Ukrainian soldiers take a selfie with President Volodymyr Zelenskyy, centre, on Monday during his visit to Kherson, Ukraine. Credit: Courtesy of the Ukrainian Presidential Press Office via AP

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The recovery of the city of Kherson is the third big victory for the Ukrainian armed forces in three months: First, the reconquest of all of Kharkiv province in September, then the partial destruction of the Kerch Strait bridge linking Crimea with Russia in October, and now the liberation of Kherson. So where next?

The decisive factor in shaping this war has been the relatively small numbers of troops engaged on either side. When the Nazi and Soviet armies were waging their titanic battles back and forth across Ukraine in 1941-43, there were several million soldiers fighting on each side, with tanks, planes and artillery to match.

Once a breakthrough occurred, in those conditions, the front could move hundreds of miles before it settled down again. Many cities changed hands not once or twice but four times. This time around, it’s very different: the armies have gotten small again.

The Russians invaded last February with fewer than 200,000 men. Even now, after considerable reinforcements but also large losses, their army in Ukraine is 250,000 at most. Ukraine’s army has grown at least as fast, but from a much lower starting point, and probably now has about the same number at the front.

The problem is that the front, the line of contact between Ukrainian and Russian troops, is less than 1,000 miles long. That means that each side has an average of only 250 soldiers per mile, or one for every four yards.

Allowing for the fact that the Ukrainian front was actually much shorter for most of the Second World War — it was usually a relatively straight line, not drawn out in a great U-shaped curve like the current line of contact — we can safely say that the density of manpower per mile of front was 10 times higher then than it is now.

This has major implications for the way the current war is fought. The front is manned so sparsely that it is fairly easy to get a breakthrough — but the attacking forces also are much smaller, so they can only hope to hold the new ground they have gained if they stop their advance fairly soon.

We saw this factor in play in the Ukrainian northern offensive in September. They managed to lure a lot of Russian troops away by feigning a major offensive on Kherson (then still Russian-occupied) in the south, and their attack in the north took the Russians completely by surprise.

The Ukrainians quickly advanced about 50 miles on a broad front — and then they stopped, although the Russian troops in front of them were still fleeing. They were spreading themselves too thin, and making themselves too vulnerable to even a modest Russian counterattack.

The great offensives of 1941-43 advanced hundreds of miles before they stopped, but those were different days. The Ukrainian army has the upper hand, but its offensives will continue to take modest bites out of the Russian positions rather than concluding in a dramatic and sweeping move that ends the Russian occupation.

So where will they attack next? Certainly not from newly liberated Kherson across the Dnieper River. It would cost too many lives to cross under fire. The Russians have been adding fortifications on the eastern front in Donetsk and Luhansk for almost a decade, and an offensive there would be a slow and painful business.

The next real strategic target for Ukraine will almost certainly be a drive from the region of Zaporizhzhya south to the Black Sea. That would leave all the Russian forces in what’s left of Kherson province and Crimea totally dependent on supplies coming across the badly damaged Kerch Strait Bridge from Russia.

Starve them out, and Ukraine will have recovered almost all of its pre-February territory. That’s the point at which negotiations would finally become possible. Many different peace deals would then be available.

If the Russian army actually collapses — unlikely, but certainly imaginable — then the borders all go back to the pre-2014 map. If it’s still standing, then maybe Ukraine gives up the Donbas in return for recovering Crimea, or the other way around, or perhaps it has to accept merely a return to the pre-February 2022 status quo.

The course of the fighting will decide which option actually materializes.

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Gwynne Dyer, Opinion columnist

Gwynne Dyer is a London-based independent journalist whose commentary is published in 45 countries.