Contrary to everyone's impulse (including my own) to explain recent events in Russia as the fruit of intelligent scheming, I now think it was all a fairly chaotic series of action/reaction. Prigozin, faced with demands to subordinate to the MOD and lose power as an independent force, mutinied against his rivals. Putin, in coming out hard against him Saturday morning, made it a do or die Prigozin vs. Putin fight. Hence the March on Moscow. Putin, realizing he does not have the troops in position to stop him, is forced to flee and negotiate. Prigozin, realizing that even if he gets into Moscow he's bitten off more than he can chew, takes a deal. See this analysis by Thomas Freedman, the best I think of several I've read:
https://samf.substack.com/p/that-was-the-coup-that-was