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  1. #1
    Community Member Therigar's Avatar
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    Default AC, Dodge, Concealment, Incorporeality and you

    Edit: As it turns out my concealment item was 20% not 10%. While the text talks about 10% concealment and an anomaly where concealment seems to have doubled, in reality the concealment I had running was 20%. I feel really stupid.

    A recent discussion caused me to explore what happens during combat and how the four corners of defense seem to be working in DDO.

    As players are aware, a character's defenses are based on four essential elements -- armor class, dodge, concealment and incorporeality. Each of these gives a chance that an attack that would otherwise record as a hit actually ends up as a miss.

    In order to test these four corners of defense I took my L25 monk into epic Gianthold and ran through encounters with CR25 and CR26 monsters. I selected this because at CR25/26 the monsters should be "at level" for my L25 character. My expectation was that my armor class would give the advertized defensive protection.

    During the test my dodge was 23%, my armor class of 114 gave 67% at level protection, my concealment was 10% and my incorporeality was 10%. I counted 107 (total) attacks from 5 different monsters.

    The expected result is 107*.77*.33*.9*.9=22 hits. The actual number of hits recorded was 22. This confirms that the four corners of defense work together to give the expected results for characters fighting "at level" monsters.

    Next, I tried to figure out the order in which the defensive elements were checked. The actual number of misses for each of them was 24 dodge, 14 blur, 8 incorporeal and 39 armor class. A straight conversion based on the defensive percentage would lead me to expect 24 dodge, 10 blur, 10 incorporeal and 71 armor class misses. The only one of these that lines up well with the actual results is dodge.

    My conclusion is that dodge is the first thing checked.

    Reworking the expected results after eliminating dodge misses shows that either concealment or incorporeality ought to give 8 misses. This lines up well with the result from incorporeality.

    My conclusion is that incorporeality is the second thing checked.

    Now, however, my numbers are way off. The expected result for concealment now drops to 7 but it the number of actual misses was 14. This is twice what I expect. This could be a bug, it could be just random impact from dice rolls. I can't tell. My guess is that concealment is actually giving twice the defense it should.

    My conclusion is that concealment is the third thing checked.

    That leaves armor class as the last thing checked.

    Determining armor class misses is a bit of a challenge because incorporeality caused misses record in the combat log using the same words as armor class misses. To know which is which you have to cross reference the floaty text with the combat log.

    Expected results if concealment had gone at expected would be 44 misses due to armor class. The actual number was 39. This, again, could just be the result of random impacts from dice rolls. It could also be the result of facing CR26 monsters during the test which would be slightly above level. If the armor class actually gave 60% defenses (as opposed to the 67% at level) the expected number of misses is 40. If that is the case then it lines up well with the 39 actual misses.

    Without additional tests it isn't really possible to know if the concealment result is an anomaly. It is certainly possible.

    It is equally possible that the sequence of incorporeality and concealment is reversed. The 14 concealment misses is closer to the 8 expected misses if it is second than it is to the 7 expected misses if it is third. However, being nearly twice the expected number really suggests that either concealment is giving more defense or the test just had a strange set of dice rolls.

    I tend to think that the dice rolls were not strange since the sample size is 107 hit opportunities. OTOH, I'm not enough of a mathematician to know if that much deviation should be considered normal.

    Anyway, I think it is useful information for players trying to estimate how much effort to put into each of the four corners of defense.
    Last edited by Therigar; 09-14-2013 at 09:22 PM. Reason: Found cause of concealment "error"

  2. #2
    Community Member skullzz's Avatar
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    Quote Originally Posted by Therigar View Post
    A recent discussion caused me to explore what happens during combat and how the four corners of defense seem to be working in DDO.

    As players are aware, a character's defenses are based on four essential elements -- armor class, dodge, concealment and incorporeality. Each of these gives a chance that an attack that would otherwise record as a hit actually ends up as a miss.

    In order to test these four corners of defense I took my L25 monk into epic Gianthold and ran through encounters with CR25 and CR26 monsters. I selected this because at CR25/26 the monsters should be "at level" for my L25 character. My expectation was that my armor class would give the advertized defensive protection.

    During the test my dodge was 23%, my armor class of 114 gave 67% at level protection, my concealment was 10% and my incorporeality was 10%. I counted 107 (total) attacks from 5 different monsters.

    The expected result is 107*.77*.33*.9*.9=22 hits. The actual number of hits recorded was 22. This confirms that the four corners of defense work together to give the expected results for characters fighting "at level" monsters.

