Map Management Resource

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AmanPoE wrote:

Why is 90% without pack size equivalent to 80% with pack size? Even with the worst pack size roll (20%), a 1.8 x 1.12 modifier is still higher than 90%. Am I interpreting the implicit mods incorrectly or are these mods really as valuable as I think?

I'd hazard a guess, that it isn't a case of 'equivalent'.
More a case of, if you don't get the 'good' rolls, the 90% is a guide that would make it probably worth running rather than spending more currency, in certain cases.

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TheAnuhart wrote:

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AmanPoE wrote:

Why is 90% without pack size equivalent to 80% with pack size? Even with the worst pack size roll (20%), a 1.8 x 1.12 modifier is still higher than 90%. Am I interpreting the implicit mods incorrectly or are these mods really as valuable as I think?

I'd hazard a guess, that it isn't a case of 'equivalent'.
More a case of, if you don't get the 'good' rolls, the 90% is a guide that would make it probably worth running rather than spending more currency, in certain cases.

I'd actually agree with Aman here, I think 100% w/o pack size or 70% with is a much more sane rating system. And in cases where Maze doubles size, it comes pretty darn close to "roll until you see it, then run it unless it'll kill you."

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ScrotieMcB wrote:

I'd actually agree with Aman here, I think 100% w/o pack size or 70% with is a much more sane rating system. And in cases where Maze doubles size, it comes pretty darn close to "roll until you see it, then run it unless it'll kill you."

That's why for higher maps, the advice is different. The quoted text is from 72 maps.

At 75, we have this.

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Accept no compromise on your rolls at this point and consider using Divine Orbs and Exalted Orbs in very rare circumstances, preferably when you yield a triple pack improving roll (on the low end) in some form or another.

As always, pace yourself and plan accordingly. At this point, it is better to hold off doing a map than to do a subpar one.

Divining and Exalting 75 maps is economic suicide. Divining a 76 Precinct *may* be worth it if the are size is very small. Divining Crema/Ship/Shrine may be worth it if you improve 2 very low rolls on Magic/Rare. Exalting is never worth it.

Once again: the map guide assumes that you cannot buy new maps, and therefore advises you to use (much) more currency than you would once you consider the alternative of buying a new map.

Then again: 75+ maps seem to be come rare these days, so the guide is becoming more accurate :)

Finally: at this moment there is so much uncertainty in the whole map system that you can only make very very rough calculations:
- I have only a rough idea on how likely you are to roll a Maze (about 1 in 6)
- If you Maze I have only a rough idea on how you benefit
- I have no idea how good more Magic/Rare monsters actually is
- I don't know how likely you are to roll Maze+something nice
- I don't know how Alt-Regalling works in cost/benefit

so only the cases where you make very optimistic/pessimistic assumptions and then can show it will never/always be better/worse than other cases, allow you to say something.

I am waiting for more data to surface (like the aforementioned 1000 maps). I would love it if someone would come up with data on:
- 1000 alt-aug rolls on maps and 1000 chaos rolls.
- how much rare/magic monsters a map normally contains. If there are only 5 rares or so, 25% or more rares is actally pretty shitty.
- how likely it is for a map to drop from a white/magic/rare/boss given that a map drops

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Flapdrol wrote:

Exalting is never worth it.

Your sample case wasn't analyzing the problem properly. I don't know if it invalidates the conclusion, but it does invalidate the method.

The most pro-Exalt case would be something like this:

Rare Shipyard Map
Item Quantity: 85%
Quality: 20%
Area is a Maze
Area has patches of burning ground
20% increased Monster Cast Speed
20% increased Monster Movement Speed
20% increased Monster Attack Speed
25% increased Monster Damage
Players have Elemental Equilibrium

Missing 1 suffix; note that "of Ice" is impossible due to burning ground.

The idea is to combine 3 perfect prefixes while eliminating the weakest suffixes from the Exalt possibilities (this usually is done by having them on the sample map, with the exception of chilled ground); if you disagree with me on the perfect prefixes, substitute those instead.

I don't see it. Could you elaborate, preferably with some guesstimated numbers?

I would assume that the ideal map would have: Maze, Pack Size, +Magic and the two worst remaining *-fixes. As Maze, packsize and +magic are all multipliers, they would multiply any additionally rolled Map Quantity, and this would provide (IMO) the most added quantity.

Why is your map a better case?

And, BTW, I would not Exalt the map above as it is too weak. I would chaos it instead to get Maze and +packsize/+magic/+rare/+2 bosses/100+%. So the map above may not be a valid counter-example.

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Flapdrol wrote:

I would assume that the ideal map would have: Maze, Pack Size, +Magic and the two worst remaining *-fixes. As Maze, packsize and +magic are all multipliers, they would multiply any additionally rolled Map Quantity, and this would provide (IMO) the most added quantity.

Why is your map a better case?

Because "ideal" and "most deserving of an Exalt" are not at all the same thing. A good candidate for an Exalt has the following properties:
1) A keeper. If we didn't care about the afffixes currently on the item, we'd just Chaos it. From a gear perspective this is pretty close to perfectionism, but maps do not have the same luxury.
2) Gains the most benefit from an additional affix, because the weakest possibilities for new affixes have been eliminated.

The intent was that any map with 3 perfect prefixes would be a keeper, and the two weakest suffixes gives the Exalt the maximum chance for improvement while minimizing the chance it would be a dud.

I mean, it's easy to agree with your initial argument if you assume that the map already has great prefixes and pack size; this means Exalt can't get pack size, so that's one huge benefit which it can't provide in that situation. A more fair contest would be to allow the Exalt to grab any of the best suffixes in the game.

