Consumables: Difference between revisions

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{{NeedsContent|Opossum/Blender change makes things less complicated, but also requires this page to be adjusted. The booze example should be changed.  The broken rounding has been fixed, the remainder gets divided by 2.  Examples should be updated.}}
{{rewrite|Examples need to be updated, since milk/ode now happen after fork/mug.}}{{NeedsSpading|When are [[The Tunger™]], [[Gar-ish]], [[Pizza Lover]], [[Saucemaven]], [[black label]], [[fudge spork]] and [[Refined Palate]] factored in? }}
==Overview==
{| class="infobox"
Consumables in KoL are computed very strangely.
| __TOC__
 
|}
Each consumable has a minadv, and a maxadv. These two values are internal to the database. The player never sees these.
[[Consumables]] in KoL are computed thusly:
*minadv is <i>always</i> an integer.
*maxadv does not necessarily have to be.


Each consumable has a range that gets computed from minadv and maxadv (quite possibly a chopped range). The minimum of this range is always an integer. The maximum doesn't have to be. When a food or drink is consumed, the following happens:
Each consumable has a minadv, and a maxadv. These two values are internal to the database. The player never sees these.  Both minadv and maxadv are integers.
#The game chooses a value between the minimum and (the integer part of) the maximum in a uniformly random fashion.
#One half of the decimal part of the maximum is used as a probability of adding another adventure.  (E.g. for a food with a maximum of 28.3, there is a 15% chance (0.3 / 2) of an extra adventure.)
#[[Munchies pill]]s are computed after a value is chosen, but before Milk is computed.
#[[Milk of magnesium]] and [[The Ode to Booze]] are calculated next.
#[[Salty Mouth]] gets added on next, for applicable drinks.
#[[Frosty's frosty mug]] and [[Ol' Scratch's salad fork]] are computed after that.
#Finally, the [[Tuxedo shirt]] gets added on after everything else, for applicable drinks.


A [[Consumables/Food|table of foods]] with various modifiers active.<br>
When a food or drink is consumed, the following happens:
A [[Consumables/Booze|table of boozes]] with various modifiers active.
#The game chooses a value between minadv and  maxadv in a uniformly random fashion.
<br>__TOC__
#{{plural|munchies pill}} bonus adventures are computed and added.
#[[Ol' Scratch's salad fork]] and [[Frosty's frosty mug]] bonus adventures are computed and added.
#[[milk of magnesium]] and [[The Ode to Booze]] bonus adventures are added.
#[[tuxedo shirt]] gets added on for applicable drinks.
#[[Salty Mouth]] gets added on, for applicable drinks.
#[[Opossum]] and [[Blender]] bonus adventures are added, if applicable.


==[[Size and Quality]]==
==[[Size and Quality]]==
Line 37: Line 33:
* B = m + floor((M-m-6)/2)
* B = m + floor((M-m-6)/2)
:T - B = M - floor((M - m - 6)/2) - m - floor((M - m - 6)/2)
:T - B = M - floor((M - m - 6)/2) - m - floor((M - m - 6)/2)
:= M - m - floor(M) + m + 6
:= M - m - 2*floor((M - m) / 2) + 6
:= [M - floor(M)] + 6
::Notice that if (M - m) is even, then it is exactly 6, and if (M - m) is odd, then it is exactly 7.
:= 6 + (0 or 1)
:= 6 + (0 or 1)


Line 48: Line 44:


==Other Consumables==
==Other Consumables==
There are also many consumables which do not follow the S/Q pattern. Supernova Champagne is an example. Its range is hardcoded 7-11.0. While that would fit with S=3, Q=5, it does not fit. These types of consumables are assumed to have their minadv and maxadv hardcoded.
There are also many consumables which do not follow the S/Q pattern. Supernova Champagne is an example. Its range is hardcoded 7-11. While that would fit with S=3, Q=5, it does not fit, due to how Blender used to work (unverifiable in-game now). These types of consumables are assumed to have their minadv and maxadv hardcoded.  Every consumable added to the game since NS13 is believed to be hardcoded.


