hi, well I will try to help you...
I think when you say "I don't wanna risk it" it means like you don't want to loose something, you don't want to put it in risk.... like if you say "I don't want to loose my money in that game" or you can say "I don't want to risk it in that game".....
"run the risk" and "take my chances" have almost the same meaning, por example you can say "I could loose everything in the game, but I'll run the risk"..... another example "I don't know if that job is dangerous, but I'll take my chances"....
well, I don't know if I explain it well, but hope this can help you Konohamaru

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