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Flapdrol wrote:

And, BTW, I would not Exalt the map above as it is too weak. I would chaos it instead to get Maze and +packsize/+magic/+rare/+2 bosses/100+%. So the map above may not be a valid counter-example.

At this point an Exalt is guaranteed to get 100% or higher; that's on a bad roll. I understand that Chaos reroll on that map would be roughly as good, but the question would be whether Exalting it would be slightly better, or slightly worse.


In order to get some guesstimiated numbers, I would have to figure out what the "equivalent quantity" is for the Champions and Commanders suffixes. They're definitely worth more than 3%. I'd also have to know the approximate probability for the Hordes, Champions, and Commanders prefixes.

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ScrotieMcB wrote:

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Flapdrol wrote:

I would assume that the ideal map would have: Maze, Pack Size, +Magic and the two worst remaining *-fixes. As Maze, packsize and +magic are all multipliers, they would multiply any additionally rolled Map Quantity, and this would provide (IMO) the most added quantity.

Why is your map a better case?

Because "ideal" and "most deserving of an Exalt" are not at all the same thing. A good candidate for an Exalt has the following properties:
1) A keeper. If we didn't care about the afffixes currently on the item, we'd just Chaos it. From a gear perspective this is pretty close to perfectionism, but maps do not have the same luxury.
2) Gains the most benefit from an additional affix, because the weakest possibilities for new affixes have been eliminated.

I see what you mean. If I reformulate the Theorem to:
Flapdrol's 2nd Theorem v2.0 There are no situations where it is better to Exalt a Rare map instead of running it or (repeatedly) Chaos-ing it. <under the assumptions listed earlier>

would you then say it is correct? Or do you think that the map you cite as an example should not be chaosed? (because I would chaos that map without thinking, as an exalt is 32 chaos and that provides about 5 chances on a better Maze, as I seem to roll a Maze every 6 attempts)

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ScrotieMcB wrote:

In order to get some guesstimiated numbers, I would have to figure out what the "equivalent quantity" is for the Champions and Commanders suffixes. They're definitely worth more than 3%. I'd also have to know the approximate probability for the Hordes, Champions, and Commanders prefixes.

These are old (I think before chaining/freezing ground), but approximately right:
https://docs.google.com/spreadsheet/ccc?key=0AlSPenusWDYUdDVyM3dTRVUxUnRYVTlhbV9rYld3Y1E#gid=0

Given that there are about 18 prefixes and suffices, you can make a pretty wild stab at their value, since it has only 1 in 10 of occurring.. Call it 20%?

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Flapdrol wrote:

These are old (I think before chaining/freezing ground), but approximately right:
https://docs.google.com/spreadsheet/ccc?key=0AlSPenusWDYUdDVyM3dTRVUxUnRYVTlhbV9rYld3Y1E#gid=0

That's most of the puzzle right there; combined with the knowledge that 1/12 Chaos rolls have 6 affixes, 4/12 have 5 affixes, and 7/12 have 4 affixes, I could also calculate with accuracy the expected number of Chaos needed to roll a better map. However, in order to complete a thorough computation, I also need "virtual quantity" numbers for the "of Champions" and "of Commanders" affixes. (I already consider Labyrinthine to be a 100% more quantity affix, as you do.)

Let me run this by you: Let's say that, in an average map, we get 15% of our items from whites, 40% of our items from blues, 35% of our items from rares, and 10% of our items from the unique boss. Under those assumptions, an average [35%, (20+50)/2] Champions roll would give (40*.35=) 14% more quantity, in addition to 3% increased quantity. Similarly, a Commanders roll would give (35*.35=) 12.25% more quantity, plus 3% increased quantity.

Those numbers seem about right to you, or do I have a particular monster demographic horribly misrepresented?

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ScrotieMcB wrote:

Let me run this by you: Let's say that, in an average map, we get 15% of our items from whites, 40% of our items from blues, 35% of our items from rares, and 10% of our items from the unique boss. Under those assumptions, an average [35%, (20+50)/2] Champions roll would give (40*.35=) 14% more quantity, in addition to 3% increased quantity. Similarly, a Commanders roll would give (35*.35=) 12.25% more quantity, plus 3% increased quantity.

Those numbers seem about right to you, or do I have a particular monster demographic horribly misrepresented?

These numbers seem right to me:
- 17% for Champions
- 15% for Commanders
From this also follows that:
- 10% for Twinned is a good assumption (since you get 10% of your items from bosses)
- 90% for Maze may be a better estimate (it doubles the map, but not the boss).

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ScrotieMcB wrote:

That's most of the puzzle right there; combined with the knowledge that 1/12 Chaos rolls have 6 affixes, 4/12 have 5 affixes, and 7/12 have 4 affixes, I could also calculate with accuracy the expected number of Chaos needed to roll a better map.

I think that we starting to hit on something much more useful than the case "Is there a pathological case where Exalting a map would be good?": a general model for when to reroll a map.

I propose we conclude the following on this particular issue:
Exalting Guideline for Maps In general, Exalting any map is a bad idea.
Exceptions:
- exalting a Shipyard with a specific combination of mods may be of minor benefit.
- if map prices rise over 3 exalted, there may be more cases.

And that we devote our brainpower to a more general map-rolling model, since we seem to have most of the building blocks:
- we need to add some assumed values for Chaining and Chilled Ground and neatly list our assumptions and values
- we can compute the expected value of an Affix/Suffix
- we can compute the expected value of a reroll (and its standard deviation)
and if a map costs X chaos, you should reroll as long as your current map roll is below the expected value of the highest of X rerolls

Is the above correct (especially the last step)?