==Examples of Size and Quality==
==Examples of Size and Quality==
===A Booze example===
===A Booze example===
Size and Quality values are added together for craftable things. Basic booze has S=3 and Q=1, basic fruits have S=1 and Q=1, and cocktail garnishes have Q=3. Therefore, [[Advanced Cocktailcrafting|Advanced Cocktails]] are S=4 and Q=5. Their minadv is 4, and their maxadv is 20. They get chopped by floor(20-4-4)/2 = 6 from both sides, producing the range 10-14.0. So the minimum is 10, and the maximum is 14.0. With no modifiers, this means that all 5 observable values are equally likely to show up, and there will never be an adventure added.
Size and Quality values are added together for craftable things. Basic booze has S=3 and Q=1, basic fruits have S=1 and Q=1, and cocktail garnishes have Q=3. Therefore, [[Advanced Cocktailcrafting|Advanced Cocktails]] are S=4 and Q=5. Their minadv is 4, and their maxadv is 20. They get chopped by floor(20-4-4)/2 = 6 from both sides, producing the range 10-14. So the minimum observable value without modifiers is 10, and the maximum is 14.


===A Food example===
===A Food example===
[[Hi mein]]s are S=5 and Q=8.9. Their minadv is 5, and their maxadv is 44.5, they get chopped by floor(44.5-5-6)/2 = 16 from both sides, producing the range 21-28.5. So the minimum is 21, and the maximum is 28.5. With no modifiers, this means that the 8 observable values (21-28) are equally likely to show up. However, there is also a 0.25 probability (25% chance) that an additional adventure will get added on. So 21 will show up 3/32 of the time, 29 will appear 1/32 of the time, and 22-28 will each appear 1/8 of the time.
[[Hi mein]]s are S=5 and Q=8.9. Their minadv is 5, and their maxadv is 44, they get chopped by floor(44-5-6)/2 = 16 from both sides, producing the range 21-28. So the minimum is 21, and the maximum is 28.
 
==Stated Consumable Quality==
Consumables give a rough indication of how good they are in their item description.  The stated quality is based solely on average  adventures per size.  This table shows the breakpoints.
<center>
{| style="text-align: center" cellspacing=0 cellpadding=5 border="1px"
|-
! Quality || Adv/Size
|-
| <span style="color: blueviolet;">'''EPIC'''</span> || 5.01+
|-
| <span style="color: blue;">'''awesome'''</span> || 3.01-5.00
|-
| <span style="color: green;">'''good'''</span> || 2.01-3.00
|-
| '''decent''' || 1.01-2.00
|-
| <span style="color: #999999;">'''crappy'''</span> || 0-1.00
|}
</center>


==Modifiers==
==Modifiers==
[[Munchies pill]]s add adventures to Food in a tiered fashion. If the actual amount that the consumable would give you is in the following ranges, then that's how much Munchies pills will add.
[[Munchies pill]]s add adventures to Food in a tiered fashion. If the actual amount of adventures that the consumable would give you is in the following ranges, then Munchies pills will add a specific amount.
*1-3 adventures, +3
<center>
*4-6 adventures, +2
{| style="text-align: center" cellspacing=0 cellpadding=5 border="1px"
*7+ adventures, +1
! Raw Food <br/>Adventures !! Bonus Munchies<br/>Adventures
 
|-
Then [[Milk of magnesium]] and [[The Ode to Booze|Ode to Booze]] are added on. Similar to Munchies Pills, Milk and Ode add adventures in tiers. If the actual amount that the consumable would give you is in the following ranges, then that's how much Milk or Ode will add.
| 1-3 || +3
*1-4 adventures, +1
|-
*5-7 adventures, +2
| 4-6 || +2
*8-10 adventures, +3
|-
*11+ adventures, +4
| 7+ || +1
|}
</center>


A consequence of this is that for a food like [[boring spaghetti]], which has a range of 4-11, applying Milk of magnesium (with no other modifiers) can give it:
As an example: A boring spaghetti giving you 4 adventures would gain +2 adventures from a munchies pill, and a boring spaghetti giving you 10 adventures would give you +1 from a munchies pill.  Alternatively, if you got 9 adventures from a boring spaghetti eaten with only a munchies pill, you would know that the base roll must have been 8 adventures.
*+1 (if a 4 is rolled)
*+2 (if 5-7 are rolled)
*+3 (if 8-10 are rolled)
*+4 (if an 11 is rolled)


After that, for applicable beers, [[Salty Mouth]] gives a 4-6 adventure boost uniform-randomly.
Then [[Milk of magnesium]] and [[The Ode to Booze|Ode to Booze]] are added on.  These will add as many adventures as the size of the consumable.  For example, a [[boring spaghetti]] will get +3 adventures from Milk, and a [[corpsedriver]] will get +6 adventures from Ode.


