High Runes and the High Council
In 1.12a, the High Council in Hell Travincal is typically the most popular target for a goldfinding character (typically a Barbarian with Find Item). The High Council also drops some pretty nice sets/uniques, as well as a quite reasonable number of charms/jewels/gems.
In the past few months, quite a few high runes have also been found from the High Council, including two I found myself; Lo #1 and Lo #2. This got me interested in how common they really are, and inspired me to do some math on the subject. I'd like to share the results and conclusions in this thread. Note that I've been using numbers that are relevant to me and my Travincal runner (such as a level 22 Find Item, and my run times), but changing around the numbers slightly shouldn't be tough if you want to adjust for your own situation.
First, the basic probabilities of high runes dropping from council members (as a sidenote, council members have identical drop rates, making it easier to calculate):
[highlight]on players 1:[/highlight]
[highlight]on players 3:[/highlight]
These numbers show how many of each rune, on average, you will get from killing one council member. For instance, on p3, you will need to kill 557531 council members, on average, to find one Ber rune, so you find 1/557531 Bers per council member killed.
Now, at first glance, these numbers don't look so hot, do they? In LK, a Ber is 1 in 65536 to drop, and there are 6 chests per run! Well, LK might be tough to compete with, but hang on for now, it gets better.
First, we must consider that there are 11 council members. Second, with a level 22 Find Item, you have a 52% chance of a successful hork. That means that you on average will kill 11 * 1.52 = 16.72 council members during each run, as far as drop odds are concerned.
So, let's figure out the true probabilities of a high rune dropping, shall we?
[highlight]p1:[/highlight] (1/95540) + (1/143311) + ... + (1/1341305) = 1/26141.76 * 16.72 = 1/1563.50
[highlight]p3:[/highlight] (1/69484) + (1/104226) + ... + (1/975495) = 1/19012.20 * 16.72 = 1/1137.09
We're starting to see some more fun numbers. If you run on players 3, you will see a rune Mal or higher once every 1137 runs. That's more often than you will find a rune Mal or higher during p3 LK runs (1 in 1560 runs if the LK FAQ thread is correct, which coincidentally is almost identical to the p1 Travincal number of 1 in 1563.5).
You might be more interested in the really high runes. Who cares about the Mals and such when we're Ber hunting? Or, in the case of Travincal, Jah and Cham hunting! Let's take a look at the numbers for runes Vex and up:
[highlight]p1:[/highlight] (1/250545) + ... + (1/1341305) = 1/67470.15 * 16.72 = 1/4035.30
[highlight]p3:[/highlight] (1/182215) + ... + (1/975495) = 1/49069.21 * 16.72 = 1/2934.76
Still comparing to p3 LK runs, in LK you would expect to find a Vex+ rune once in 3641 runs. More often than p1 Travincal runs, but less often than p3 Travincal runs.
Does this mean Travincal is a better target for dedicated high rune hunters? Probably not. All of the above doesn't take into account that LK runs are significantly faster than Travincal runs. When I max out on speed in my goldfind setup, my average run time on p3 is around 50 seconds. In LK, my average run time is around 29 seconds.
Finally, there's the question of relative rune rarity (again I'm calculating only with runes Vex and up, it's just more interesting to me). In LK this is easy; in 10923 runs you will find 1 Ber, 1 Sur and 1 Lo. That's the equivalent of 28 Vex. That means in LK, you will find a Vex every 10923 / 28 = 390 runs, or 1 Vex every 390 * (29/60) = 189 minutes, or 3 hours and 9 minutes.
With Travincal, the calculation is a bit more complicated. Here's one possible, if a bit cumbersome, way of calculating it. I'm putting it in Spoiler tags because it's kinda long and kinda uninteresting for most of you, I'm sure:
Summary of spoiler:
[highlight]p1:[/highlight] 1 Vex every 5 hours and 31 minutes.
