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Confirming 57% chance per weapon.

Odds to pen per shot (X) = 0.66667 x [1 - ( Odds to fail to Pen) ]

X = 0.66667 x [ 1 - ( [5/6] ^ 4 ) ] -> Due to having Ord + TH, you would need to fail 4 attempts at rolling a 6. "1" subtract odds of failure = odds of success.
X = 0.66667 x [ 1 - 0.48225 ]
X = 0.34517 Success Rate

Fail rate = 1- Success Rate = 0.65483

Odds to Pen per weapon (Y) = 1- Odds to fail to pen twice [Ie fail rate ^ 2]

Y = 1 - [ 0.65483 ^ 2 ]
Y = 0.57120

You can determine the fail rate per "Z" weapons by using the fail rate per weapon [Ie. 0.42880] to the exponent of Z. To determine the success rate, take 1 and subtract your "Z exponent" value, and ta-daah!

For example, Z=3, then the success rate is...

Success for 3 Weapons = 1 - [ 0.4288 ^3]
= 1- 0.07885
= 0.92115

However, per your question, the odds of success for 2 weapons is 81.613% If that's good enough, that's up to you. I'd say pretty damned reliable, for taking on AV 15.

I made an account specifically to post this. Ordinance is not a rerolled pen, it is roll 2d6 and pick the highest correct? Therefore a pen occurs (11/36) rolls. Tank hunter let's you reroll failed pens, which happens (25/36) times.
Math:
2 shots * bs4 * pen chance + rerolled failed pens=pens/rd
2*2/3*11/36+2*2/3*11/36*25/36= pens /round of shooting
My math puts that at .69 pens/ Rd with the above assumptions on rule implementation.

He's saying that he has both Ordinance AND Tank Hunter though, so he gets to reroll the pen result of a failed Ordinance shot too.


Automatically Appended Next Post:
Out of curiosity, I quickly programmed an excel sheet to generate random results. Each was two rolls. If a roll was 3 or higher, there were two more d6 rolls (ordinance). If neither of those rolls were a 6, then both were re-rolled (tank hunter). If any of the previous four rolls were a 6, then the result of "Pen" was recorded. If either of the two to-hit rolls resulted in a "Pen", then this was just recorded as at least one Pen.

I took the total number of at least one Pens, divided by the total number of tests (about 1500 results). I ran this test a few times, and achieved results between 55%-58% 8 out of 10 times. The outliers were 54.9%, and the highest was 58.8%. I think this verifies my previous post.

http://www.mathhammer40k.com/shooting/armor

Thanks guys. I think an 81% chance with four shots isn't bad. If we are playing apocalypse I might bring another Valdor, but I do need to focus on units protecting them (since they have a short range) and other units to strip void shields/etc.


Automatically Appended Next Post:

Naaris wrote:
http://www.mathhammer40k.com/shooting/armor

Unfortunately that website does not recognize the Warlord's armour value of 15 nor will it allow me to take into account the Tank Hunter special rule (which is the hard one to calculate as it interacts with Ordnance).