[[Frosty's frosty mug]] increases adventures gained from booze by 30%, rounded down. If the booze is a beer, however, adventures are increased by 50%, also rounded down.
[[Frosty's frosty mug]] increases adventures gained from booze by 30%, rounded down. If the booze is a beer, however, adventures are increased by 50%, also rounded down.


[[Ol' Scratch's salad fork]] increases adventures gained from food by 30%, rounded up. If the food is a salad, however, adventures are increased by 50%, also rounded up.
[[Ol' Scratch's salad fork]] increases adventures gained from food by 30%, rounded up. If the food is a salad, however, adventures are increased by 50%, also rounded up.
After that, for applicable beers, [[Salty Mouth]] gives a 4-6 adventure boost uniform-randomly.


Finally, for applicable boozes, the [[Tuxedo shirt]] gives a 1-3 adventure boost uniform-randomly.
Finally, for applicable boozes, the [[Tuxedo shirt]] gives a 1-3 adventure boost uniform-randomly.
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It may be easier to follow along with this example by looking at the table below, since sometimes it is not readily clear why the math works out the way it does.
It may be easier to follow along with this example by looking at the table below, since sometimes it is not readily clear why the math works out the way it does.


Superhuman Cocktails are minadv 4, with maxadv 28. This means the chop is floor(28-4-4)/2 = 10. This means that the base range is 14-18.0. The average of this range is 16.0.
Superhuman Cocktails are minadv 4, with maxadv 28. This means the chop is floor(28-4-4)/2 = 10. This means that the base range is 14-18. The average of this range is 16.0.


Applying Ode to this increases all values of this chopped range by 4, since they're all above 11 (the threshold above which Ode always adds 4 adventures). This makes the range 18-22.0. The average of this range is 20.0.
Applying Ode to this increases all values of this chopped range by 4, which makes the range 18-22. The average of this range is 20.0.


Finally, drinking with Frosty's Mug increases all values of the range by 30%, but they are floored. This can be seen in the table below. Frosty's Mug acts after everything else, so 18-22 are chosen to be modified.
Finally, drinking with Frosty's Mug increases all values of the range by 30%, but they are floored. This can be seen in the table below. Frosty's Mug acts after everything else, so 18-22 are chosen to be modified.


The average must be calculated by finding the weighted average of each possible value that's produced from the range. The minimum of the range occurs with probability (1/num_values)*(1-chance of adding an adventure), where the chance of adding an adventure is the decimal portion of the max, in this case it is 0.0, since the max is 22.0. The maximum of the range occurs with probability (1/num_values)*(chance of adding an adventure). All other values in the range occur with probability 1/num_values.
The average must be calculated by finding the weighted average of each possible value that's produced from the range.  
*floor(18 * 1.3) = 23, occurs with probability (1/num_values)*(1-chance of adding an adventure) = 20% chance
*floor(18 * 1.3) = 23, occurs with a 20% chance
*floor(19 * 1.3) = 24, occurs with probability (1/num_values) = 20% chance
*floor(19 * 1.3) = 24, occurs with a 20% chance
*floor(20 * 1.3) = 26, occurs with probability (1/num_values) = 20% chance
*floor(20 * 1.3) = 26, occurs with a 20% chance
*floor(21 * 1.3) = 27, occurs with probability (1/num_values) = 20% chance
*floor(21 * 1.3) = 27, occurs with a 20% chance
*floor(22 * 1.3) = 28, occurs with probability (1/num_values)*(chance of adding an adventure) = 20% chance
*floor(22 * 1.3) = 28, occurs with a 20% chance


The weighted average is the sum of each possible value multiplied by its probability of occurring. In this case, the range is 23-38, and the average is 25.6.
The weighted average is the sum of each possible value multiplied by its probability of occurring. In this case, the range is 23-38, and the average is 25.6.  Frosty's mug affects the drink's observable values in a predictable way, and that's why there are jumps in the observable values between 24 and 26.
 
