Peter has nine four-sided (pyramidal) dice, each with faces numbered $1,2,3,4$.
Colin has six six-sided (cubic) dice, each with faces numbered $1,2,3,4,5,6$.

Peter and Colin roll their dice and compare totals: the highest total wins. The result is a draw if the totals are equal.

What is the probability that Pyramidal Peter beats Cubic Colin? Give your answer rounded to seven decimal places in the form 0.abcdefg.