Which definition best describes the great game

The Great Game is best describe as the strategic rivalry and conflict between the British Empire and the Russian Empire for supremacy in Central Asia.  
I hope this helps!

Neteenth century between the British Empire and the Russian Empire over Afghanistan and neighbouring territories in Central and Southern Asia. Russia was fearful of British commercial and military inroads into Central Asia, and Britain was fearful of Russia adding "the jewel in the crown", India, to the vast empire that Russia was building in Asia. This resulted in an atmosphere of distrust and the constant threat of war between the two empires.[1][2][3]

The Great Game began on 12 January 1830 when Lord Ellenborough, the President of the Board of Control for India, tasked Lord William Bentinck, the Governor-General, to establish a new trade route to the Emirate of Bukhara.[2][3][4] Britain intended to gain control over the Emirate of Afghanistan and make it a protectorate, and to use the Ottoman Empire, the Persian Empire, the Khanate of Khiva, and the Emirate of Bukhara as buffer states between both empires. This would protect India and also key British sea trade routes by stopping Russia from gaining a port on the Persian Gulf or the Indian Ocean.[2][3] Russia proposed Afghanistan as the neutral zone.[5] The results included the failed First Anglo-Afghan War of 1838, the First Anglo-Sikh War of 1845, the Second Anglo-Sikh War of 1848, the Second Anglo-Afghan War of 1878, and the annexation of Khiva, Bukhara, and Kokand by Russia.

Historians consider the end of the Great Game to be 10 September 1895 signing of the Pamir Boundary Commission protocols,[6] when the border between Afghanistan and the Russian empire was defined.[7][8][9][10]:p14 The 1901 novel Kim by Rudyard Kipling made the term popular and introduced the new implication of great power rivalry. It became even more popular after the 1979 advent of the Soviet–Afghan War.

African americans at the time just came out of slavery and needed money to provide for there families. so they joined for the money mainly.