Morale and opinions

Morale and opinions

[Lincoln Peters]

I've been studying the documentation for morale and opinions, and based
on the documentation, both features appear to be incomplete.  In the
case of morale, I can find tables to control how it rises and falls
based on various situations, but I can't find a way to actually make
morale affect a unit!  In the case of opinions, I can find a mechanism
to make a unit revolt if its opinion of its own side drops too low, but
I can't find a way to make those opinions change from their starting
points during the game!

This would make it hard to implement traditionally unreliable units,
such as orc hordes, as without either morale or opinions, the side has
no way to affect the chance of the unit revolting.

I can think of a few other things that should affect morale and/or
opinions (e.g. fighting against or alongside a traditional enemy [e.g.
orcs and elves], being repaired [or just being near a unit capable of
performing repairs], watching as a friendly repair unit is destroyed,
etc.), but they're irrelevant as long as the morale and opinions code is
in a non-functional state.

---
Lincoln Peters
<sampln@sbcglobal.net>

E = MC ** 2 +- 3db

Re: Morale and opinions

[Stan Shebs]

Lincoln Peters wrote:

>I've been studying the documentation for morale and opinions, and based
>on the documentation, both features appear to be incomplete.  In the
>case of morale, I can find tables to control how it rises and falls
>based on various situations, but I can't find a way to actually make
>morale affect a unit!  In the case of opinions, I can find a mechanism
>to make a unit revolt if its opinion of its own side drops too low, but
>I can't find a way to make those opinions change from their starting
>points during the game!
>
All half-thought-through. The concept is that morale and opinion are
two different axes (low morale but high opinion runs away but remains
loyal, high morale but low opinion is going to rebel and be dangerous
subsequently), but useful parametrization was hard, very many different
things that one might want to affect. To make progress, you'd probably
want to pick a simplified situation that is interesting for a real game,
make that work first.

Stan

Re: Morale and opinions

[Lincoln Peters]

On Mon, 2004-09-13 at 17:18, Stan Shebs wrote:
> Lincoln Peters wrote:
> 
> >I've been studying the documentation for morale and opinions, and based
> >on the documentation, both features appear to be incomplete.
> All half-thought-through. The concept is that morale and opinion are
> two different axes (low morale but high opinion runs away but remains
> loyal, high morale but low opinion is going to rebel and be dangerous
> subsequently), but useful parametrization was hard, very many different
> things that one might want to affect. To make progress, you'd probably
> want to pick a simplified situation that is interesting for a real game,
> make that work first.

As I see it:
* High morale and high opinion would (mostly?) negate a unit's chance of
retreating from combat or surrendering to another side.
* Low morale and high opinion would increase a unit's chance to retreat
as per withdraw-chance-per-attack or retreat-chance, or both.  If the
unit can get out of the fight, it would most likely proceed to repair
itself by whatever means are available to it.  Of course, that last part
would only apply if the unit is under AI control (although a human
player would probably order it to do the same).
* High morale and low opinion would have results comparable to the orc
horde scenario: the unit has a higher chance of surrendering to an
opposing side, as per surrender-chance or (maybe) revolt-chance.
* Low morale and low opinion would affect both the chance of retreating
and revolting/surrendering.  This could easily mean that the unit would
switch sides but refuse to fight for the new boss until some action is
taken to raise its morale.

I can think of a few factors to affect morale and opinions.  The
following would raise a unit's morale:
1. Defeating (or damaging) an enemy unit
2. Capturing an enemy unit
3. Being repaired

The following would lower a unit's morale:
1. Being damaged
2. Being captured

The following would raise a unit's opinion of its own side:
1. An enemy unit defeated (or damaged) within its vision-range
2. An enemy unit captured within its vision-range
3. An enemy unit within its vision-range revolts and joins its side*

The following would lower a unit's opinion of its own side:
1. A friendly unit killed within its vision-range
2. A friendly unit captured within its vision-range
3. A friendly unit within its vision-range revolts and joins the enemy
side*

The following would raise a unit's opinion of an enemy side:
1. Enemy kills a friendly unit**
2. Enemy captures a friendly unit

The following would lower a unit's opinion of an enemy side:
1. An enemy unit defeated (or damaged) within its vision-range
2. An enemy unit captures within its vision-range

* This should also work in situations where a unit is killed, wrecks
into another unit, and the wreck joins the other side.  I think that
this can happen in wreckreation.g, but I don't know about any other
games.