    Next, I tried to figure out the order in which the defensive elements were checked. The actual number of misses for each of them was 24 dodge, 14 blur, 8 incorporeal and 39 armor class. A straight conversion based on the defensive percentage would lead me to expect 24 dodge, 10 blur, 10 incorporeal and 71 armor class misses. The only one of these that lines up well with the actual results is dodge.

    My conclusion is that dodge is the first thing checked.

    Reworking the expected results after eliminating dodge misses shows that either concealment or incorporeality ought to give 8 misses. This lines up well with the result from incorporeality.

    My conclusion is that incorporeality is the second thing checked.

    Now, however, my numbers are way off. The expected result for concealment now drops to 7 but it the number of actual misses was 14. This is twice what I expect. This could be a bug, it could be just random impact from dice rolls. I can't tell. My guess is that concealment is actually giving twice the defense it should.

    My conclusion is that concealment is the third thing checked.

    That leaves armor class as the last thing checked.

    Determining armor class misses is a bit of a challenge because incorporeality caused misses record in the combat log using the same words as armor class misses. To know which is which you have to cross reference the floaty text with the combat log.

    Expected results if concealment had gone at expected would be 44 misses due to armor class. The actual number was 39. This, again, could just be the result of random impacts from dice rolls. It could also be the result of facing CR26 monsters during the test which would be slightly above level. If the armor class actually gave 60% defenses (as opposed to the 67% at level) the expected number of misses is 40. If that is the case then it lines up well with the 39 actual misses.

    Without additional tests it isn't really possible to know if the concealment result is an anomaly. It is certainly possible.

    It is equally possible that the sequence of incorporeality and concealment is reversed. The 14 concealment misses is closer to the 8 expected misses if it is second than it is to the 7 expected misses if it is third. However, being nearly twice the expected number really suggests that either concealment is giving more defense or the test just had a strange set of dice rolls.

    I tend to think that the dice rolls were not strange since the sample size is 107 hit opportunities. OTOH, I'm not enough of a mathematician to know if that much deviation should be considered normal.

    Anyway, I think it is useful information for players trying to estimate how much effort to put into each of the four corners of defense.

    Therigar,

    First, Nice testing.

    I just think the explanation for the order of what is tested does not make sense.
    Just because your numbers seem to fit this order does not make them true.
    Since your test sample is so small there is not really a way to make a definitive conclusion.
    Also with 2 of the parameters the same it makes the conclusion even hard to digest.


    I would recommend trying with a different concealment value or incorporeal value. Concealment is easier since blur gives 20% and displacement gives 50% (non-stacking)
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  3. #3
    Community Member Kalimah's Avatar
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    Great read Skullz. Its in line with what I've thought I've observed (without the detailed testing). I think the to hit process now borks the crud outa AC so hard to say how its acting. I tend to not worry as much about AC and do all possible to max dodge and conceal/incorp.

  4. #4
    Community Member Therigar's Avatar
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    Definitely true that the sample size is not yet large enough to draw definitive conclusions. I do think that it is worth noting the connections with dodge, incorporeality and concealment simply because the dodge and incorporeal numbers fit exactly what would be expected if they check in that order and the concealment is exactly twice what would be expected if checked third.

    I do intend to conduct additional tests to see if my initial look has any legitimacy. I'll be sure to post after I do.

    One thing that I think people have wrong is concluding that AC should be disregarded. Even if it checks last it still accounts for 39 of the 85 misses in the test. That is 46% of the misses. I think people should be drawing the opposite conclusion -- AC matters quite a lot.

    Anyway, I'll post to the thread again when I've had a few more opportunities to test things.

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    Quote Originally Posted by Therigar View Post
    Definitely true that the sample size is not yet large enough to draw definitive conclusions. I do think that it is worth noting the connections with dodge, incorporeality and concealment simply because the dodge and incorporeal numbers fit exactly what would be expected if they check in that order and the concealment is exactly twice what would be expected if checked third.

    I do intend to conduct additional tests to see if my initial look has any legitimacy. I'll be sure to post after I do.

    One thing that I think people have wrong is concluding that AC should be disregarded. Even if it checks last it still accounts for 39 of the 85 misses in the test. That is 46% of the misses. I think people should be drawing the opposite conclusion -- AC matters quite a lot.

    Anyway, I'll post to the thread again when I've had a few more opportunities to test things.
    AC doesn't matter because it simply doesn't work in quests where having high defenses (EE) does matter. It might matterslightly heroic, but endgame the quest is either easy enough to outheal mobs with pots, or even 160 AC doesn't work if you know what I mean
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    Community Member Teh_Troll's Avatar
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    Quote Originally Posted by keveniaftw View Post
    even 160 AC doesn't work if you know what I mean
    He will argue this with you and carve a statue full of BS, screenshots, and made up numbers.

