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I''m looking for peoples thoughts on how to measure vulnerability for RTS agents at the individual, unit and army level. What do you believe the important variables to be and what are their relative importances to the computation. Should it be one number to represent total vulnerability or different numbers for distinctly important factors. I have developed my own idea of what contributes to vulnerability, however I don''t want to bias the conversation with that just yet... I will say that I believe that variables like level of cover (location), unit health and movement rate are important, but their contribution to the vulnerability score alters when considering different kind of attacks... and these are by no means the only important factors. Finally, let me be clear about my definition of vulnerability. I define vulnerability as the level of risk of a detrimental event occuring. So, in RTS, we might be vulnerable to taking damage from artillery fire, vulnerable to being flanked, or vulnerable to running out of resources, etc. If you have a different definition of vulnerability, please provide it with some explanation... and some notion of whether it is better or worse than my definition (in other words, could you justify why I should abandon my definition for yours)! Cheers and thanks, Timkin

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Also type of unit , if we are talking about combat here, should be considered. A mortar team is usually more vulnerable than a typical rifle fire team. A command team is much more vulnerable than any other small section.

Also profile of unit , which is a factor of how easy it is to spot. Like the antenna farm that typically follows a unit commander, makes that team easier to spot. This is not just cover, but a factor in target selection.

Whether a unit is engaged or not. A unit engaged is firing its weapons, and thus revealing its location, and thus is more vulnerable than a unit that is hunkered down, unengaged and not firing its weapons.

Those are just a few aspects we considered in Full Spectrum Command .

Eric

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One measure of a units vulnerability would be how many opposing units can fire at it effectivley. If you created a matrix of wepon effectivness -vs- units (ie: SAMs are deadly towards helicopters, etc..) you might get better results.

Another would be how far away it is how far it is from the front line, with an increasing amout of threat as it moves behind thenemy lines. You might want to base this on time, as slower moving units are more vulnerable than faster ones which can retreat easily.

The units own stats (health, ammo remaining, fuel remaining, etc...) would obviously be a factor.

If you factor in artillery / air strikes, a units proximity to a strategic target would also affect it''s vulnerability. ie: dont stand next to the fuel depot when you know enemy jets are coming in to bomb it.

I''m not exactly sure how this would work, but if you have a group of units you could work out how much time would be required by the group to eliminate certain enemies. Once you have this number, you could then compare opposing forces and make quick predictions about the battles outcome. This would be a good short-range threat indicator. ie: 7 grunts -vs- 1 tank. Grunts require 30 seconds to eliminate tank. Tank requires 1 second to eliminate grunts. Grunts saftey = (tank power(1) * infantry(7) = 7) - (infantary power (30) * 1= 30) = -23. The infantary are in grave danger.

Cheers,
Will

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RPGeezus,

Does it take 7 infantry 30 seconds to eliminate a tank or does it take 1 infantry 30 seconds to eliminate a tank? If it takes 1 infantry 30 seconds, then shouldn''t it take 7 infantry around 5 to 6 seconds (since power will be decreased as infantry are killed off by tank). If so then 1 to 2 infantry could very well survive even though heavy losses are sustained, possibly giving oncoming reinforcements an advantage. How would factors such as these be considered. If it takes 7 infantry 30 seconds to eliminate a tank then the question is moot - infantry is in deep ...

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Several factors that change vulnerability depend on how likely the enemy is to know where that unit is(and how likely the enemy is to find out where it is). If the enemy doesn''t know where the unit is, its hard(if not impossible) to attack it.

In order to know how likely the enemy is to know where the unit is, you''d need to take into account the last known location of advancing enemy units, how close the unit is to the last known location of the enemy''s unit-producing buildings, when the unit was last engaged, where it was last engaged, etc.

A large part of ''vulnerability'' depends on the rules as well. In some games, a unit on high ground does more damage in which case being on low ground near high ground increases vulnerability.

"You are my friends if you do what I command you."
[edited by - Big Brother on January 1, 1984 12:00:00 AM]

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A corollary to knowing where the enemy is... what are the nearby places that we don''t know WHAT is there? In an urban setting, for example, what really IS in those windows? While this may not increase actual vulnerability, it may increase perceived vulnerability.