It should be noted that if the chance of adding an extra adventure is zero, then all values will occur with probability 1/num_values, where num_values = the number of observable values.  If chance of adding an extra adventure is not zero, then num_values is equal to the number of observable values minus one, because the highest value is a special case of getting added when the game chooses the amount of adventures you get from the consumable.
 
For SHCs with no modifiers (14-18.0), this produces a value for num_values of 5; and for the above example from 24-31, this also produces a num_values of 5, since there are six possible values, but the highest value is a special case of being seen only after the game chooses the maximum value and adds one. Frosty's mug affects the drink's observable values in a predictable way, and that's why there are jumps in the observable values between 24 and 26.


{| style="text-align: center" cellspacing=0 cellpadding=5 border="1px"
{| style="text-align: center" cellspacing=0 cellpadding=5 border="1px"
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|+ [[hi mein|Hi Meins]]
|+ [[hi mein|Hi Meins]]
|-
|-
! Modifiers || colspan=9 | Possible Values || Average
! Modifiers || colspan=8 | Possible Values || Average
|-
|-
! <font color="blue">Chance</font> || <font color="blue">6.25%</font>|| <font color="blue">12.5%</font>|| <font color="blue">12.5%</font>|| <font color="blue">12.5%</font>|| <font color="blue">12.5%</font> || <font color="blue">12.5%</font>|| <font color="blue">12.5%</font>|| <font color="blue">12.5%</font>|| <font color="blue">6.25%</font> ||  
! <font color="blue">Chance</font> || <font color="blue">12.5%</font>|| <font color="blue">12.5%</font>|| <font color="blue">12.5%</font>|| <font color="blue">12.5%</font>|| <font color="blue">12.5%</font> || <font color="blue">12.5%</font>|| <font color="blue">12.5%</font>|| <font color="blue">12.5%</font> ||  
|-
|-
! Base
! Base
| 21 || 22 || 23 || 24 || 25 || 26 || 27 || 28 || 29 || 25.00
| 21 || 22 || 23 || 24 || 25 || 26 || 27 || 28 || 24.50
|-
|-
! +Munchies
! +Munchies
| 22 || 23 || 24 || 25 || 26 || 27 || 28 || 29 || 30 || 26.00
| 22 || 23 || 24 || 25 || 26 || 27 || 28 || 29 || 25.50
|-
|-
! +Milk
! +Milk
| 25 || 26 || 27 || 28 || 29 || 30 || 31 || 32 || 33 || 29.00
| 26 || 27 || 28 || 29 || 30 || 31 || 32 || 33 || 29.50
|-
|-
! +Fork
! +Fork
| 28 || 29 || 30 || 32 || 33 || 34 || 36 || 37 || 38 || 33.00
| 28 || 29 || 30 || 32 || 33 || 34 || 36 || 37 || 32.80
|-
|-
! +Munchies and Milk
! +Munchies and Milk
| 26 || 27 || 28 || 29 || 30 || 31 || 32 || 33 || 34 || 30.00
| 27 || 28 || 29 || 30 || 31 || 32 || 33 || 34 || 30.50
|-
|-
! +Milk and Fork
! +Milk and Fork
| 33 || 34 || 36 || 37 || 38 || 39 || 41 || 42 || 43 || 38.12
| 34 || 36 || 37 || 38 || 39 || 41 || 42 || 43 || 38.75
|-
|-
! +Munchies, Milk, Fork
! +Munchies, Milk, Fork
| 34 || 36 || 37 || 38 || 39 || 41 || 42 || 43 || 45 || 39.44
| 36 || 37 || 38 || 39 || 41 || 42 || 43 || 45 || 40.12
|}
|}
==How to Spade==
Many players will only try to find the observed range of a consumable with no modifiers.  While this gives a good approximation of what the consumable will do, it does not tell the whole story, due to many consumables not having an integer maxadv value.
In order to properly spade a consumable, all observed values must be recorded, and the frequency of those values must be calculated.
At that point, the middle values of the range will all occur at the same rate, and the bottom and top of the range will occur at rate*(1-chance_of_extra) and rate*(chance_of_extra), respectively.  Where chance_of_extra is the decimal portion of maxadv.
[[spooky mushroom|Spooky mushrooms]] are a nice example of this, their observed range is 2-3, however, 3 will be observed 80% of the time, due to the maxadv actually being 2.8, so the range is really 2-2.8.
There are some consumables for which the maxadv cannot be ascertained without using modifiers. [[Imp Ale]] is an example of this, the observed range is 1-2, and with no modifiers, a player will see each at 50% likelihood. However, Imp Ale is actually 1-1.5.


