I don't think looking at the problem from computational point of view is somehow interesting and all this talk about the size of the universe for the comparison. That's just a bruteforce, but there are others methods to potentially solve the game.

Edited 11/28/2023 15:13:56

All integers lead to 1, given two statements. But we don’t have the computing ability to prove this is true, and if it is true, I am unsure what it implies. Beyond this how would it ever be possible to calculate infinities, especially if we know not all infinities are the same

What does your last sentence mean, Tacky?

Not all infinities are equal, in the sense; we have infinite counting numbers, and if there are infinite counting, there will be even more infinite irrational.

You never approach problems that include infinities with computations. And I am not sure what do you mean by

All integers lead to 1, given two statements

is this about my example? If so, then we don't know if it is true, that's the point.

Edited 11/28/2023 15:25:47

I agree with you Rufus. Pattern recognition trains us to think that throwing more and more computational resources at the problem will eventually work because it works for problems as complex as image search, or natural language processing, or operating a motor vehicle.

The thing is, playing *perfect* chess is really really hard. I’m trying to provide quantitative context for just how difficult it is and why our pattern recognition may be failing us in this instance.

I know that not all infinities are equal, my question was directed at the statement that we couldn't calculate infinities

Edited 11/28/2023 15:26:57

Infinity cannot be measured currently, so lots of math problems and other questions are left unsolved

I don't think looking at the problem from computational point of view is somehow interesting and all this talk about the size of the universe for the comparison. That's just a bruteforce, but there are others methods to potentially solve the game.

this is what i tried to showcase with the "who says a higher number" - game. Chess is to complex to brute force it, quantum computing wont change that. Still there is a chance it can be solved, just like other complex games (or even infinite games, as the simple higher number game) can be solved - not by brute force tho.

Infinity cannot be measured currently, so lots of math problems and other questions are left unsolved

i m not sure if i understand where this aims at. In measure theory infinite sets are measured all the time.

I think what Tacky meant is that if the problem has some infinite components and every single one of them has to be proven for one reason or another, then it makes no sense how you can prove them "all". Which in some sense has (or more like had) some philosophical implications. But all I am going to say is that mathematics are fine with infinities and you don't have to check "every number of it" in order to solve a problem. Mathematics is not about computation. We have the whole field of computational science. The pure mathematics do not use computations as proof methods.

This is getting into cuckoo talk, so I am not sure if I want to continue this conversation about the very basics of these subjects.

Edited 11/28/2023 15:40:55

We're uneducated, Rufus, educate us :0

I’m not a mathematician. Just saying if we could compute infinity then collatz would be solved? Idk measure theory, but it sounds more like estimate. Interested ofcourse

If we could compute infinity, all of our problems would be solved. ;)

Edited 11/28/2023 15:47:28

I’m not a mathematician. Just saying if we could compute infinity then collatz would be solved? Idk measure theory, but it sounds more like estimate. Interested ofcourse

There are not estimates in measure theory, but i see rather than measureing something infinite you are interested in making an infinite amount of calculations. That indeed seems impossible, but that doesnt imply that we cant prove something for an infinite set.
There are simple proofs that show there is an infinite number of prime numbers.
Or you could yourself proof for all integers that if they are divisable by 2 and 3, they will also be divisable by 6. You dont do that by going through all infinite integers. You use characteristics that they share that are sufficient for the proof.

i feel like my comment got lost in the infinity talk but again, you can use logic to deduce the likely size and landing spot of an airlift so therefore it's not random. not sure why the strategic community hasn't realized this

For instance, I'm sure Platinum and Rento will agree that "no army has to stand guard" is a poor setting. But I can't predict if they will agree whether ME or British Raj is the better template. Subjective taste also hits in etc.

No, actually I will disagree. 'No army has to stand guard' might be a poor choice if you try to fit it into an existing, tried-out template like French Brawl. But I don't think it's impossible to build a good template around it.

I don't think any setting in isolation is strategic or not strategic. And trying to put that border right between Airlift and Emergency Blockade of all places is really strange, no offense.
The only exception could be Auto-Dist, since it can put you at a disadvantage even before your first click, before you even attempt to think about your strategy, so it could be argued that this setting is inherently not strategic.

Anyway, the community has been arguing for a decade on whether SR is more strategic than WR and even here we can't get a definite answer on that so ¯\_(ツ)_/¯ .

My final thoughts:
1. Settings exist in combinations. You say that gift is objectively more strategic than airlift? Good luck using a gift card on LD template. You likely won't help your teammate that much.
2. To be fair, airlifts pretty much make blockade cards worthless, which imo is the best argument you could make against them. I don't think anyone mentioned it?

Sorry for going offtopic, you can carry on with your chess discussion :)

There are places that favour being airlifted to but you can't know for sure and you can't know the amount of armies which will be airlifted. If there are multiple fronts, which do or don't you attack? If you don't attack you could lose advantage. If you do attack, you could run into a wall and lose advantage that way. The airlifts also happen before attacks, so if you attack somewhere that gets airlifted to, you will run into a stack and lose lots of armies. This can make the card overpowered because firstly you lose armies from running into the stack and secondly there's new armies.

If airlifts happened at end of turn, you still have a reasonable chance of your attacks working and not running into a stack of unknown size.

If there's no fog or light fog, it becomes easier to predict amount of armies, but there's still too many choices for which territories will receive an airlift.

prepare for the worst, hope for the best. there's always a level of unpredictability when playing against another player.

so you look at the board, use your team's positioning/distribution to deduce the most likely distribution for the enemy (actually not that hard in manual distribution games), use that to determine the likelihood they've taken a bonus. now you have a good idea of your opponent's likely income, and the airlift is no longer an unpredictable size.

so then you look at any enemy territories you share a border with and assess the likelihood of an airlift being used. once you have this, you can choose the most strategic way to execute your orders.

strategic weaklings will say "but you can't know for sure how big the stack is and you might run into it and lose armies" well I guess your strategy failed then, do better next time.

let's look at a real life parallel: the trick play in american football. if a trick play succeeds and the offense achieves a first down, or better yet, a touchdown, is that pure luck on the part of the offense. No, absolutely not. it's purely the result of the defense being too focused on what a logical opponent would do, and not staying a step ahead and looking at a deeper strategy. the offense showed a higher strategic acumen by targeting the areas that the defense isn't prioritizing. unpredictability has been a part of competitive strategy since humans figured out the concept of games.

am i actually doing this much calculation on every turn? actually, no. this is a risk app i play on the toilet, I don't have time to watch the turns most of the time. but that doesn't mean that someone else who cares about optimizing strategy can't do this

I guess I will have to step up into this discussion about airlifts... As I said previously, it may be that any setting has potential to be strategic if it fits well with other settings. But, airlift in general is a pretty messy concept that can easily make a template less strategic. How so? Because it disturbs the natural flow of expansion, defense or offense attributes. If you be too passive in contact where you could have taken an advantage (without airlift turned on), or overdeploy in case reinforcements may come, then you are risking on losing the game by the most advanced (as far as I know) concept in such strategy games - tempo. If you are a casual player of this game, then these concepts can be meaningless to you, but believe me that they exist.

That being said, it does not mean necessary that the airlift card can not be used right in principle. You may find such settings, where you have a very low income for the whole game and "once in a lifetime" airlift card adds some strategy/safety on not being afraid of overstacking in some place and lose in the other as part of a bait. Or some other circumstances.

Edited 11/28/2023 17:32:39

Airlifts are strategic.