Dave Mark - President and Lead Designer
Intrinsic Algorithm -
"Reducing the world to mathematical equations!"

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quote:
Original post by Code-Junkie
RPGeezus,

Does it take 7 infantry 30 seconds to eliminate a tank or does it take 1 infantry 30 seconds to eliminate a tank? If it takes 1 infantry 30 seconds, then shouldn''t it take 7 infantry around 5 to 6 seconds (since power will be decreased as infantry are killed off by tank). If so then 1 to 2 infantry could very well survive even though heavy losses are sustained, possibly giving oncoming reinforcements an advantage. How would factors such as these be considered. If it takes 7 infantry 30 seconds to eliminate a tank then the question is moot - infantry is in deep ...




You are quite right, the example I gave doesn''t work. I did say "I''m not sure how this would work" though... My example was 1 infantary takes 30 seconds to kill a tank. So, seven infantry should take 5 seconds to kill a passive tank. As you mentioned, the tank would fire back, so if each unit fires every second.... The tank would win. ( tank has 100 hp, it takes 30 seconds for 1 grunt to kill the tank, grunt = 3.333 damage / sec.. It takes 7 seconds for tank to destroy all grunts. Total damage by grunts (7=23, 6=20, 5=17, 4=13,3=9, 2=7, 1=3) = 92ish in 7 seconds, or 92% of the tank).

The general idea is to get another way to measure a threat. If a group of units will lose a battle, but take a long time to be destroyed, the threat is not as high as the same group of units getting destroyed in less time. I''m sure there is a flaw with that (mate in 7 is just as bad as mate in 2), but it''s at least an estimate.

Will

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I''m not sure how much this will help, but I have considered vulnerability in the game of chess. In thinking about piece vulnerability or square vulnerability, one main thing that I found was that vulnerability had an inverse relationship to mobility, activity, and speed. So if a piece was trapped or blocked off (low mobility), it was more vulnerable. If a piece was slow, it was more vulnerable to faster pieces (Ex. pawn vs. queen). Vulnerability of squares (maybe paralleled with territory in RTS games) had a lot to do with (1) the value of the defending units, and (2) the mobility of the pieces to flock to the defense of the square. In (1), if a pawn is guarding a square by itself, and two enemy rooks are attacking it, the pawn still controls it, because it would cost the enemy a rook to gain control of it. Of course it gets more complicated, because you might be able to checkmate after sacrificing a rook, but that''s beside the point. (2) has a lot to do with sacrificing pieces for an attack on the enemy king. If the opponent''s pieces are blocked off and can''t come quickly to the aid of the squares surrounding the king, then those pieces might as well not even be on the board. So the squares around the king are vulnerable, as well as the king itself.

So, vulnerability has an inverse relationship to mobility, or piece/unit activity, and speed. Give it some thought and tell me what you think.

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Another big issue is whether or not the unit has combat experience. For example, a crack veteran rifle squad is going to be a lot better than a green squad fresh out of basic training... you get the idea. HTH, sounds like you have something revolutionary on the horizon.

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There are some useful thoughts above (thanks heaps!), although there also seems to be an inherent bias in some peoples mind between vulnerability and damage taking. While this is certainly one type of vulnerability - that is, a vulnerability to harm - in my opinion there are others.

Russell, I had given thought to the relationship between vulnerability and manouverability, although a little more generally. I had considered vulnerability as being inversely correlated with the rate at which an agent could change state (in a given state space, but not just a spatial space). It also depends on whether there exists an accessible invulnerable (or lesser vulnerable) state as well. If an agent can move from a vulnerable to an invulnerable state quickly, then it is certainly less vulnerable than if it cannot move to an invulnerable state at all. So in this sense, time plays an important role.

One of my key ideas was that the level of risk was related to the probability of achieving the invulnerable state before succumbing to the threat. That is, if the probability of reaching this invulnerable state was p, then the risk afforded by the threat was q=1-p. I have some ideas about more complex models of this that utilise Dempster-Shafer Theory, but I think this one will suffice for now... so I''m not delving into them unless I really need to.