    I sense much greatness in this thread.
    Last edited by Teh_Troll; 09-13-2013 at 11:01 PM.

  7. #7
    Community Member Therigar's Avatar
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    Quote Originally Posted by keveniaftw View Post
    AC doesn't matter because it simply doesn't work in quests where having high defenses (EE) does matter. It might matterslightly heroic, but endgame the quest is either easy enough to outheal mobs with pots, or even 160 AC doesn't work if you know what I mean
    Actually, I think that this is incorrect. I think that the evidence is that 160AC will be very worthwhile in eElite and that players are misunderstanding what is happening when they are hit. But, to make sense of how the defenses work it is important to know a bit about the order in which they are applied.

    This is the reason for discussing percent protection and expected numbers. It is also the reason for pointing out that in an "at level" test AC gave the greatest amount of protection (even though the number of misses was lower than expected).

    In any case, more later when I've had a chance to run several more tests.

  8. #8
    Community Member Therigar's Avatar
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    Quote Originally Posted by Teh_Troll View Post
    I sense much greatness in this thread.
    I have to credit Teh_Troll with being the motivation for my effort. Although his baseless claims concerning the value of AC were definitively shown to be wrong in a previous thread there was one piece of value to his criticisms.

    Because of Teh_Troll I began making video clips of the tests. I've actually conducted several small scale tests learning how to make the video software work and making note of anomalies that I encountered. Most important was that I was not seeing anything indicating misses due to incorporeality. This is how I discovered that players have to cross reference floating text on the screen with combat log entries as both incorporeal misses and armor class misses give the same feedback in the combat log.

    Once I figure out how to get video to display inside of forum messages (or make YouTube work for me) I will make the videos used in this thread's tests available.

    If it works you can see my first recorded test of an eElite Cabal encounter on YouTube. Warning, my allergies were acting up and there are some sneezes in the recording. I also miscounted the attacks during the dialogue (I think the actual number is 1 fewer than I counted*). Still, it is a starting point.

    *Actually, my counting is correct. I looked at the video and counted dodge, incorporeal, miss and hit numbers. They are 10, 9, 2, 9 for a total of 30 attacks. That is what I count in the video. If sequence is dodge, incorporeal, concealment, armor class then the expected results would have been 7, 6, 8 instead of 10, 9, 2. This shows that I need more tests and more numbers.
    Last edited by Therigar; 09-14-2013 at 02:43 AM.

  9. #9
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    Quote Originally Posted by Therigar View Post
    Definitely true that the sample size is not yet large enough to draw definitive conclusions. I do think that it is worth noting the connections with dodge, incorporeality and concealment simply because the dodge and incorporeal numbers fit exactly what would be expected if they check in that order and the concealment is exactly twice what would be expected if checked third.

    I do intend to conduct additional tests to see if my initial look has any legitimacy. I'll be sure to post after I do.

    One thing that I think people have wrong is concluding that AC should be disregarded. Even if it checks last it still accounts for 39 of the 85 misses in the test. That is 46% of the misses. I think people should be drawing the opposite conclusion -- AC matters quite a lot.

    Anyway, I'll post to the thread again when I've had a few more opportunities to test things.
    Or it could be that AC is checked first, as would seem logical as checking to see if the static effects avoid hits that are actually misses seems a rather silly way of doing things, and gives much less protection than whatever "miss chance at level" is suggesting. It's such a vague term when mobs of the same CR have such a conceivably broad range of attack bonuses.

  10. #10
    Community Member Pilgrim1's Avatar
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    I am not 100% sure of this but I would expect that a monster rolling a 1 would be a automatic miss and a monster rolling a 20 would be a automatic hit, this might change your numbers.

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    Community Member FestusHood's Avatar
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    Would it be possible to remove other forms of protection to just test the efficacy of the individual types? I realize this would be hard to do with dodge, but incorporality and blur you can likely disable, just to test for misses from ac.

    Testing on epic elite is probably not possible, as you won't be able to survive long enough to get meaningful numbers. Epic hard should be doable though.

  12. #12
    Community Member Therigar's Avatar
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    Quote Originally Posted by Gremmlynn View Post
    Or it could be that AC is checked first, as would seem logical as checking to see if the static effects avoid hits that are actually misses seems a rather silly way of doing things, and gives much less protection than whatever "miss chance at level" is suggesting. It's such a vague term when mobs of the same CR have such a conceivably broad range of attack bonuses.
    I am absolutely certain that AC is NOT checked first.