** This may depend on the general attitude of the unit, although if its
opinion of an enemy is not raised by the enemy's skill, it probably
shouldn't be affected by morale and/or opinions at all.

There is a significant overlap between all of these statistics.  If two
sides are evenly matched and killing each other's units at the same
rate, the surviving units will see their opinions of both sides vary
slightly but remain steady over time.  Morale, however, would be more
variable as it would represent the unit's opinion of itself, not its
side.  Thus, if a unit were successful in battle even when its side is
losing, its morale would be rising as its opinion of its side is
falling, and its chance of changing sides would rise.  If, on the other
hand, the unit was severely damaged in battle while its side is winning,
its morale would be falling as its opinion of its side is rising, and
its chance of retreating would rise.

The aforementioned factors that would affect morale and opinions are by
no means all of the factors that one might want to use in a game, but I
think that they would handle most situations properly.


I was hoping to use morale and opinions in the new version of knights.g,
so that certain kinds of cowardly and/or greedy soldiers (e.g. bugbears,
gnolls, goblins, ogres, orcs, troglodytes) would be generally unreliable
but could be made more reliable if they receive good treatment.

---
Lincoln Peters
<sampln@sbcglobal.net>

 anyone know if there is a version of dpkg for redhat?

Re: Morale and opinions

[Elijah Meeks]

[-- Attachment #1: Type: text/plain, Size: 1559 bytes --]

> This would make it hard to implement traditionally
> unreliable units,
> such as orc hordes, as without either morale or
> opinions, the side has
> no way to affect the chance of the unit revolting.

I attempted to use the 'has-opinions' unit attribute
but GDL didn't recognize it.  This was some time ago,
and who knows, there may have been a syntax error, but
I ended up resorting to a straight revolt-chance for
my Ogres, Demons, Iblis and other fickle creatures in
Opal.  If you could get this to work, that'd be great.
 However, any work on morale would leave, I'd assume,
to retreating, and keep in mind that the XConq retreat
still has issues when called in a game that usese ZOC
rules.

Also, on an unrelated note, I'd lik to give everyone
my buggy little arena.g, which is not fun* or very
functional.  It's meant as a testbed for XConq
item-like units, but I've had a hell of a time getting
the protection tables to do what I want, and swords
keep jumping from owner to owner of their own
volition.  If anyone gets a chance to look at it, I'm
specifically  vexxed by the protection, especially
setting up armor and shield units to absorb some
blows, thereby representing armor class. 

Elijah

*Well, there's a certain visceral pleasure in cutting
down farmers and jesters and hunchbacks, and a rather
ironic pleasure in that it's called Arena, but there's
no arena to speak of, but other than that...


	
		
__________________________________
Do you Yahoo!?
New and Improved Yahoo! Mail - 100MB free storage!
http://promotions.yahoo.com/new_mail 

[-- Attachment #2: arena.g --]
[-- Type: application/octet-stream, Size: 10653 bytes --]

(game-module "arena"
  (title "The Arena")
  (version "1.00")
  (blurb "Just a test of item units.")
  )

(set terrain-seen true)
(set indepside-has-ai true)
(set self-required true)



;;; Types -- Heroes must be self-units or unused weapons will live on

(unit-type hero (name "Hero") (image-name "ang-pirate-red-cap")
  (acp-per-turn 6) (hp-max 50) (vision-range 3)
  (point-value 10) (can-be-self true) (self-resurrects true)
  (help "A tough guy, stuck in the Arena, just trying to make a buck, or something."))

(unit-type fodder (name "Fodder") (image-name ("ang-hunchback-buff" "ang-jester-orange-bell" "ang-man-brown-drunk" "ang-man-cap-pitchfork" "ang-man-brown-hypnotized"))
  (acp-per-turn 6) (hp-max 10) (vision-range 2)
  (point-value 10)
  (help "Not so tough at all, in fact, they're just good for testing sword sharpness."))

(unit-type sword (name "Sword") (image-name "ang-scroll-sword-green")
  (acp-per-turn 2) (hp-max 1) (vision-range 0)  
  (point-value 10)
  (help "A sword, for killing people."))