Furthermore, if there are no accessible invulnerable states (as is the case in most domains) then the important factor would be the maximal rate at which vulnerability could be decreased and the probability of being able to achieve this. Thus the risk is associated with a particular plan to decrease vulnerability... read this as risk to attribute A afforded by threat X given that plan P is executed in response to threat X .


I think that this notion of vulnerability encapsulates all of the ideas mentioned by previous posters since things like terrain, unit type, health, weaponry and enemy disposition all affect the probability mentioned. If anyone disagrees, please point out a counter example where this notion of vulnerability fails.

As to how this gets used... well that''s related to utility theory. While an agent might be quite vulnerable to a specific threat, it will only be concerned with that threat if the expected loss caused by the threat eventuating is significant to the agent. The expected cost is the product of the threat risk and the threat cost given that it eventuates.


I''d be happy (ish) for someone to provide a different/better model of vulnerability or provide examples where mine fails. Ultimately I will require my agents to react to threats by choosing actions/plans that minimise their expected loss, given their goals...

The real fun is learning this agent function through simulation/playing of the game, since it really depends on the opponent and the sorts of threats they present!

Any and all help/advice is most welcome.

Thanks,

Timkin

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I would drop the "unit type" factor in the vulnerability calculations. The "Unit Type" factor is just a measure for a collection of other scores, some of which you have already accounted for in another way. You would be using these scores twice.

Let''s expand on Geta''s example. Take 3 types of units: A mortar team, A rifle team and a grunt team (your basic cannon fodder). Clearly their relative "Unit type" vulnerabilities are:

High: grunt team
Medium: mortar team
low: rifle team

These rates are made up of several other scores. Grunts rank high vulnerability because they are your basic troops (and usually considered ''expendable'' by HQ) so they get mediocre armour and weapons. Only basic training gives them average movement rates. They''re usually plunged in the front line of combat.

Mortar teams rank Medium. They are a big and attractive target (high profile and high potential damage from the mortar). They are usually deployed in the rear of the army so they don''t get real fancy armour because, being in the back, they seldom have to deal with regular gun fire (maybe the odd sniper). Most of the weapons fired at them will be high damage and/or long range blast weapons. They are very immobile because the guys need to take their mortar with them. The mortar does act as a shield for the team to hide behind. All in all it''s less dangerous than the front line.

Rifle teams rank pretty low. They have had good training, giving them good movement and they can make better use of cover (hiding). They''re not expandable so they''re given better armour and weapons. Their only vulnerability comes from the fact that they are deployed to the front line.

All in all I think that "Unit type" vulnerability really is a collection from the unit training (skill), equiptment and especially the tactical use by the HQ. Better let the player decide the tactics and let the game rules factor in the other two components. Maybe you could pick up a Warhammer 40.000 rulebook (borrow it from a friend. They''re really expensive). It''s a tabletop battle game and IMHO the second edition has some very good rules for handling shooting. Here''s a short overview:

1) A unit can only fire at a target it can see or at a target with a known position (eg hidden troops that fire guns, or troops spotted by scouts etc.)

2) Make a check to see if the shot hits. Check is influenced by:
- skill of the shooter
- type of weapon (range, precision, blast radius)
- distance to target
- amount of cover for target
- speed at which target is moving

3) Check to see if a hit target is wounded. This depends on the strength of the weapon and the toughness (physical) of the target.

4) Check to see if the armour will save the target. This is influenced by the armour piercing capabilities of the gun (ammo) and the type of armour. I always found this separate armour test pretty important since armour saves you from being mortally wounded and not from being hit (as used in a lot of games). Real armour only saves your life so you can fight another day, but usually leaves you bruised, out-of-action or knocked down nontheless.

5) substract damage

Sander Maréchal
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Vulnerability of an unit can depend a lot on the perceived threat of that unit. This only happens if the enemy has the ability to strike where he chooses (even if this ability is limited).

