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Theres no heroic setting for ulduar. What I do is just log into my toon holding the lockout, invite a friend, convert to raid, make sure its on 25m, give friend assist, jump on one of my other toons outside ulduar, ask for an invite, and waltz in. The toon with the lockout can be anywhere. I do the same for firelands for rags mount. I was full clearing ICC for the shadowmourne quest when I got invincible so I wasnt too concerned about lockouts. I know its a bit trickier because of heroic.
I farmed it weekly across 11 toons for myself, my brother, and a friend. we saw 3 of them drop in a total of about 200 kills.
You can do it on your own using the group finder;
1) Make a group on the one you want to kill the boss on, and set the group to "auto invite"
2) Log on the toon that is saved up to just before the boss and then look for and join your own alts group, you should get auto invited.
3) Switch back to the one you want to kill with and then enter the raid and accept the lockout.
$) Kill boss then disband the group and repeat with alts.
1% chance every time.
Doesn't matter if you kill it with 50 chars per week.
What? That's standard probability. You're only looking for one 'success' (the mount dropping). Someone that kills Arthas 100 times has a better chance that he'll have the mount overall than someone who only kills Arthas once. To put it another way, yes, someone who has killed Arthas 99 times has the same chance on his 100th kill as someone killing him for the first time. That's the same- but the odds that he's already seen the mount drop at some point in his 100 kills is much higher than someone who has only killed him once.
The math Bodom is doing works like this: You calculate the chance that you won't get the mount after a number of times in a row, and the chance of 'failure' is the chance we'll get the mount. This is because it doesn't matter if it drops on the first time, the second, or the hundredth. We don't care if it drops more than once either- we're just looking for the chance that we'll fail at not getting the mount (In other words, we get it) at some point.
Wowhead puts the drop chance at 1.5% (not 1%) so I'm going to use that. That means there's a 98.5% chance that the mount won't drop.
If we take one group of 1,000 people and have them each kill Arthas once, on average, we can expect 985 people not to get the mount. 15 (1.5%) will have the mount drop for them.
If we take a second group of 1,000 people and them each kill Arthas twice, we can calculate the odds they won't get the mount both times: 0.985 * 0.985 = ~0.970 which means, again on average, out of those 1000 people 970 won't see the mount. 30 people, on the other hand will either have seen it drop on their first kill (and not their second), on their second kill (but not the first) or even may have seen it drop on twice.
If we scale that group of 1000 people up to 100 kills each instead of two, we get: 0.985 ^ 100 = ~0.22 or 22% that will not see the mount over the course of 100 kills. On the other hand, while 220 people (on average) won't have the mount over 100 kills, that means 780 people will. Again, some (15 or so) will have seen it on their first kill. Some might see the drop twice in a row, others see it on their first and 100th kill. It doesn't matter- on average, 780 out of 1000 people will have seen Invincible drop at least once after killing Arthas 100 times.
For bmfstunner that means he has ~78% chance to be one of those people that gets the mount to drop after 10 weeks (10 kills per week with his 10 characters for 10 weeks is 100 kills).
You'll note that you'll never obtain 100% this way. You can, in theory, flip a coin a million times and get 'tails' with every flip, as unlikely as it is. Same with the mount- but with every kill you make (individually 1.5% each time), you'll get closer 100%.
Here's the breakdown (using the 1.5% from WoWhead):
Week 1 (10 kills): ~14.03%
Week 2 (20 kills): ~26.09%
Week 3 (30 kills): ~36.45%
Week 4 (40 kills): ~45.37%
Week 5 (50 kills): ~53.03%
Week 6 (60 kills): ~59.62%
Week 7 (70 kills): ~65.28%
Week 8 (80 kills): ~70.15%
Week 9 (90 kills): ~74.34%
Week 10 (100 kills): ~77.94%
Week 15 (150 kills): ~89.64%
Week 20 (200 kills): ~95.13%
Week 25 (250 kills): ~97.71%
Week 30 (300 kills): ~98.93%
Week 40 (400 kills): ~99.76%
Week 50 (500 kills): ~99.947%
Week 100 (1000 kills): ~99.999973%