[highlight]p3:[/highlight] 1 Vex every 4 hours and 28 minutes.
[highlight]LK p3:[/highlight] 1 Vex every 3 hours and 9 minutes.
([highlight]1.07 LoD HF Rushing:[/highlight] 1 Vex every 2 hours and 34 minutes)
You can of course complicate it further if you like. For instance, one could certainly argue that Cham shouldn't be considered twice as "valuable" as Jah, as the rune economy tends to stop at Jah, it being the most useful rune for runewords and everything. I think this is in-depth enough as it is though
Some more semi-useless numbers:
[highlight]Summary Section[/highlight]
[highlight]Q:[/highlight] Jesus christ dude, is this thread a joke? In English please!
[highlight]A:[/highlight] Well, the gist of it is Hell Travincal is a pretty nice place to hunt for high runes. It's unlikely to beat out LK or HF rushing in terms of runes / hour in any sort of reasonable scenario, but it's not that far behind, and in Hell Travincal you can collect lots and lots of gold, or reasonable amounts of sets, uniques, charms, gems and jewels, depending on what your goals are. You might want to view the quite decent possibility of high runes as a bonus perk for running Travincal, much like you might want to consider high runes a bonus of running LK.
[highlight]Q:[/highlight] What's with all the numbers? Do you not realize how luck based LK running is, you can't calculate it exactly like this!
[highlight]A:[/highlight] I do realize the variance of both LK running and Travincal running is very very high indeed as far as finding high runes goes. However, the expected value of these practices can be very accurately calculated, as long as your assumptions (such as average run time) are accurate. The numbers in this thread are just averages and/or approximations, nothing more. In no way am I claiming to predict exactly how long it will take to find a Jah rune from the High Council, I'm just calculating how long it will take on average.
Hope this was interesting to some of you, feel free to ask or comment or anything. Thanks for reading!
In 1.12a, the High Council in Hell Travincal is typically the most popular target for a goldfinding character (typically a Barbarian with Find Item). The High Council also drops some pretty nice sets/uniques, as well as a quite reasonable number of charms/jewels/gems.
In the past few months, quite a few high runes have also been found from the High Council, including two I found myself; Lo #1 and Lo #2. This got me interested in how common they really are, and inspired me to do some math on the subject. I'd like to share the results and conclusions in this thread. Note that I've been using numbers that are relevant to me and my Travincal runner (such as a level 22 Find Item, and my run times), but changing around the numbers slightly shouldn't be tough if you want to adjust for your own situation.
First, the basic probabilities of high runes dropping from council members (as a sidenote, council members have identical drop rates, making it easier to calculate):
[highlight]on players 1:[/highlight]
Code:
Mal 1:95540
Ist 1:143311
Gul 1:167030
Vex 1:250545
Ohm 1:292137
Lo 1:438206
Sur 1:511070
Ber 1:766606
Jah 1:894203
Cham 1:1341305[highlight]on players 3:[/highlight]
Code:
Mal 1:69484
Ist 1:104226
Gul 1:121476
Vex 1:182215
Ohm 1:212463
Lo 1:318695
Sur 1:371687
Ber 1:557531
Jah 1:650330
Cham 1:975495These numbers show how many of each rune, on average, you will get from killing one council member. For instance, on p3, you will need to kill 557531 council members, on average, to find one Ber rune, so you find 1/557531 Bers per council member killed.
Now, at first glance, these numbers don't look so hot, do they? In LK, a Ber is 1 in 65536 to drop, and there are 6 chests per run! Well, LK might be tough to compete with, but hang on for now, it gets better.
First, we must consider that there are 11 council members. Second, with a level 22 Find Item, you have a 52% chance of a successful hork. That means that you on average will kill 11 * 1.52 = 16.72 council members during each run, as far as drop odds are concerned.
So, let's figure out the true probabilities of a high rune dropping, shall we?