For instance, the huge artillery used by the Germans against Sevastopol in 1942 were quite safe thanks to local air supremacy, but would be extremely vulnerable otherwise.

If the enemy can choose a target for an attack between a number of friendly targets (with similar damage (received and inflicted) effects), the vulnerability focuses on the one the enemy perceives would better further his means.

This gives interesting twists. Most often, the more troops are concentrated around one the safer he is. In the Iraq war things were exactly reversed: the farther away from any Iraqi troops or tanks or guns an Iraqi soldier was the safer he was.

[edited by - Diodor on June 4, 2003 4:12:04 AM]

[edited by - Diodor on June 4, 2003 4:40:46 AM]

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I still think people are seeing vulnerability as how quickly someone will die when taking damage... or being targeted... etc. If you think of being invulnerable as the state of not being able to be harmed, then this is an acceptable definition. However, I don''t see invulnerable as that definition. I see it more broadly as not being able to be deflected from the current state. I.e., impervious to an external influence. Thus, vulnerability is related to how susceptible a unit is to being affected by the domain (which includes other agents). More generally though, I see vulnerability as being inversely related to the ability (and time) to change state to an invulnerable state (or more ''safe'' state).

So, I would disagree with the idea that grunts are more vulnerable than than say a tank. It totally depends on the type of attack, local terrain, etc... A grunt can hide in a bunker and receive little damage from, say, an RPG. However a tank on the other hand can be decimated by a well aimed RPG. The further from the bunker the grunt is, the more vulnerable they are to such attacks (because they''re further from safety). Conversely, if the grunts have a tank with them, they''re less vulnerable because of the lowered likelihood of a successful attack against them. Assuming a single ''vulnerability number'' for a given unit type is contrary to the model and use of vulnerability that I proposed above, even though it''s closer to what has been done in the past.

I don''t want this idea of vulnerability to only be related to combat units. It should also apply to abstract concepts like supply lines , defensive structures , unit placements , etc., etc. Hence I want to ensure that the model I have come up with is appropriate for that. Nobody seems to have taken that into account and critically pulled my ideas apart. Hopefully someone can take a look at my ideas above and offer counter examples as to why they wont work, or even better, ideas to tweak my model to be more realistic. I don''t see that any of the models offered above sufficiently describes vulnerability for the purposes I have listed.

Along these lines, what factors do people see as influencing the probability of being able to change state. Some that come to mind are: availability of supplies, reinforcements, covering fire, air support; open communication lines, command ability, terrain, enemy disposition, location of threat, type of threat, structural design.

In addition, what sorts of threats does an army face? Footrot, propoganda, coming under fire, lack of food/water/ammunition/shelter.

Thanks,

Timkin

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quote:
Original post by Timkin
So, I would disagree with the idea that grunts are more vulnerable than than say a tank. It totally depends on the type of attack, local terrain, etc...

Exactly. That's why I proposed to drop the "Unit Type" factor from the vulnerability calculations. Anyway, here are some factors off the top of my head:

Supply Lines:
Type of goods transported (ammo, food or the HQ's expensive wine?), transport size (ammount of vehicles), transport fequency

Unit placement:
besides cover/terrain etcetera there's tactical advantage from high ground and buildings, unit type variation in an army (50 tanks + 50 choppers is less vulerable than 100 tanks in most cases)

Defensive structures:
Besides the material, placement etcetera there's also fame or symbolism. Structures who are more famous or are national symbols of pride will usually get attacked more fequently to demoralize the opposing force.

Other:
Diseases, demoralisation, friendly fire, (counter)intelligence, misinformation, support (or hostility) from the local population (rebels? local resistance force?) and weather ofcourse!

Hope this helps,


Sander Maréchal
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[edited by - smarechal on June 5, 2003 2:52:45 AM]

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I appreciate the comments smarechal, but you seem to be equating vulnerability with how attractive the target looks to the opposition . I don't believe that more attractive targets are more vulnerable than less attractive targets, only that they are more likely to be attacked.

