Ordnance Armour Penetration, 2d6 Highest Roll Statistics, and the Melta Gun

One of the positive points about taking ordnance weapons and tank-mounted ordnance weapons such as vindicators is their special rule that they get to roll two die and pick the highest score. This means that they're probably going to penetrate a target quite often. But what are the statistics on "2d6 and pick the highest?". How does a demolisher cannon stack up against a melta gun at close range?

"2d6 and pick highest statistics".
These statistics apply to other situations apart from penetrating armour with a demolisher cannon - such as moving through difficult ground and so forth.

There are 36 possible combinations for rolling 2d6. I'm going to be incredibly dull and list them all here. I'm also going to detail the highest die roll (i.e. the outcome!) alongside them.

(1,1)= 1  (1,2)=2  (1,3)=3  (1,4)=4  (1,5)=5  (1,6)=6 
(2,1)= 2  (2,2)=2  (2,3)=3  (2,4)=4  (2,5)=5  (2,6)=6 
(3,1)= 3  (3,2)=3  (3,3)=3  (3,4)=4  (3,5)=5  (3,6)=6 
(4,1)= 4  (4,2)=4  (4,3)=4  (4,4)=4  (4,5)=5  (4,6)=6 
(5,1)= 5  (5,2)=5  (5,3)=5  (5,4)=5  (5,5)=5  (5,6)=6 
(6,1)= 6  (6,2)=6  (6,3)=6  (6,4)=6  (6,5)=6  (6,6)=6 

So, the final probabilities for each roll are:

Prob(1) = 1 in 36 = 0.028
Prob(2) = 3 in 36 = 0.083
Prob(3) = 5 in 36 = 0.139
Prob(4) = 7 in 36 = 0.194
Prob(5) = 9 in 36 = 0.250
Prob(6) = 11 in 36 = 0.306

Or, put another way, the cumulative probabilities are:

Prob(2+) = 1 - 0.028 = 0.972
Prob(3+) = 0.972 - 0.083 = 0.889
Prob(4+) = 0.889 - 0.139 = 0.750
Prob(5+) = 0.750 - 0.194 = 0.556

That means that you've got great than even odds of rolling a 5+ on "2d6 and pick the highest".

Demolisher Cannon vs. Melta Gun.
Here's the probabilities to penetrate a given AV using both a demolisher cannon and a melta gun at close range:

AV: Prob(Demolisher), Prob(Melta)
AV=10: 1.000, 0.972
AV=11: 0.972, 0.917
AV=12: 0.889, 0.833
AV=13: 0.750, 0.722
AV=14: 0.556, 0.583

Hence, the demolisher cannon is superior at penetrating all targets except AV=14, where a close range melta gun has the upper hand by a slim margin.

But!
But the second major difference between ordnance and a melta gun is that a melta gun is a melta gun. What do I mean by that? Melta guns get a +1 on the result of the armour penetration roll since they're AP=1; conversely, at AP=2, demolisher cannons are worse at destroying vehicles. This is ultimately why meltas are so useful in 5th edition.