(unit-type dagger (name "Dagger") (image-name "ang-scroll-sword-hit")
  (acp-per-turn 3) (hp-max 1) (vision-range 0)  
  (point-value 10)
  (help "A knife, for stabbing people and thereby pissing them off."))

(unit-type claymore (name "Claymore") (image-name "ang-scroll-sword-red")
  (acp-per-turn 2) (hp-max 1) (vision-range 0)  
  (point-value 10)
  (help "A big sword, for killing many, many people."))

(unit-type bow (name "Bow") (image-name "ang-arrow-red-right")
  (acp-per-turn 2) (hp-max 1) (vision-range 0) (acp-to-fire 1) (range 5)  
  (point-value 10)
  (help "A bow, for shooting people."))

(unit-type crossbow (name "Crossbow") (image-name "ang-arrow-green-up")
  (acp-per-turn 1) (hp-max 1) (vision-range 0) (acp-to-fire 1) (range 5)  
  (point-value 10)
  (help "A crossbow, for shooting less people but killing more of the people you hit."))

(unit-type leatherarmor (name "Leather Armor") (image-name "ang-scroll-armor-blue")
  (acp-independent true) (hp-max 1) (vision-range 0)  
  (point-value 10)
  (help "Thin, light armor."))

(unit-type chainarmor (name "Chain Mail Armor") (image-name "ang-scroll-armor-green")
  (acp-independent true) (hp-max 1) (vision-range 0)  
  (point-value 10)
  (help "Thickish, heavyish armor."))

(unit-type platearmor (name "Plate Mail Armor") (image-name "ang-scroll-armor-red")
  (acp-independent true) (hp-max 1) (vision-range 0)  
  (point-value 10)
  (help "Thick, heavy armor."))

(unit-type smallshield (name "Small Shield") (image-name "ang-chest-small-wood")
  (acp-independent true) (hp-max 1) (vision-range 0)  
  (point-value 10)
  (help "A wee, little shield."))

(unit-type largeshield (name "Large Shield") (image-name "ang-chest-large-metal")
  (acp-independent true) (hp-max 1) (vision-range 0)  
  (point-value 10)
  (help "A big shield that really helps against arrows and such."))


(define people-types (hero fodder))

(define item-types (sword dagger claymore bow crossbow leatherarmor chainarmor platearmor smallshield largeshield))

(define melee-weapon-types (sword dagger claymore))

(define ranged-weapon-types (bow crossbow))

(define armor-types (leatherarmor chainarmor platearmor))

(define shield-types (smallshield largeshield))

;; TERRAIN

(terrain-type sea (char ".")
  (help "deep water"))
(terrain-type shallows (char ",")
  (help "shallow coastal water and lakes"))
(terrain-type swamp (char "="))
(terrain-type desert (image-name "adv-desert") (char "~")
  (help "dry open terrain"))
(terrain-type land (image-name "adv-plain") (char "+")
  (help "open flat or rolling country"))
(terrain-type forest (image-name "adv-forest") (char "%"))
(terrain-type mountains (image-name "adv-mountains") (char "^"))
(terrain-type ice  (image-name "adv-ice") (char "_"))
(terrain-type neutral (image-name "gray") (char "-"))
(terrain-type hills (image-name "adv-hills"))
(terrain-type semi-desert (image-name "adv-semi-desert"))
(terrain-type steppe (image-name "adv-steppe"))
(terrain-type deepforest (image-name "adv-forest"))
(terrain-type wasteland (image-name "gray"))
(terrain-type river (char "<")
  (subtype border) (subtype-x river-x))
(terrain-type beach (char "|")
  (subtype border))
(terrain-type cliffs (image-name "cliffs")
  (subtype border))
(terrain-type road (char ">")
  (subtype connection) (subtype-x road-x))
(terrain-type mud (image-name "brown")
  (subtype coating))
(terrain-type snow (image-name "ice")
  (subtype coating))
(terrain-type jungle (image-name "adv-forest"))

(terrain-type p-land (name "Phantom Plains") (image-name "blue") (char "+")
  (help "Wispy plains."))
(terrain-type p-forest (name "Phantom Forest") (image-name "blue") (char "%"))
(terrain-type p-mountains (name "Phantom Mountains") (image-name "blue") (char "^"))
(terrain-type p-hills (name "Phantom Hills") (image-name "blue"))
(terrain-type p-river (name "Phantom River") (image-name "blue")
  (subtype border) (subtype-x river-x))
(terrain-type p-cliffs (name "Phantom Cliffs") (image-name "blue")
  (subtype border))



(add (sea shallows) liquid true)

(define sea-t* (sea shallows))

(define land-t* (jungle deepforest wasteland desert semi-desert hills steppe land forest mountains river))

(define phantom-t* (p-land p-forest p-mountains p-hills p-river p-cliffs))

;;; Unit-unit capacities.


