help me understand probability case work

i've been trying to calculate the probability of winning. and here what i came up.

x my roll add 2 meaning X = 1 => 3

y friend roll

x roll p(x > y|X=x) p(X=x) p( x > y |y n X = x)

1 = 3 2/8 1/6 2/48

2 = 4 3/8 1/6 3/48

3 = 5 4/8 1/6 4/48

4 = 6 5/8 1/6 5/48

5 = 7 6/8 1/6 6/48

6 = 8 7/8 1/6 7/48

(sorry for the weird format, tried to do a table)

which adds up to 27/48 = 0.5625

but in the solution they say 7/12

what am i missing in my case work?

thanks.

#Algebra

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$