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The most well-known land run is of course the Great Run of 1889, in which the land now containing Oklahoma City and its suburbs was settled. That land, known as the Unassigned Lands, was originally part of the Creek and Seminole lands. But after the Civil War, in which many tribes allied with the Confederate States, the U.S. government punished them by shrinking their reservations. Although it was a punishment, the government did pay the tribes for the land -- sort of. The Creek lands were bought for the princely sum of $0.30 per acre:
[...] in consideration of said cession of the west half of their lands, estimated to contain 3,250,560 acres, the United States agree to pay the sum of thirty (30) cents per acre, amounting to $975,168 [...]
Some of this money was held back to pay for damages incurred in the war, so the actual price was somewhat less.
The Seminole lands fetched half that price, a mere 15 cents per acre:
In consideration of said grant and cession of their lands, estimated at 2,169,080 acres, the United States agree to pay said Seminole Nation the sum of $325,362, said purchase being at the rate of fifteen cents per acre.
This was for the western part of the Seminole lands; to make enough room for the whole tribe, the Seminoles were forced by the same treaty to spend $100,000 of the money buying 200,000 acres of the newly ceded Creek land at 50 cents per acre, earning the government a tidy profit on that bit.
The other, smaller land runs in what would become Oklahoma were the result of the government's shift in policy from reservations held for the entire tribe to individual plots of land. The Indian tribes were compensated for the value of the land, although in many instances it later turned out that the oil rights were more valuable than the land itself.
In other western territories, the lands were settled more gradually, so there was nothing like the land runs seen in Oklahoma.