(add hero capacity 4)

(table unit-size-as-occupant
  ;; Disable occupancy by default.
	(u* u* 99)
	(item-types hero 1)
	(ranged-weapon-types hero 2)
)

(table occupant-max
	(fodder item-types 0)
	
)

;;; Unit-terrain capacities.

(table unit-size-in-terrain
  (u* t* 25)
)

(add t* capacity 100)


;;; Movement.

(table mp-to-enter-terrain
  (u* t* 2)
  (people-types sea-t* 99)
  (people-types cliffs 99)
  (people-types river 3)
  (people-types (hills forest semi-desert swamp jungle) 3)
  (people-types (desert wasteland deepforest) 4)
  (people-types mountains 6)
  (item-types t* 99)
)

(table mp-to-leave-terrain
  (people-types sea-t* 99)
)




(add hero hp-recovery 5)

(set combat-model 0)


(table acp-to-attack
  (u* u* 0)
  (hero people-types 3)
  (fodder people-types 3)
  (melee-weapon-types people-types 1)
  (fodder item-types 3)
)

(table acp-to-defend
   (u* u* 99)
)



(table fire-hit-chance
	(u* u* 0)
	(ranged-weapon-types u* 75)
)


(table fire-damage
	(bow people-types 1d8)
	(crossbow people-types 2d6)
	(ranged-weapon-types item-types 0)

)





(table hit-chance
	(u* u* 0)
	(people-types people-types 75)
	(melee-weapon-types u* 75)
	(fodder item-types 100)
)



(table damage
	(u* u* 0)
	(people-types people-types 1d3)
	(sword people-types 1d10)
	(dagger people-types 1d6)
	(claymore people-types 3d6)
	(melee-weapon-types item-types 0)
)

(table capture-chance
	(fodder item-types 100)
)

(table ferry-on-entry
	(u* u* 0)
	(people-types item-types over-all)
)

(table ferry-on-departure
	(u* u* 0)
;;	(people-types item-types over-all)
)

(table mp-to-leave-unit
	(item-types people-types 99)
)

(table protection
  ;; Ground units protect cities.

  (leatherarmor people-types 20)
  (chainarmor people-types 40)
  (platearmor people-types 60)
  (smallshield people-types 10)
  (largeshield people-types 20)
  (ranged-weapon-types people-types 0)
  (melee-weapon-types people-types 0)


  (people-types leatherarmor 80)
  (people-types chainarmor 60)
  (people-types platearmor 40)
  (people-types smallshield 90)
  (people-types largeshield 80)
  (people-types ranged-weapon-types 100)
  (people-types melee-weapon-types 100)


)



(table occupant-combat
	(u* u* 0)
	(melee-weapon-types people-types 100)
	(ranged-weapon-types people-types 100)
)



(add u* lost-vanish-chance 0)

;;; The world.

(world 360 (year-length 12) (axial-tilt 22))


(set calendar '(usual month))

(set season-names
  ;; 0 is January, 3 is April, 6 is July, 9 is October
  ((0 2 "winter") (3 5 "spring") (6 8 "summer") (9 11 "autumn")))


;;; River generation.

(add (land forest mountains) river-chance (10.00 25.00 25.00))

(set river-sink-terrain shallows)

;;; Road generation.

(table road-into-chance
  (t* land 100)
  (land (desert forest mountains) (50 40 20))
  )

(define cell-t* (steppe sea swamp desert forest land mountains ice))

;                               		sea 	lak	swa 	des 	pla 	for 	mou 	ice
; ---------------------------------------------------------------------

(add cell-t* alt-percentile-min 	(  	0  	27 	30  	30  	30	30  	90  	99	))
(add cell-t* alt-percentile-max 	( 	28  	30  	33  	90  	90	89  	99 	100	))
(add cell-t* wet-percentile-min 	(  	0   	0  	20   	0  	20	70   	0   	0	))
(add cell-t* wet-percentile-max 	(	100 	100 	100	20  	70	100 	100 	100	))

;;;	Some defns for the fractal percentile generator.

