IntroductionI'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 urn | Take two urns |
| Fill no urns | Good! | Bad! |
| Fill one urn | Bad(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 urns | Take one urn | Take two urns |
| Fill no urns | 28 ores, xp wasted | 27 ores | 26 ores |
| Fill one urn | Impossible | 28 ores, xp wasted | 27 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.
MiningWe'll start with Mining. As noted above, our outcome table is
| | Take no urns | Take one urn | Take two urns |
| Fill no urns | 28 ores, xp wasted | 27 ores | 26 ores |
| Fill one urn | Impossible | 28 ores, xp wasted | 27 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 full | the urn will not be filled |
| 41% full | 11/13 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% full | The urn will be filled after 27 iron are mined |
| 44% or more full | The 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 urns | Take one urn | Take two urns |
| Fill no urns | 1 | 1 | 1 |
| Fill one urn | 0 | 0 | 0 |
41% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.6824 | 1 |
| Fill one urn | 0 | 0.3176 | 0 |
42-43% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.04724 | 1 |
| Fill one urn | 0 | 0.9528 | 0 |
44-45% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.001092 | 0.04553 |
| Fill one urn | 0 | 0.9990 | 0.9545 |
46-47% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 1.626E-5 | 0.001013 |
| Fill one urn | 0 | 1.000 | 0.9990 |
48%:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 4.197E-6 | 2.640E-4 |
| Fill one urn | 0 | 1.000 | 0.9997 |
>48%:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 1.746E-7 | 1.448E-5 |
| Fill one urn | 0 | 1.000 | 1.000 |
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 urns | Take one urn | Take two urns |
| Expected time wasted | 12.3 | 0 | 1 |
41% full:
| Take no urns | Take one urn | Take two urns |
| Expected time wasted | 12.3 | -0.1666 | 1 |
(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 urns | Take one urn | Take two urns |
| Expected time wasted | 12.3 | -0.3703 | 1 |
43% full:
| Take no urns | Take one urn | Take two urns |
| Expected time wasted | 12.3 | -0.1762 | 1 |
44% full:
| Take no urns | Take one urn | Take two urns |
| Expected time wasted | 12.3 | 0.03006 | 0.04553 |
45% full:
| Take no urns | Take one urn | Take two urns |
| Expected time wasted | 12.3 | 0.2675 | 0.04553 |
46% full:
| Take no urns | Take one urn | Take two urns |
| Expected time wasted | 12.3 | 0.4705 | 0.001013 |
47% full:
| Take no urns | Take one urn | Take two urns |
| Expected time wasted | 12.3 | 0.6743 | 0.001013 |
48% full:
| Take no urns | Take one urn | Take two urns |
| Expected time wasted | 12.3 | 0.9120 | 2.640E-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.
CookingHere our outcome table is
| Take one urn | Take two urns |
| Fill no urns | 27 food cooked | 26 food cooked, space wasted |
| Fill no urns | 27 food cooked, xp wasted | 26 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.
FishingAssumptions 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 urns | Take one urn | Take two urns |
| Fill no urns | +1 fish, -urn xp | +0 fish, normal urn xp | -1 fish, normal urn xp |
| Fill one urn | Can't happen | +1 fish, some wasted xp | +0 fish, normal urn xp |
In terms of time wasted (or gained),
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 17.307 | 0 | 1.053 |
| Fill one urn | 0 | Some Amount-1.053 | 0 |
"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 urns | Take one urn | Take two urns |
| Fill no urns | 1 | 1 | 1 |
| Fill one urn | 0 | 0 | 0 |
27% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 1.000 | 1 |
| Fill one urn | 0 | 3.934E-13 | 0 |
28% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 1.000 | 1 |
| Fill one urn | 0 | 1.1913E-10 | 0 |
29% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 1.000 | 1 |
| Fill one urn | 0 | 4.624E-9 | 0 |
30% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 1.000 | 1.000 |
| Fill one urn | 0 | 7.145E-8 | 2.085E-11 |
31% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 1.000 | 1.000 |
| Fill one urn | 0 | 9.309E-7 | 7.683E-10 |
32% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 1.000 | 1.000 |
| Fill one urn | 0 | 1.777E-6 | 1.595E-8 |
33% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.9999 | 1.000 |
| Fill one urn | 0 | 1.185E-4 | 2.621E-7 |
34% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.9994 | 1.000 |
| Fill one urn | 0 | 6.168E-4 | 6.728E-6 |
35% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.9970 | 0.9999 |
| Fill one urn | 0 | 0.002966 | 5.196E-5 |
36% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.9856 | 0.9997 |
| Fill one urn | 0 | 0.01438 | 3.061E-4 |
37% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.9585 | 0.9984 |
| Fill one urn | 0 | 0.04151 | 0.001650 |
38% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.9002 | 0.9908 |
| Fill one urn | 0 | 0.09977 | 0.009191 |
39% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.7799 | 0.9711 |
| Fill one urn | 0 | 0.2201 | 0.02894 |
40% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.5892 | 0.9250 |
| Fill one urn | 0 | 0.4107 | 0.07503 |
41% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.4012 | 0.8220 |
| Fill one urn | 0 | 0.5988 | 0.1780 |
42% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.2302 | 0.6429 |
| Fill one urn | 0 | 0.7698 | 0.3571 |
43% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.09004 | 0.4539 |
| Fill one urn | 0 | 0.9100 | 0.5461 |
44% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.02754 | 0.2711 |
| Fill one urn | 0 | 0.9725 | 0.7289 |
45% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.006805 | 0.1120 |
| Fill one urn | 0 | 0.9932 | 0.8880 |
46% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0.001085 | 0.03576 |
| Fill one urn | 0 | 0.9989 | 0.9642 |
47% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 2.640E-5 | 0.009198 |
| Fill one urn | 0 | 1.000 | 0.9908 |
48% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0 | 0.001525 |
| Fill one urn | 0 | 1 | 0.9985 |
49% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0 | 3.096E-5 |
| Fill one urn | 0 | 1 | 1.000 |
>49% full:
| Take no urns | Take one urn | Take two urns |
| Fill no urns | 1 | 0 | 0 |
| Fill one urn | 0 | 1 | 1 |
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/StilesIt'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.
ConclusionI 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.
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