Has anyone done the math for Lightning Maces?

[ddude987]

Critting on 15-20/x4 with 4 attacks (though would be perferrable to have X attacks, X being the number of attacks one is making). A friend and I have been struggling to figure this out... at this point we are doing sums of geometric sums and (stuff I don't understand). I recognize a pattern but I can't quite fit it into an equasion. Anybody who knows, or has better google-fu than I (as my search returned nothing), please help. Thanks!

[mattie_p]

Not quite sure what you are asking, but Attila's math desk (http://www.giantitp.com/forums/showthread.php?t=270188) seems like the best place to get your answer.

[Phelix-Mu]

There is a thread for math questions on the forum...it's a pretty current thread, and the guy who runs it is quite impressive. I'll try to dig up a link.

EDIT: Righteously ninja'd.

[ddude987]

Not quite sure what you are asking, but Attila's math desk (http://www.giantitp.com/forums/showthread.php?t=270188) seems like the best place to get your answer.

Wow! Learn something new every day. Thanks!!! /thread

[Gotterdammerung]

Well first of all you don't have to hit to gain an extra attack via lightning mace. You just have to roll in your threat range. This is important because it gives a flat % chance of activation per full round attack.

your example 15-20 crit range has a total of 6 possible sides of a d20 that could activate lightning mace. Each side of a D20 represents a 5% chance. So you have a 30% chance of activating the feat each time you swing.

If you have 4 attacks in a round that is 4 chances at a 30% chance.

Here it gets a little tricky.

You have a 75.99000% probability of using all 4 rolls to trigger 1 bonus roll

If you trigger the feat on the first roll (30% probability)-
you have a 75.99000% probability of rolling a second trigger off of your remaining rolls.

If you trigger the feat on the second roll (51% probability)-
you have a 65.7% probability of rolling a second trigger of off your remaining rolls.

If you trigger the feat on the third roll (65.7% probability)-
you have a 51% probability of rolling a second trigger of off your remaining rolls.

If you trigger the feat on your 4th roll, the last base roll, (75.99% probability)-
you have a 30% probability of rolling a second trigger of off your remaining 1 roll.



So basically this data can go off into infinite. You can possibly roll attack rolls forever. But plotting out this base tier of probability gives us the information needed to know that activating the ability on your earlier rolls will give you a larger probability of activating the ability more total times in the round.

Raising your crit range will make the ability activate more reliably. Adding additional attacks will make the likelihood of at least 1 bonus swing much more probable.

I would say because of its infinite possibilities it is mechanically better than other "additional attack" mechanics like rapid shot, haste, snap kick, ect.
But that is just weighing the probabilities to gauge its mechanic potential. You must take into account the huge feat tax to decide if it is a truly better alternative.

[ddude987]

Well first of all you don't have to hit to gain an extra attack via lightning mace. You just have to roll in your threat range. This is important because it gives a flat % chance of activation per full round attack.

your example 15-20 crit range has a total of 6 possible sides of a d20 that could activate lightning mace. Each side of a D20 represents a 5% chance. So you have a 30% chance of activating the feat each time you swing.

If you have 4 attacks in a round that is 4 chances at a 30% chance.

Here it gets a little tricky.

You have a 75.99000% probability of using all 4 rolls to trigger 1 bonus roll

If you trigger the feat on the first roll (30% probability)-
you have a 75.99000% probability of rolling a second trigger off of your remaining rolls.

If you trigger the feat on the second roll (51% probability)-
you have a 65.7% probability of rolling a second trigger of off your remaining rolls.

If you trigger the feat on the third roll (65.7% probability)-
you have a 51% probability of rolling a second trigger of off your remaining rolls.

If you trigger the feat on your 4th roll, the last base roll, (75.99% probability)-
you have a 30% probability of rolling a second trigger of off your remaining 1 roll.



So basically this data can go off into infinite. You can possibly roll attack rolls forever. But plotting out this base tier of probability gives us the information needed to know that activating the ability on your earlier rolls will give you a larger probability of activating the ability more total times in the round.

Raising your crit range will make the ability activate more reliably. Adding additional attacks will make the likelihood of at least 1 bonus swing much more probable.

I would say because of its infinite possibilities it is mechanically better than other "additional attack" mechanics like rapid shot, haste, snap kick, ect.
But that is just weighing the probabilities to gauge its mechanic potential. You must take into account the huge feat tax to decide if it is a truly better alternative.

Yes of course it can go onto infinite but the probobilities of an infinite summation add up to a final number. After asking maths and finally writing a program that does it by brute force (it simulates a player doing it 1 trillion times) I came out with 7.4 attacks if you crit from 15-20 and have 5 attacks. I asked on the math thread for a full formula to calculate average damage from all this.

[Malroth]

the infinite series adds up to a finite number if and only if the crit range is smaller than 11+ if its 10 or less it no longer converges as a series