[[Category:Game Mechanics]]
[[Category:Game Mechanics]]

Latest revision as of 22:09, 10 October 2022

The Hermit humbly requests that this page be rewritten or expanded.

Examples need to be updated, since milk/ode now happen after fork/mug.
There are some vague or non-exact figures and information on this page. Some spading is required.

When are The Tunger™, Gar-ish, Pizza Lover, Saucemaven, black label, fudge spork and Refined Palate factored in?

Consumables in KoL are computed thusly:

Each consumable has a minadv, and a maxadv. These two values are internal to the database. The player never sees these. Both minadv and maxadv are integers.

When a food or drink is consumed, the following happens:

  1. The game chooses a value between minadv and maxadv in a uniformly random fashion.
  2. munchies pills bonus adventures are computed and added.
  3. Ol' Scratch's salad fork and Frosty's frosty mug bonus adventures are computed and added.
  4. milk of magnesium and The Ode to Booze bonus adventures are added.
  5. tuxedo shirt gets added on for applicable drinks.
  6. Salty Mouth gets added on, for applicable drinks.
  7. Opossum and Blender bonus adventures are added, if applicable.

Size and Quality

Many consumables also have a Size (equal to the fullness/drunkenness of that item) and a Quality (value chosen to make adventure gains better). The S/Q paradigm denotes that a food uses Size and Quality to determine its minadv and maxadv. Most older (NS11) consumables follow S/Q. Size and Quality are very important for crafted consumables, when two craftable things are put together, the Size and Quality values of the two get added together.

For any consumables following S/Q:

  • minadv=Size
  • maxadv=Size*Quality

Range Chopping

For a Food, if the difference between minadv and maxadv is greater than 7, then a chop is performed from either end of the range. For a Booze, if the difference between minadv and maxadv is greater than 5, a chop is performed. This chop is equal to:

  • Food: floor((maxadv-minadv-6)/2) from both sides.
  • Booze: floor((maxadv-minadv-4)/2) from both sides.

Consequences

Because of this, a food that has been chopped will always have its unmodified observed range be 6 or 7, due to the following:

  • T = top of range, B = bottom of range, M=max, m=min.
  • T = M - floor((M-m-6)/2)
  • B = m + floor((M-m-6)/2)
T - B = M - floor((M - m - 6)/2) - m - floor((M - m - 6)/2)
= M - m - 2*floor((M - m) / 2) + 6
Notice that if (M - m) is even, then it is exactly 6, and if (M - m) is odd, then it is exactly 7.
= 6 + (0 or 1)

Similarly, a booze that has been chopped will always have its unmodified observed range be 4 or 5.

What to take away from this: If a food's unmodified observed range is not 6 or 7, then either it has not been chopped, or the food has been messed with in some way by the game designers. Similar logic can be applied for a booze which has a range that is not 4 or 5.

Furthermore, if a food's unmodified observed range is less than 6, and the minimum of the range is not equal to the Size, then the food is messed with. Similarly for a booze's unmodified observed range being less than 4.

Other Consumables

There are also many consumables which do not follow the S/Q pattern. Supernova Champagne is an example. Its range is hardcoded 7-11. While that would fit with S=3, Q=5, it does not fit, due to how Blender used to work (unverifiable in-game now). These types of consumables are assumed to have their minadv and maxadv hardcoded. Every consumable added to the game since NS13 is believed to be hardcoded.

Examples of Size and Quality

A Booze example

Size and Quality values are added together for craftable things. Basic booze has S=3 and Q=1, basic fruits have S=1 and Q=1, and cocktail garnishes have Q=3. Therefore, Advanced Cocktails are S=4 and Q=5. Their minadv is 4, and their maxadv is 20. They get chopped by floor(20-4-4)/2 = 6 from both sides, producing the range 10-14. So the minimum observable value without modifiers is 10, and the maximum is 14.

A Food example

Hi meins are S=5 and Q=8.9. Their minadv is 5, and their maxadv is 44, they get chopped by floor(44-5-6)/2 = 16 from both sides, producing the range 21-28. So the minimum is 21, and the maximum is 28.