[highlight]p1:[/highlight] (1/95540) + (1/143311) + ... + (1/1341305) = 1/26141.76 * 16.72 = 1/1563.50
[highlight]p3:[/highlight] (1/69484) + (1/104226) + ... + (1/975495) = 1/19012.20 * 16.72 = 1/1137.09
We're starting to see some more fun numbers. If you run on players 3, you will see a rune Mal or higher once every 1137 runs. That's more often than you will find a rune Mal or higher during p3 LK runs (1 in 1560 runs if the LK FAQ thread is correct, which coincidentally is almost identical to the p1 Travincal number of 1 in 1563.5).
You might be more interested in the really high runes. Who cares about the Mals and such when we're Ber hunting? Or, in the case of Travincal, Jah and Cham hunting! Let's take a look at the numbers for runes Vex and up:
[highlight]p1:[/highlight] (1/250545) + ... + (1/1341305) = 1/67470.15 * 16.72 = 1/4035.30
[highlight]p3:[/highlight] (1/182215) + ... + (1/975495) = 1/49069.21 * 16.72 = 1/2934.76
Still comparing to p3 LK runs, in LK you would expect to find a Vex+ rune once in 3641 runs. More often than p1 Travincal runs, but less often than p3 Travincal runs.
Does this mean Travincal is a better target for dedicated high rune hunters? Probably not. All of the above doesn't take into account that LK runs are significantly faster than Travincal runs. When I max out on speed in my goldfind setup, my average run time on p3 is around 50 seconds. In LK, my average run time is around 29 seconds.
Finally, there's the question of relative rune rarity (again I'm calculating only with runes Vex and up, it's just more interesting to me). In LK this is easy; in 10923 runs you will find 1 Ber, 1 Sur and 1 Lo. That's the equivalent of 28 Vex. That means in LK, you will find a Vex every 10923 / 28 = 390 runs, or 1 Vex every 390 * (29/60) = 189 minutes, or 3 hours and 9 minutes.
With Travincal, the calculation is a bit more complicated. Here's one possible, if a bit cumbersome, way of calculating it. I'm putting it in Spoiler tags because it's kinda long and kinda uninteresting for most of you, I'm sure:
[highlight]p1:[/highlight]
In 250545 / 16.72 = 14985 runs, you will have found 1 Vex. In that time, you will also have found the following numbers of the higher runes:
Ohm: 250545/292137 = 0.85762844 * 2 = 1.715 Vex
Lo: 250545/438206 = 0.57175164 * 4 = 2.287 Vex
Sur: 250545/511070 = 0.490236171 * 8 = 3.922 Vex
Ber: 250545/766606 = 0.3268236877 * 16 = 5.229 Vex
Jah: 250545/894203 = 0.2801880557 * 32 = 8.966 Vex
Cham: 250545/1341305 = 0.1867919675 * 64 = 11.955 Vex
Adding the above together, we get the equivalent of 33.931 Vex. 14985 runs at about 45 seconds apiece would mean 1 Vex every 14985 * (45/60) / 33.931 = 331 minutes, or 5 hours and 31 minutes.
[highlight]p3:[/highlight]
In 182215 / 16.72 = 10898 runs, you will have found 1 Vex. In that time, you will also have found the following numbers of the higher runes:
Ohm: 182215/212463 = 0.85763168 * 2 = 1.715 Vex
Lo: 182215/318695 = 0.57175356 * 4 = 2.287 Vex
etc, the ratios are practically the same, so the end result is also the same, 33.931 Vex.
10898 runs at about 50 seconds apiece would mean 1 Vex every 10898 * (50/60) / 33.931 = 268 minutes, or 4 hours and 28 minutes.