(set alt-blob-density 10000)
(set alt-blob-height 500)
(set alt-blob-size 100)
(set alt-smoothing 4)
(set wet-blob-density 2000)
(set wet-blob-size 100)


(table favored-terrain
  (u* t* 0)
  (people-types land-t* 100)
  (item-types land-t* 100)

	)


(set edge-terrain ice)


(add hero start-with 3)
(add fodder start-with 10)
(add item-types start-with 1)

(scorekeeper (do last-side-wins))





(game-module (design-notes
  "It is ambitious"
  ))

(imf "ang-hunchback-buff" ((32 32) (file "dg_monster132.gif" std 0 0)))

(imf "ang-scroll-sword-red" ((32 32) (file "dg_misc32.gif" std 1 15)))
(imf "ang-scroll-sword-hit" ((32 32) (file "dg_misc32.gif" std 2 11)))
(imf "ang-scroll-sword-green" ((32 32) (file "dg_misc32.gif" std 2 15)))

(imf "ang-scroll-armor-red" ((32 32) (file "dg_misc32.gif" std 3 14)))
(imf "ang-scroll-armor-green" ((32 32) (file "dg_misc32.gif" std 4 11)))
(imf "ang-scroll-armor-blue" ((32 32) (file "dg_misc32.gif" std 5 11)))

(imf "ang-arrow-red-right" ((32 32) (file "dg_effects32.gif" std 1 9)))
(imf "ang-arrow-green-up" ((32 32) (file "dg_effects32.gif" std 8 9)))
(imf "ang-jester-orange-bell" ((32 32) (file "dg_people32.gif" std 0 1)))
(imf "ang-man-brown-drunk" ((32 32) (file "dg_people32.gif" std 0 2)))
(imf "ang-man-cap-pitchfork" ((32 32) (file "dg_people32.gif" std 1 0)))
(imf "ang-man-brown-hypnotized" ((32 32) (file "dg_people32.gif" std 1 1)))

(imf "ang-pirate-red-cap" ((32 32) (file "dg_abyss.gif" std 3 0)))
(imf "ang-chest-small-wood" ((32 32) (file "dg_misc32.gif" std 0 0)))
(imf "ang-chest-large-metal" ((32 32) (file "dg_misc32.gif" std 5 0)))

Re: Morale and opinions

[Lincoln Peters]

On Mon, 2004-09-13 at 18:16, Elijah Meeks wrote:
> I attempted to use the 'has-opinions' unit attribute
> but GDL didn't recognize it.  This was some time ago,
> and who knows, there may have been a syntax error, but
> I ended up resorting to a straight revolt-chance for
> my Ogres, Demons, Iblis and other fickle creatures in
> Opal.  If you could get this to work, that'd be great.
>  However, any work on morale would leave, I'd assume,
> to retreating, and keep in mind that the XConq retreat
> still has issues when called in a game that usese ZOC
> rules.

I wouldn't be surprised if opinions, like so many other things, are
described in the documentation but don't exist in the code.

> 
> Also, on an unrelated note, I'd lik to give everyone
> my buggy little arena.g, which is not fun* or very
> functional.  It's meant as a testbed for XConq
> item-like units, but I've had a hell of a time getting
> the protection tables to do what I want, and swords
> keep jumping from owner to owner of their own
> volition.  If anyone gets a chance to look at it, I'm
> specifically  vexxed by the protection, especially
> setting up armor and shield units to absorb some
> blows, thereby representing armor class. 

One huge bug I see is that you've set up lighter armor to have a lower
protection value.  As counter-intuitive as it may be, lower numbers
actually mean *greater* protection, so that in this game, a guy with
leather armor and a small shield is pretty much invincible.

The ideal way to handle weapons would be if they had no ACP's and
affected their owner via occupant-affects-attack, but the last time I
checked, that table only works in Combat Model 1.


It might also help if you add a line such as:

(set country-separation-min 20)

That would guarantee each side some time to arm itself before
confronting the other side.


Unfortunately, item-like units are going to remain awkward for the
foreseeable future.