Stated Consumable Quality

Consumables give a rough indication of how good they are in their item description. The stated quality is based solely on average adventures per size. This table shows the breakpoints.

Quality Adv/Size
EPIC 5.01+
awesome 3.01-5.00
good 2.01-3.00
decent 1.01-2.00
crappy 0-1.00

Modifiers

Munchies pills add adventures to Food in a tiered fashion. If the actual amount of adventures that the consumable would give you is in the following ranges, then Munchies pills will add a specific amount.

Raw Food
Adventures		 Bonus Munchies
Adventures
1-3 +3
4-6 +2
7+ +1

As an example: A boring spaghetti giving you 4 adventures would gain +2 adventures from a munchies pill, and a boring spaghetti giving you 10 adventures would give you +1 from a munchies pill. Alternatively, if you got 9 adventures from a boring spaghetti eaten with only a munchies pill, you would know that the base roll must have been 8 adventures.

Then Milk of magnesium and Ode to Booze are added on. These will add as many adventures as the size of the consumable. For example, a boring spaghetti will get +3 adventures from Milk, and a corpsedriver will get +6 adventures from Ode.

Frosty's frosty mug increases adventures gained from booze by 30%, rounded down. If the booze is a beer, however, adventures are increased by 50%, also rounded down.

Ol' Scratch's salad fork increases adventures gained from food by 30%, rounded up. If the food is a salad, however, adventures are increased by 50%, also rounded up.

After that, for applicable beers, Salty Mouth gives a 4-6 adventure boost uniform-randomly.

Finally, for applicable boozes, the Tuxedo shirt gives a 1-3 adventure boost uniform-randomly.

Example with Modifiers

This example will show how Superhuman Cocktails behave when modified by Ode and Frosty's Mug.

It may be easier to follow along with this example by looking at the table below, since sometimes it is not readily clear why the math works out the way it does.

Superhuman Cocktails are minadv 4, with maxadv 28. This means the chop is floor(28-4-4)/2 = 10. This means that the base range is 14-18. The average of this range is 16.0.

Applying Ode to this increases all values of this chopped range by 4, which makes the range 18-22. The average of this range is 20.0.

Finally, drinking with Frosty's Mug increases all values of the range by 30%, but they are floored. This can be seen in the table below. Frosty's Mug acts after everything else, so 18-22 are chosen to be modified.

The average must be calculated by finding the weighted average of each possible value that's produced from the range.

  • floor(18 * 1.3) = 23, occurs with a 20% chance
  • floor(19 * 1.3) = 24, occurs with a 20% chance
  • floor(20 * 1.3) = 26, occurs with a 20% chance
  • floor(21 * 1.3) = 27, occurs with a 20% chance
  • floor(22 * 1.3) = 28, occurs with a 20% chance

The weighted average is the sum of each possible value multiplied by its probability of occurring. In this case, the range is 23-38, and the average is 25.6. Frosty's mug affects the drink's observable values in a predictable way, and that's why there are jumps in the observable values between 24 and 26.

Superhuman Cocktails
Modifiers Possible Values Average
Chance 20% 20% 20% 20% 20%
Base 14 15 16 17 18 16.00
+Ode 18 19 20 21 22 20.00
+Frosty 18 19 20 22 23 20.40
+Ode and Frosty 23 24 26 27 28 25.60


A Food Example

The math is the same idea for Food and Booze alike, here is an example of hi meins. Notice that, like with the Booze example above, there are jumps in the amount of adventures that are observable. So with a Fork, a player will never see an adventure gain of 31 or 35 for a hi mein.

Hi Meins
Modifiers Possible Values Average
Chance 12.5% 12.5% 12.5% 12.5% 12.5% 12.5% 12.5% 12.5%
Base 21 22 23 24 25 26 27 28 24.50
+Munchies 22 23 24 25 26 27 28 29 25.50
+Milk 26 27 28 29 30 31 32 33 29.50
+Fork 28 29 30 32 33 34 36 37 32.80
+Munchies and Milk 27 28 29 30 31 32 33 34 30.50
+Milk and Fork 34 36 37 38 39 41 42 43 38.75
+Munchies, Milk, Fork 36 37 38 39 41 42 43 45 40.12
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