I'm not wanting to compute vulnerability from the perspective of the opposition, but rather objectively in terms of the risk that a given threat poses to a given entity... so the assumption is that the entity IS being attacked and we want to know how vulnerable the entity is given the particular threat, for the purpose of choosing a plan that decreases this vulnerability (or removes it all together).

Does that help clarify things?

Timkin

[edited by - Timkin on June 5, 2003 5:21:44 AM]

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quote:
Original post by smarechal
Exactly. That''s why I proposed to drop the "Unit Type" factor from the vulnerability calculations. Anyway, here are some factors off the top of my head:



Actually, the US Army tends to consider the type of unit in their assessment of vulnerability. Unit types referred to as "antenna farms" are considered highly vulnerable, because they typically represent C&C capabilities, and US Army military doctrine lends itself to the "cut off the head" philosophy of combat.

I suspect, if one removes the consideration of likliness to be attacked from their definition of vulnerability, then I can see why one may not wish to consider type of unit in the assessment. However, if one really analyzes the considerations that go into target selection, then I think the importance of unit type becomes apparent. If I can kill your C&C and reduce overall unit cohension and coordination or support, then I can do far more damage than simply killing a grunt unit.

Eric

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quote:
Original post by Geta
Actually, the US Army tends to consider the type of unit in their assessment of vulnerability. Unit types referred to as "antenna farms" are considered highly vulnerable, because they typically represent C&C capabilities, and US Army military doctrine lends itself to the "cut off the head" philosophy of combat.


True, but for a game this would not work very well, since the tactics employed by the player can quite different and may not lend itself to the "cut off the head" philosophy, hence invalidating the "Unit Type" vulnerability scores. For the US army, this works great because they know what their global tactic is (information warfare ATM) and if tactics changes, they will probabely change te scores.

Anyway, more on topic. Factors that can change vulnerability scores given that a unit is under attack, second attempt (hope I do better now I love army tactics!):
Camouflage. It''s hard to shoot something wich is hard to see.
Accelleration: Fast targets are hard to kill. If you can change your speed rapidly, it would make you less vulnerable.
Comms equiptment: How fast can you call for backup/airstrike?
Defensive weapons like smoke grenades or something



Sander Maréchal
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Most of this is all fine and good, but most of this discussion appears to be about things which cannot be properly expressed in a computer.

It''s one thing to say ''supply line'' or even ''front line'', but what specifically are those things, and how is it that one can express them?

Even the idea of mobility is a flawed one. If you can move 99 places, but only one of them is worth moving too, are your really mobile? How do know that the other 99 places are not worth moving too?

Timkin: You should check out some of the chess literature. Most of these ideas have already been explored within that context.

Will

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quote:
Original post by Geta However, if one really analyzes the considerations that go into target selection, then I think the importance of unit type becomes apparent.



But we''re not talking about target selection... as I stated above, we are assuming that a given threat is already present and that the assessment of vulnerability is objective and relative to a given entity.

Target selection criteria lead to a computation of the probability of being attacked... but I don''t believe this has anything to do with the vulnerability of an entity (think of a unit if you must) to a given form of threat, just their likelihood of facing threats.

RPGeezus, perhaps you should reread what I said about changing state. I specifically noted that I wasn''t limiting myself to spatial states... and if there is only 1 out of 100 states that is a good target state to try and get to, then it is likely that the probability of reaching that state is low and thus the risk faced by the threat is high.

As to expressing concepts like ''front line'' or ''supply line'', these are relationships between units, possibly of opposing armies. For instance, a supply line is an accessible path between a supply depot and a forward base of operations. It''s fairly trivial to determine if such a path exists. It''s also possible to determine, using influence maps, the level of threat posed to a supply line from opposing units. In the case of a supply line, it''s states can be expressed as travel velocity and direction of each unit in the line, defensive capability and internal communication capability (and probably some other factors I haven''t considered yet). The plan that the supply line is executing is the path that the units are following. It should be fairly obvious to see that given a threat and an assessment of vulnerability to that threat, a commander in charge of the supply line can determine a new plan that minimises the expected cost of the threat (as I described in an earlier post).