    From a math standpoint it does not matter what gets checked first. Because each item gets checked only if an attack would register a hit, the total impact of all the reductions ends up giving the same results.

    Using the reported test with 67% AC at level, 10% concealment, 10% incorporeal, 23% dodge we can arrange the four numbers in any combination. Using the first letter of each defense type we could have any of these as the order in which things get checked: ACDI, ACID, ADCI, ADIC, AICD, AIDC, CADI, CAID, CDAI, CDIA, CIAD, CIDA, DACI, DAIC, DCAI, DCIA, DIAC, DICA, IACD, IADC, ICAD, ICDA, IDAC, IDCA.

    But, when we work out the expected results using the percentage values the final number is always the same. Pick any combination and try it. I'll just do a couple of them.

    ACID -- 107*.33*.9*.9*.77=22.022847. We expect 22 hits to get through. In fact, 22 hits did get through.
    CIDA -- 107*.9*.9*.77*.33=22.022847. This is the same number showing 22 hits should get through.
    IDCA -- 107*.9*.77*.9*.33=22.022847. So, no matter what the order we check, the final result is always the same.

    Why did I use .33 for A (armor class)? Because the defense is .67 (67%) so the undefended part is .33 (33% gets through).

    For ACID, if we break it down step by step as each defense is applied, we get 107*.33=35.31. We expect armor to stop all but 36 attacks. That means if armor was checked first it would stop 71 attacks but it did not. Armor stopped 39 attacks. So I know that armor did not get checked first.

    In fact, I know from the first test that the most likely thing to have been checked first is dodge. 107*.77=82.39. We expect dodge to stop all but 83 attacks. In fact, dodge stopped 24 attacks. 83+24=107 -- this is exactly the expected result.

    So I believe that it is highly probable that dodge gets checked before anything else.

    In the same way, of the 82.39 attacks that dodge lets through I can see expected results by looking at incorporeality. 82.39*.9=74.151. I expect roughly 8 attacks to miss with incorporeality and that is exactly how many misses I observed.

    My conclusion is that the order is NOT armor class first. It is highly probable that the order is DICA -- dodge, incorporeality, concealment, armor class.

    But, the concealment result is anomalous*. The next expected result would be 7 misses but instead there were 14 due to concealment. I find it a bit odd that there would be exactly twice as many misses as expected. I speculate that concealment is getting a double counting somehow -- or that my concealment item is wrongly labeled 10% when it is really 20%.

    This is where I need to do further tests. If I continue to get higher than expected concealment numbers then I know that something there is buggy.

    In the first test my actual results indicate that dodge was 23%, incorporeality 10%, concealment 20% and armor class ~63%. Using these numbers gives the same 22 expected hits that I saw in the test and fits with the observed results.

    As I said before, I'm not a mathematician so I don't know if the observed results are well enough inside the margin of error that the original numbers are instead valid.

    Only more testing will confirm that.

    *Edit: See the edit on the first post in this thread. It turns out the concealment item I had on was 20% not 10%. This means that the results of the test were actually very accurate and that the check order is almost certainly dodge, incorporeality, concealment, armor.
    Last edited by Therigar; 09-14-2013 at 09:25 PM.

  13. #13
    Community Member Therigar's Avatar
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    Quote Originally Posted by FestusHood View Post
    Would it be possible to remove other forms of protection to just test the efficacy of the individual types? I realize this would be hard to do with dodge, but incorporality and blur you can likely disable, just to test for misses from ac.

    Testing on epic elite is probably not possible, as you won't be able to survive long enough to get meaningful numbers. Epic hard should be doable though.
    Yes. It would be easy to remove incorporeal and concealment items to just leave dodge and armor class. My eElite Cabal run was without a concealment item -- just incorporeal, dodge and armor class. I can easily run just dodge and armor class.

  14. #14
    Community Member Therigar's Avatar
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    Quote Originally Posted by Pilgrim1 View Post
    I am not 100% sure of this but I would expect that a monster rolling a 1 would be a automatic miss and a monster rolling a 20 would be a automatic hit, this might change your numbers.
    I think from a purist's standpoint this is correct. However, over time it should still balance out so that the on-average result will be the same. I think a 1 would just result in a "Miss" display and, of course, a 20 would result in a damage display. We could probably adjust for auto miss/hit by reducing the count of hits by 5% and the count of misses by 5%. That's more math than I'm willing to do right now.

