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 Ana's Guide to Urn Management

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PostSubject: Ana's Guide to Urn Management   Wed Jul 13, 2016 7:52 am

Introduction

I've noticed that a lot of people take two urns with them when fishing/mining/cooking whether they'll finish off the first urn or not. However, this isn't quite ideal, since you could have cooked an extra fish, mined an extra ore and fished an extra fish. I'd like to supply some details as to when to take one (partially full) urn rather than two.

The model to keep in mind is this table:

Take one urnTake two urns
Fill no urnsGood!Bad!
Fill one urnBad(ish)!Good!
For the sake of concreteness, let's consider Mining and banking iron ore (say at Rimmington mine, so that you actually go to a bank every trip). Lets count how many ores we mine in each situation.

Take no urnsTake one urnTake two urns
Fill no urns28 ores, xp wasted27 ores26 ores
Fill one urnImpossible28 ores, xp wasted27 ores
Since a round trip (from the mine to the bank and back to the mine) at Rimmington Mine takes about 27 seconds (using the Clan Vexillium), only getting 26 ores in a trip wastes some time relative to getting 27 ores: roughly a second.

Conversely, getting 28 ores gives you a second, but wastes potential experience from the urns.

In order to decide when to take one urn or two urns (or no urns at all!), we have to do some analysis.

Mining

We'll start with Mining. As noted above, our outcome table is

                Take no urnsTake one urnTake two urns
Fill no urns28 ores, xp wasted27 ores26 ores
Fill one urnImpossible28 ores, xp wasted27 ores
The only randomness in mining comes from the possibility of getting gems. Assuming you want to keep these gems the gem takes up an inventory space and hence affects the probability of filling an urn.

In my quest for 99 Mining, I mined (about) 299325 iron ores and got 536 gems (not counting those obtained by mining clay). This gives a probability of about 0.001791 (~1/558) for getting a gem for a given iron rock. Thus the probability of getting a gem in 26 iron rocks is about 0.04553 (~1/22)

The other numbers we need are simple. It takes 1625 experience to fill a Mining urn, or 46.43 iron mined, since iron gives 25 experience. Thus, 27 iron fills 945/1625 or 58.15% of the urn.

We can summarize this like so: if you get your partially full urn before the trip and the urn is

40% or less fullthe urn will not be filled
41% full11/13 of the time this means the urn will not be filled (because of rounding). The other 2/13 of the time the urn will be filled after 27 iron are mined
42-43% fullThe urn will be filled after 27 iron are mined
44% or more fullThe urn will be filled after 26 iron are mined
We can use this to fill in the probabilities for the above outcomes. Note that this includes the possibility of getting a gem.

Given the choice of number of urns taken, either no urn or one urn will be filled. Thus each column should add to 1.

40% or less full:

Take no urnsTake one urnTake two urns
Fill no urns111
Fill one urn000
41% full:

Take no urnsTake one urnTake two urns
Fill no urns10.68241
Fill one urn00.31760
42-43% full:

Take no urnsTake one urnTake two urns
Fill no urns10.047241
Fill one urn00.95280
44-45% full:

Take no urnsTake one urnTake two urns
Fill no urns10.0010920.04553
Fill one urn00.99900.9545
46-47% full:

Take no urnsTake one urnTake two urns
Fill no urns11.626E-50.001013
Fill one urn01.0000.9990
48%:

Take no urnsTake one urnTake two urns
Fill no urns14.197E-62.640E-4
Fill one urn01.0000.9997
>48%:

Take no urnsTake one urnTake two urns
Fill no urns11.746E-71.448E-5
Fill one urn01.0001.000
There's always the possibility that you get a ton of gems and fill no urns, but this is incredibly unlikely.

We can now fill in the expected gain or loss from each choice. Recall that we're treating 28 ores/inv as 1 second gain and 26 ore/s inv as one second loss. Additionally, I'll treat not filling up an urn as a loss of 1 second per 14.7 experience wasted. (This assumes a rate of 53k xp/hour. Higher rates are possible with tick manipulation and mining at the wilderness location, but it doesn't really matter too much here.)

40% or less full:

Take no urnsTake one urnTake two urns
Expected time wasted12.301
41% full:

Take no urnsTake one urnTake two urns
Expected time wasted12.3-0.16661
(It's a negative expected value since you have a good chance of getting 28 ores, but you fill the urn at the last moment, so not much xp is wasted)

42% full:

Take no urnsTake one urnTake two urns
Expected time wasted12.3-0.37031
43% full:

Take no urnsTake one urnTake two urns
Expected time wasted12.3-0.17621
44% full:

Take no urnsTake one urnTake two urns
Expected time wasted12.30.030060.04553
45% full:

Take no urnsTake one urnTake two urns
Expected time wasted12.30.26750.04553
46% full:

Take no urnsTake one urnTake two urns
Expected time wasted12.30.47050.001013
47% full:

Take no urnsTake one urnTake two urns
Expected time wasted12.30.67430.001013
48% full:

Take no urnsTake one urnTake two urns
Expected time wasted12.30.91202.640E-4
TL;DR: Check how full your urn is before banking. If it's 44% full or less, just take the partially filled urn. If it's 45% full or more, take the partially full urn and a new urn. This can be accomplished by having a preset for each.

