But now they are the invaders in a foreign land, without protection from trenches, minefields, or infrastructure under their control. Shouldn't we expect the Ukrainians in the same situation to suffer 3x the losses as the Russians?
My understanding is that this 3x generalization is for capturing a fortified position. The rule falls apart when there's not an adequate number of troops or fortifications to put up a coherent defense.
I'm not sure we can count the Kursk region as "fortified" in the traditional sense (and owing to how easily Ukraine gained over 100 km2 in a few short days).
Half correct. The 3x and 10x for cities are not losses (though that often happens) but the numerical advantage you need to win.
2x for open field battle, where the defender has no or only rudimentary, temporary defenses. 3x for fortified positions the defender has erected (like mine fields) and artillery in position etc. 5 times for something like the main defense line in a good position that has been prepared for months (mine fields, fire tables, bunkers...)
Now, it's probably still pointless and most likely more of a propaganda exercise than anything, and it will probably lead to nothing significant, but it's not just throwing away troops.
I think it's a lot more. Russia has been throwing all it has against Ukraine for half a year now and in the last weeks we have seen increasing gains. Still small, but the accelerating rate even after the new artillery munition arrived is not a good thing.
(That said Russia has only reached the main fortified line at 2 points. Which might have been a bit of the reason Ukraine did that now.)
That Russia was able to do that was mainly because of their overwhelming numbers. Along the whole front we have indeed that 3x or even more relation. So you can imagine how concentrated it is in some parts.
But Ukraine has started to recruit more soldiers a bit back and I think those units attacking now are those - western trained, probably western equipment, but still very green.
Put them into the stalemate battle with the other units or let them get experience against an unprepared enemy, in a new field, where they can act freely?
Stretch the Russians so they have to relocate troops from the attacks that have Ukrainians struggle heavily at the moment?
Get some pressure on Putin for the rumored peace talks? Make it look to the more important western Russians that they might be in danger?
Get the morale up both in the country and international that is down?
Do not ask what is the reason for a certain move. Ask what are the reasonS for it. Strategy is never about only one goal. It's how to get to several goals in one move.
That is why Go is still mandatory game for Chinese officiers. It teaches you exactly that.
There is a famous move
https://en.wikipedia.org/wiki/Ear-reddening_game - have a look at that. Even if you know nothing about the game, it should be visible that the "ear reddening move" marked with 1 connectes the whole board - it connects 3 sides and prevents white connecting left and right. That is strategy, a single move that redefines the whole situation. While being far away from any front.
And I think Ukraine is trying something similar here. The stillness of Ukraine and the visible panic on the Russian side is reassuring for me they might be ablet o pull something like that off.