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    Community Member AbyssalMage's Avatar
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    Quote Originally Posted by Therigar View Post
    As I said before, I'm not a mathematician so I don't know if the observed results are well enough inside the margin of error that the original numbers are instead valid.

    Only more testing will confirm that.
    I wish I could help you with the margin of error and sampling size. I know most sample sizes want a 3-4% margin and working on a d20 spectrum (assuming NPC's still use a D20) makes me believe you need at least a 1k sample size but that seems large I'll sleep on it and maybe someone else who actually enjoys statistics can give you a number.

    On second thought....d20

    100+ would give you 5 sets of d20 (100+ individual sample /20 possible combinations = 5 "full" sets)
    ...
    ...
    Never mind, too tired to think about it Maybe after some sleep

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    Quote Originally Posted by Therigar View Post
    I think from a purist's standpoint this is correct. However, over time it should still balance out so that the on-average result will be the same. I think a 1 would just result in a "Miss" display and, of course, a 20 would result in a damage display. We could probably adjust for auto miss/hit by reducing the count of hits by 5% and the count of misses by 5%. That's more math than I'm willing to do right now.
    That's what spreadsheet apps are for. Let the machine do the math, you just gather and input the data (after you enter in the formulae).
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    Community Member AtomicMew's Avatar
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    It doesn't matter what the exact mechanics are, as long as you can determine a specific probability for a given hypothesis, you can determine whether your results are statistically significant or not. The statistical test you want to use is the exact binomial test. Give me some numbers and I can run it for you.

    E.g.:

    Number of trials: 100
    Number of hits: 15
    Expected number of hits: 20

  18. #18
    Community Member visibleman's Avatar
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    I had always assumed that AC was tested first because that is how it is done in PnP.

    Nice work. Keep digging, more evidence is needed though before a solid conclusion can be reached.


    Quote Originally Posted by Therigar View Post
    I am absolutely certain that AC is NOT checked first.

    From a math standpoint it does not matter what gets checked first. Because each item gets checked only if an attack would register a hit, the total impact of all the reductions ends up giving the same results.
    It may not make any difference from a Math POV however, from a coders POV the order does make a difference.

    The AC/ToHit calc has more variables and therefore requires more calculations than the Dodge calc. So it would be more efficient code to do the AC test last.
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    Quote Originally Posted by Therigar View Post
    Actually, I think that this is incorrect. I think that the evidence is that 160AC will be very worthwhile in eElite and that players are misunderstanding what is happening when they are hit. But, to make sense of how the defenses work it is important to know a bit about the order in which they are applied.

    This is the reason for discussing percent protection and expected numbers. It is also the reason for pointing out that in an "at level" test AC gave the greatest amount of protection (even though the number of misses was lower than expected).

    In any case, more later when I've had a chance to run several more tests.
    I have run a monk with 160 AC, he never, ever, ever got missed by AC in EE, except on the occasional 1 roll of a mob. AC is worthless in EE, and if you decide to build AC on your toons, feel free but know two things.
    1) You'll only be disappointed and don't come cry because it doesn't work.
    2) Don't act towards other players like it works, it doesn't. You not only will disappoint yourself, but also other players...

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    Last edited by IWCoppercrest; 09-15-2013 at 09:51 AM.
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    When attacking a monster the first thing checked is incorpeality. Ever see a roll of 20 that shows +0 at the end and Incorp on the on screen attack dice? The same probably applies to players. As for sample sizes 1000 would be a good sample size. 10% of that would be 100 for incorp, 100 for concealment, 23% for dodge (unless some monsters bypass dodge, have seen a few player abilities that can bypass dodge) gives you 230 misses due to dodge and finally 67% from your at level AC for 670 misses from that. So we get 100+100+230+670= 1100 total missed attacks... out of 1000 total attacks. Now whichever type comes first would cause diminishing returns on the following types.

    Knowing about diminishing returns lets start over with 1000 total attacks. First comes incorp at 10%, so 100 attacks miss leaving 900 that can go through concealment, dodge and AC. Now it is just a guessing game of what comes next, i will go with concealment since it has the least numerical impact. Of the 900 remaining attacks 10% miss due to concealment, 810 remain to miss due to AC or be dodged. Which now? If Dodge comes next 623 attacks remain, after AC 205 of those would connect. How about if AC comes befofe dodge? 67% out of 810 leaves 267 attacks to be dodged. After 23% dodge 205 hit. Surprising that it didn't seem to matter if dodge or AC came first at those numbers, perhaps a sample size of 10,000 is needed so the decimals i dropped will show the difference more.

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