Cooking

Here our outcome table is

Take one urnTake two urns
Fill no urns27 food cooked26 food cooked, space wasted
Fill no urns27 food cooked, xp wasted26 food cooked
With cooking, urn management doesn't have as much effect since banking is so fast. In typical cases, banking takes 2 ticks (1.2 seconds) with presets. If you're lagging, this'll be longer. It may be shorter in NXT (never tried it). Under this assumption, taking only one urn is rarely advantageous. The loss due to only cooking 26 food is less than a twentieth of a second per inventory.

If you're lighting your own fires, it's much more worth it to have your two presets both with two urns, but one with a log in it as well. Manually taking a log out of the bank wastes much more time no matter how you do it.

1) Deposit the cooked food you have and pull out both the log and raw food.

2) Pull out the preset, then open the bank again and replace a raw food with a log.

3) Have a third preset with the log (costs 533 Runecoins or 3 Bonds) and open the preset menu to pull out the third preset.

All three of these take enough time that the time saved from urn management is not worth it.

If you aren't lighting your own fires (BTW, is it supposed to be possible for IM to cook on other people's fires?) then you can do urn management. I don't suggest this though, since either the fires aren't lit very fast, or there's a crowd around it, which makes cooking difficult.

If you do decide to do urn management, you should know that 26 trout fill up 38.3% of the urn (so you should pull out 2 urns if the urn is 61% full or higher). 26 salmon fill up 49.3% of an urn so you should pull out 2 urns if the urn is 50% full or more.

Urn management was much more useful for the Fourth of July Event, since banking actually took a bit of time and there were no fires to worry about.

TL;DR: don't bother with urn management when cooking. Instead, use one of your two presets to make taking a log out much faster.

Fishing

Assumptions for this section:

1. You're fishing at the Combat Academy (parts of this analysis also apply to the Gunnarsgrunn location during the Fourth of July Event)
2. The ratio of trout to salmon is 3:2 on average.
3. Fishing experience is valued at 60k/hour. This number is lower at lower levels, but it doesn't matter very much for these calculations.
4. Your fishing urns are always filled by multiples of 10 experience.
5. It takes 2 ticks to bank with presets.
6. There are 8 possible locations for the fish to appear. Does anyone know if the fish can appear in the middle square of the north locations? Right now all I've seen are these locations: XXOXX.
7. You always fish from the northernmost location available (obviously you don't want to move if you don't need to; Make your decision when you come back from the bank)
8. Jagex hasn't fixed the bug where you can't fish if you have 1 feather and a full inventory.

Under these assumptions, the average number of ticks to get to the bank is (7*20+6*21+5*22+4*22+3*24+2*25+1*25+0*26)/(7+6+5+4+3+2+1+0) = 21.821 ticks. (Note that under our assumptions, you'll never use the southernmost fishing location, since the other location will be farther north). Hence, a round trip takes on average 2*21.821+2=45.643 ticks=27.386 seconds.

If we take 26 fish as the default, then being able to fish an extra saves you 1/26 of a trip, or 1.053 seconds. Fishing fewer fish than 26 has the opposite effect.

We can also give value to the experience wasted by not using an urn. Fishing is roughly 60k xp/hour, or 16.667 xp/second, so for every 83.333 experience NOT put into an urn, you waste one second worth of fishing training.



Our outcome table is thus

Take no urnsTake one urnTake two urns
Fill no urns+1 fish, -urn xp+0 fish, normal urn xp-1 fish, normal urn xp
Fill one urnCan't happen+1 fish, some wasted xp+0 fish, normal urn xp
In terms of time wasted (or gained),

Take no urnsTake one urnTake two urns
Fill no urns17.30701.053
Fill one urn0Some Amount-1.0530
"Some Amount" depends on how much xp is gained after the urn is teleported.

Given how full the urn is at the start, we can calculate the probability that the urn is filled during that trip.

<27% full:

Take no urnsTake one urnTake two urns
Fill no urns111
Fill one urn000
27% full:

Take no urnsTake one urnTake two urns
Fill no urns11.0001
Fill one urn03.934E-130
28% full:

Take no urnsTake one urnTake two urns
Fill no urns11.0001
Fill one urn01.1913E-100
29% full:

Take no urnsTake one urnTake two urns
Fill no urns11.0001
Fill one urn04.624E-90
30% full:

Take no urnsTake one urnTake two urns
Fill no urns11.0001.000
Fill one urn07.145E-82.085E-11
31% full:

Take no urnsTake one urnTake two urns
Fill no urns11.0001.000
Fill one urn09.309E-77.683E-10
32% full:

Take no urnsTake one urnTake two urns
Fill no urns11.0001.000
Fill one urn01.777E-61.595E-8
33% full:

Take no urnsTake one urnTake two urns
Fill no urns10.99991.000
Fill one urn01.185E-42.621E-7
34% full:

Take no urnsTake one urnTake two urns
Fill no urns10.99941.000
Fill one urn06.168E-46.728E-6
35% full:

Take no urnsTake one urnTake two urns
Fill no urns10.99700.9999
Fill one urn00.0029665.196E-5
36% full:

Take no urnsTake one urnTake two urns
Fill no urns10.98560.9997
Fill one urn00.014383.061E-4
37% full:

Take no urnsTake one urnTake two urns
Fill no urns10.95850.9984
Fill one urn00.041510.001650
38% full:

Take no urnsTake one urnTake two urns
Fill no urns10.90020.9908
Fill one urn00.099770.009191
39% full:

Take no urnsTake one urnTake two urns
Fill no urns10.77990.9711
Fill one urn00.22010.02894
40% full:

Take no urnsTake one urnTake two urns
Fill no urns10.58920.9250
Fill one urn00.41070.07503
41% full:

Take no urnsTake one urnTake two urns
Fill no urns10.40120.8220
Fill one urn00.59880.1780
42% full:

Take no urnsTake one urnTake two urns
Fill no urns10.23020.6429
Fill one urn00.76980.3571
43% full:

Take no urnsTake one urnTake two urns
Fill no urns10.090040.4539
Fill one urn00.91000.5461
44% full:

Take no urnsTake one urnTake two urns
Fill no urns10.027540.2711
Fill one urn00.97250.7289
45% full:

Take no urnsTake one urnTake two urns
Fill no urns10.0068050.1120
Fill one urn00.99320.8880
46% full:

Take no urnsTake one urnTake two urns
Fill no urns10.0010850.03576
Fill one urn00.99890.9642
47% full:

Take no urnsTake one urnTake two urns
Fill no urns12.640E-50.009198
Fill one urn01.0000.9908
48% full:

Take no urnsTake one urnTake two urns
Fill no urns100.001525
Fill one urn010.9985
49% full:

Take no urnsTake one urnTake two urns
Fill no urns103.096E-5
Fill one urn011.000
>49% full:

Take no urnsTake one urnTake two urns
Fill no urns100
Fill one urn011
I'm going to skip showing the expected time wasted for each of these, since that'll take a lot of space. Instead I'll skip right to the TL;DR

TL;DR:Check your urn before banking. If it's 43% full or more, take out 2 urns. Otherwise take out 1 urn. Your preset with 1 urn should have at least 27 feathers because there's a small but significant probability that you'll teleport that urn and be left with 27 spaces (plus feathers). The other preset should have at least 26 feathers.

(btw, sorry for those of you who saw my earlier recommendation. I severely overestimated the cost of teleporting an urn and finishing the inventory with no urn. It turns out that the low probability of this happening combined with the small amount of xp wasted makes it worth it to only take one urn up to much higher percentages.)

Urns and deposit boxes/Stiles

It's generally worth it to take urns with you when banking iron at the Dwarven Mine Resource Dungeon and when fishing on Karamja. However, if you take too many urns, you'll end up making many trips to the deposit box/Stiles with little benefit. However, if you take too few you'll end up having to bank to get more urns more often. I've set up a model for this, and for plausible numbers, it's most beneficial to take 8-12 urns in both situations.

If anyone would be kind enough to provide more precision, I'd be happy to calculate the ideal number of urns for each. Hecate claims that taking 10 urns is the best for Dwarven Mine banking, but I don't know his methods.

Numbers I'd need:
Average number of ores/fish per hour NOT counting banking/noting time. (=Number_per_hour/(1-trip_time*trips_per_hour)
Average time to make a trip to the deposit box/Stiles and back.
Average amount of time it takes to get urns and come back.

Conclusion
I know my methods are fairly crude, but I hope you're convinced that you can save yourself time by paying attention to how full your urns are. Feedback is welcome and suggestions for improving the formatting of the tables is very welcome.


Last edited by Anafunctor on Sat Jul 16, 2016 6:39 pm; edited 6 times in total
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Treemaid
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PostSubject: Re: Ana's Guide to Urn Management   Wed Jul 13, 2016 8:30 am

That's incredibly detailed Ana, very impressive!
Thank you for sharing those tips with us.
My problem is remembering to take any urns at all! lol
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PostSubject: Re: Ana's Guide to Urn Management   Wed Jul 13, 2016 8:49 am

Incredibly useful, thanks Ana Smile
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PostSubject: Re: Ana's Guide to Urn Management   Wed Jul 13, 2016 9:58 pm

I've added the analysis for Fishing. Sorry to those of you who took my earlier uninformed advice.

If anyone wants to see my (TI-89) code for how I calculated probabilities and expected time loss for fishing, you can PM me and I'll gladly send it to you. I'm also hoping to write an equivalent program for mining so I can check my work.

EDIT: I've written the Mining equivalent of the fishing code (it was way easier to convert than I thought it'd be). Upon checking my work, it appears I was valuing the wasted xp from teleporting an urn early 5 times as much as it should have been. As such, it now appears that the 1 second saved from mining 28 ores outweighs the extra experience from having an urn the whole time by quite a bit more than I thought. It now seems that you should only take two urns if the first urn is 47% or more full.

Upcoming Updates: I'd like to go into the concepts behind these computations and replace all the tables with graphs. This should make it easier to understand what's going on.
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