The cooperation between the Christian Norman knights and the Muslim emir Betumen (ibn-Thinma) was a crucial factor in Roger's ambition to conquer Sicily. By working together, they were able to combine their strengths and weaken their enemies. Betumen and his Muslim troops provided valuable knowledge of the terrain and local customs, while the Christian Normans brought their military prowess to the battlefield. This collaborative effort allowed Roger to conquer Sicily more quickly and effectively than he would have been able to on his own. Furthermore, the alliance between the Normans and the Muslims helped to maintain order and stability in Sicily after the conquest.