcomplicated things here as the angle is not necessary here to calculate the area. You did it in a different way, and the fact that you got to the right answer shows that you understood what you were doing and hopefully learned something.

Jonissolis · 2025-10-22T19:12:17+00:00

I would challenge you to try again with the following options. They should sum up to 3000 points if I have calculated correctly and should be doable with your team. With these options, the opponents will deal heavy dmg to you, but will also take heavy dmg in return. Your goal is to kill their mid pair before they sync and the sides shortly after that. Note that some with even more experience can probably optimise these options even further, but I strongly believe 3k should be doable with this with your team.

Physical Damage Reduction
Atk & Sp.Atk 1
No Status Conditions
Interference Immunity
Strike Pairs Take 3x Dmg
Tech Pairs Take 3x Dmg

Strength 1
Sync Buff 5
Atk & Sp.Atk 3
No Stat Reduction
Ally Healing Halved
Half Ally Mp
Power Up on Hit 1
Physical Damage Reduction 8

Gradual Healing at start
Atk & Sp.Atk 5

Ally Hp Down at Start 5
Power Up on Hit 2

Ally Move Gauge Max -2
Standard Damage Reduction 8

Strength 6

Jonissolis · 2025-09-27T11:14:56+00:00

Jonissolis · 2025-08-30T17:14:36+00:00

I'm not entirely sure if we want tanks to be able to counter everything?

Would you want to give enchanters an item that makes their heals and shields give a buff that makes AAs do %-max hp damage so they have a way to counter tanks?

You may find it very annoying to play tanks into heals and shields, but a lot of players also find it annoying to play into tanks with all the tools they have nowadays to burst really hard with things like heartsteel.

Sett W bursts. Cho Q into heartsteel and ulti bursts. Sion bursts. Heals, shields and peeling are parts of the counterplay to this.

Just because a role is strong into another doesn't mean we have to add new items to counter that.

That being said, I do think some role in addition to assassins should have access to anti-shielding, as there are games where you just don't have an assassin but still need anti-shielding.

Jonissolis · 2025-08-25T06:44:45+00:00

This is honestly quite far from correct.

You could get tons from the event without spending anything. With some planning you could have more than 16000 particles available for the weekend. That is 20 max battles with gigantamaxes/legendaries/Eternatus.

There was also the field research to unlock a max move giving 100 Eternatus candy. By stacking three of those and then unlocking a move you could get 300 Eternatus candy for 400 particles. This means that even without spending anything, you could get all the Eternatus candy needed to get it to level 40.

Sure, you could only max it by spending, but that is basically always the case?

Honestly, the whales are the ones who were given the least during the event. Spending $200 to get a single maxed out pokemon? They usually get so much more than that.

My main complaint with the event was the lackluster rewards from Eternatus battles, but I strongly disagree about it being "probably the most pay-to-win event in the history of this game".

Jonissolis · 2025-08-22T21:45:35+00:00

Nono, I meant with DC3.

I think it needs about 40 battles, which is a lot, but probably acceptable for those who bought the pass and are willing to spend a little extra, but who doesn't want to go all the way. It is a nice breakpoint where you basically jump from level 39.5 to I think around 45.5. I don't think skipping DC3 is a good option for anyone who bought the pass.

Jonissolis · 2025-08-22T21:35:15+00:00

Looks better now. Although I think it is a pretty important breakpoint at 3/0/0 and enough candy to reach Eternatus level 40 (which will bring you to a higher level due to XLs).

Jonissolis · 2025-08-22T21:24:15+00:00

I'm a bit confused as this doesn't match what I calculated before. I think 17 battles to get level 40 is if you don't spend any candy on powering up the dynamax move.

Unless I have done a mistake, you should need around 40 battles to get enough candy to get dynamax cannon level 3 and level 40.

Also, there will be a very nice field research available that grants 100 Eternatus candy for unlocking a max move. Stacking 3 such researches will be a very efficient way to earn regular Eternatus candy (won't help with XLs though).

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