> *Well, there's a certain visceral pleasure in cutting
> down farmers and jesters and hunchbacks, and a rather
> ironic pleasure in that it's called Arena, but there's
> no arena to speak of, but other than that...

Maybe I should post my test module for unit control and see how you
respond to *that* (it involved necromancers and all sorts of twisted
stuff).

---
Lincoln Peters
<sampln@sbcglobal.net>

Saints should always be judged guilty until they are proved innocent.
		-- George Orwell, "Reflections on Gandhi"

Re: Morale and opinions

[Eric McDonald]

Elijah Meeks wrote:

> Also, on an unrelated note, I'd lik to give everyone
> my buggy little arena.g, which is not fun* or very
> functional.  It's meant as a testbed for XConq
> item-like units, but I've had a hell of a time getting
> the protection tables to do what I want,

Same comment as Lincoln. The tables are actually "vulnerability" tables 
rather than protection tables.

> and swords
> keep jumping from owner to owner of their own
> volition.  

As mentioned in previous discussions, I think get/drop would be a good 
idea. Of course, this would need to be coupled with 
'occupant-adds-hit-chance', 'occupant-adds-damage', etc....

> *Well, there's a certain visceral pleasure in cutting
> down farmers 

Hay, farmers are productive members of society (at least when they're 
not hanging out in arenas). Leave 'em alone.

Eric

Re: Morale and opinions

[Elijah Meeks]

> Same comment as Lincoln. The tables are actually
> "vulnerability" tables 
> rather than protection tables.

Yep, switched 'em and it seems to work the way it's
supposed to.

> Hay, farmers are productive members of society (at
> least when they're 
> not hanging out in arenas). Leave 'em alone.

Not these farmers.  They had it coming...


		
_______________________________
Do you Yahoo!?
Declare Yourself - Register online to vote today!
http://vote.yahoo.com

Re: Morale and opinions

[Lincoln Peters]

On Tue, 2004-09-14 at 20:18, Eric McDonald wrote:
> > *Well, there's a certain visceral pleasure in cutting
> > down farmers 
> 
> Hay, farmers are productive members of society (at least when they're 
> not hanging out in arenas). Leave 'em alone.

I had been thinking that, if the material extraction code (still) works,
I might implement farmer units in knights.g to collect food from terrain
that's out of a city's reach.  Maybe also something similar with miner
units to extract ores, and possibly mystic units to extract ideas (kind
of weird, but it works).

If you don't take a visceral pleasure in cutting down farmers, you might
take some pleasure in cutting them down for the logistical consequences
to your opponent.  And if the AI were to decide to launch a horde of
pitchfork-wielding farmers to attack a pit fiend...you get the idea.

---
Lincoln Peters
<sampln@sbcglobal.net>

Never volunteer for anything.
		-- Lackland

Re: Morale and opinions

[Eric McDonald]

Lincoln Peters wrote:

> I had been thinking that, if the material extraction code (still) works,

I hope so. It was one of the things I had planned on adding unit action 
buttons for in the SDL interface. If not, then I guess there is one more 
bug to fix.

> If you don't take a visceral pleasure in cutting down farmers, you might
> take some pleasure in cutting them down for the logistical consequences
> to your opponent.  And if the AI were to decide to launch a horde of
> pitchfork-wielding farmers to attack a pit fiend...you get the idea.

It would be a "pitched" battle, no doubt....

Eric

Re: Morale and opinions

[Eric McDonald]

Elijah Meeks wrote:

> I attempted to use the 'has-opinions' unit attribute
> but GDL didn't recognize it.  

It appears to be 'opinions' and not 'has-opinions'.
 From looking at the code, I would say that its format is:
   (opinions ((side1 val1) (side2 val2) #| etc, etc... |#))
where 'side1', 'side2', and so on can either be a side number or a side 
symbol (such as "fed", without the double-quotes), and where 'val1', 
'val2', etc... are numbers reflecting the degree of the opinion.
Alternatively, you can simply specify that an unit has opinions about a 
side, but in no particular quantity:
   (opinions (side1 side2 #| etc... |#))
where 'side1', 'side2', and so on must be side symbols, and not numbers.
Or, you can specify:
   (opinions (val1 val2 #| etc... |#))
where 'val1' is the unit's opinion of the first side, 'val2' is the 
unit's opinion of the second side, etc.... These are numbers.

Eric