In 250545 / 16.72 = 14985 runs, you will have found 1 Vex. In that time, you will also have found the following numbers of the higher runes:
Ohm: 250545/292137 = 0.85762844 * 2 = 1.715 Vex
Lo: 250545/438206 = 0.57175164 * 4 = 2.287 Vex
Sur: 250545/511070 = 0.490236171 * 8 = 3.922 Vex
Ber: 250545/766606 = 0.3268236877 * 16 = 5.229 Vex
Jah: 250545/894203 = 0.2801880557 * 32 = 8.966 Vex
Cham: 250545/1341305 = 0.1867919675 * 64 = 11.955 Vex
Adding the above together, we get the equivalent of 33.931 Vex. 14985 runs at about 45 seconds apiece would mean 1 Vex every 14985 * (45/60) / 33.931 = 331 minutes, or 5 hours and 31 minutes.
[highlight]p3:[/highlight]
In 182215 / 16.72 = 10898 runs, you will have found 1 Vex. In that time, you will also have found the following numbers of the higher runes:
Ohm: 182215/212463 = 0.85763168 * 2 = 1.715 Vex
Lo: 182215/318695 = 0.57175356 * 4 = 2.287 Vex
etc, the ratios are practically the same, so the end result is also the same, 33.931 Vex.
10898 runs at about 50 seconds apiece would mean 1 Vex every 10898 * (50/60) / 33.931 = 268 minutes, or 4 hours and 28 minutes.
Summary of spoiler:
[highlight]p1:[/highlight] 1 Vex every 5 hours and 31 minutes.
[highlight]p3:[/highlight] 1 Vex every 4 hours and 28 minutes.
[highlight]LK p3:[/highlight] 1 Vex every 3 hours and 9 minutes.
([highlight]1.07 LoD HF Rushing:[/highlight] 1 Vex every 2 hours and 34 minutes)
I figure a rush takes 65 minutes, collecting the Hell forges takes 30, so 95 minutes total. Average number of cubable (Pul+) runes per rush amounts to 1.23295 Gul, which means 1 Vex takes 2 / 1.23295 = 1.622 rushes, or 95 * 1.622 = 154 minutes = 2 hours 34 minutes
You can of course complicate it further if you like. For instance, one could certainly argue that Cham shouldn't be considered twice as "valuable" as Jah, as the rune economy tends to stop at Jah, it being the most useful rune for runewords and everything. I think this is in-depth enough as it is though
Some more semi-useless numbers:
I haven't included any p7 calculations here, as a goldbarb isn't equipped to handle that player setting. As a curiosity, it could be worth nothing that you'd have to do 9808 p7 runs to get that same 33.931 Vex. For p7 to be as effective as p3, then, the p7 run time would have to be 55.6 seconds. For p7 to "beat" LK p3 runs, the p7 run time would have to be 39.2 seconds. For p3 runs to "beat" LK p3 runs, the run time would have to be 35.3 seconds.
[highlight]Summary Section[/highlight]
[highlight]Q:[/highlight] Jesus christ dude, is this thread a joke? In English please!
[highlight]A:[/highlight] Well, the gist of it is Hell Travincal is a pretty nice place to hunt for high runes. It's unlikely to beat out LK or HF rushing in terms of runes / hour in any sort of reasonable scenario, but it's not that far behind, and in Hell Travincal you can collect lots and lots of gold, or reasonable amounts of sets, uniques, charms, gems and jewels, depending on what your goals are. You might want to view the quite decent possibility of high runes as a bonus perk for running Travincal, much like you might want to consider high runes a bonus of running LK.
[highlight]Q:[/highlight] What's with all the numbers? Do you not realize how luck based LK running is, you can't calculate it exactly like this!
[highlight]A:[/highlight] I do realize the variance of both LK running and Travincal running is very very high indeed as far as finding high runes goes. However, the expected value of these practices can be very accurately calculated, as long as your assumptions (such as average run time) are accurate. The numbers in this thread are just averages and/or approximations, nothing more. In no way am I claiming to predict exactly how long it will take to find a Jah rune from the High Council, I'm just calculating how long it will take on average.
Hope this was interesting to some of you, feel free to ask or comment or anything. Thanks for reading!
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