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What if, instead of embracing Judaism as a neutral option the the face of pressure from both the Byzantines and Caliphate, the Khazar rulers decide that their interests lie with the Caliphate and embrace Islam. In particular:
How effective would a joint Khazar-Caliphate alliance be against the Byzantines, particularly with the Khazar's ability to raid and attack their Black Sea holdings?
What effect is this going to have the the Rus'? Would the Khazars potentially cutting the Byzantines off from their northern trade routes make the Rus' less likely to convert to Christianity or would the prospect of a united front against Khazar expansion mean that they would still seek closer ties with Constantinople?
With stronger ties to potential allies to the south how much longer would the Khazar Khanate last for?