As for the chess literature, I''ll try and track something appropriate down. If you have specific references I would appreciate that... or perhaps Russell does?

Thanks,

Timkin

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quote:
Original post by Timkin But we''re not talking about target selection... as I stated above, we are assuming that a given threat is already present and that the assessment of vulnerability is objective and relative to a given entity


So you mean the enviromental situation of a unit? Like is it exposed or in cover? Does it have back up or another unit covering it? More to do with the likelyhood of surving an attack rather than the likelyhood of being attacked?

DanielB

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quote:
Original post by Timkin
Original post by Geta: However, if one really analyzes the considerations that go into target selection, then I think the importance of unit type becomes apparent.


But we''re not talking about target selection... as I stated above, we are assuming that a given threat is already present and that the assessment of vulnerability is objective and relative to a given entity.



I can''t believe you guys are saying this. So, basically, the way you guys look at this problem, is that a unit more likely to be attacked has exactly the same vulnerability as a unit less likely to be attacked? LOL. You guys might want to consider reading up on Lessons Learned (search the web) about RL combat experiences (btw, more than just the US Army has articles on LL).

Eric

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quote:
Original post by Timkin
RPGeezus, perhaps you should reread what I said about changing state. I specifically noted that I wasn''t limiting myself to spatial states... and if there is only 1 out of 100 states that is a good target state to try and get to, then it is likely that the probability of reaching that state is low and thus the risk faced by the threat is high.



This approach would be a bad one, for chess anyway. Just because most of the moves available lead to doom does not at all mean that the position is a bad one.

Imagine this scenario: I have mega super weapon that will wipe out my enemy in one shot. All I need to do is press a button and I win. If I don''t use it, no matter what I do, I will loose. 1 out of 100 states is a good targe state. By your logic, I would never press the button because it''s too risky.

A popular chess quote is "The only move worth considering is the right one."..

quote:

a commander in charge of the supply line can determine a new plan that minimises the expected cost of the threat (as I described in an earlier post).



I''m skeptical. If it were that easy Chess wouldn''t be so hard. This higher level of stratagem is difficult enough, and often impossible, to implement for turn based games. I can only see it being even more complex in a RTS setting.

Best of luck,
Will

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quote:
Original post by Geta
So, basically, the way you guys look at this problem, is that a unit more likely to be attacked has exactly the same vulnerability as a unit less likely to be attacked?


No. That''s exactly NOT what I''m saying! I''m trying to separate the issue of target selection from the issue of how vulnerable a given unit is to a given threat/attack .

So what you''re missing Geta is that I''m assuming that both of these units - the one more likely to be attacked and the one less likely to be attacked - are both being attacked... now I don''t care about whether they''re going to be attacked or not... because they are being attacked... and now I want to work out how vulnerable they are to this given attack .

I suspect the problem here is that you have this idea of what vulnerability means and I have a different idea of what vulnerability means and we can''t seem to talk about the same thing.

This is frustrating.

Timkin

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quote:
Original post by RPGeezus
Imagine this scenario: I have mega super weapon that will wipe out my enemy in one shot. All I need to do is press a button and I win. If I don''t use it, no matter what I do, I will loose. 1 out of 100 states is a good targe state. By your logic, I would never press the button because it''s too risky.



Actually, your talking about action selection there and assuming there is a one-to-one mapping between actions and states. For complex domains and plans of length greater than one, this is not usually the case. It''s quite often possible to achieve the same final state with different actions.

Furthermore, I don''t really see how your example relates to my model of vulnerability to an attack. Could you elucidate further please?

quote:

I''m skeptical. If it were that easy Chess wouldn''t be so hard. This higher level of stratagem is difficult enough, and often impossible, to implement for turn based games. I can only see it being even more complex in a RTS setting.



This idea is a variation on my PhD research, which worked quite well for an autonomous aircraft operating in a real world, highly non-linear, complex and extremely dynamic domain (cylcones/hurricanes). Based on the fact that I have solved a very similar problem in a more complex, dynamic domain, I believe I can get this to work in a game!

Timkin

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