Why is the right atrio-ventricular valve tri-cuspid and the left only bicuspid?

The right valve has three flabs because there is less pressure on this side of the heart. It is pumping deoxygenated blood from the heart to return to the lungs. There is more pressure on the left side of the heart so bicuspid valves so it has 2 flaps, its reciving oxygenated blood from the lungs.

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Answer:
The short answer is God made it that way. One might speculate that the bicuspid structure is a more effective and fail-safe way to provide hemodynamic competence in the much higher pressure system on the left side of the heart.