AHC: Have the 'Great Game' lead to a 'Great War'

With a post 1860 POD have the 'Great Game' between Britain and Russia lead to a World War by the early 1900s.
 
Theres at least 3 points when it easily could have kicked off post 1900. I'll go into more details when I have time but I want get my foot in as it were.
 
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