Difference between revisions of "Aim & Shoot"

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[[Category:Patterns]]
 
[[Category:Patterns]]
[[Category:Needs work]]
 
 
[[Category:Needs revision]]
 
[[Category:Needs revision]]
[[Category:Staffan's current workpage]]
 
[[Category:Needs examples]]
 
 
[[Category:Needs references]]
 
[[Category:Needs references]]
[[Category:Stub]]
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''The action of taking aim at something and then shooting at it.''
''The act of taking aim at something and then shooting at it.''
+
  
 
Combat is a common occurrence in games, and then many times through players having to [[Aim & Shoot]]. However, one of the most natural ways of showing attention to something is to look or point at it, and the action of [[Aim & Shoot]] can be generalized to describe any action where one indicates what one wants to affect through pointing.
 
Combat is a common occurrence in games, and then many times through players having to [[Aim & Shoot]]. However, one of the most natural ways of showing attention to something is to look or point at it, and the action of [[Aim & Shoot]] can be generalized to describe any action where one indicates what one wants to affect through pointing.
  
 
=== Examples ===
 
=== Examples ===
 +
The wargames [[Advanced Squad Leader]] and [[Warhammer Fantasy Battle]] requires that shooters have a clear line of sight to fire. They do also include indirect fire, but since this does not require calculations of trajectories it is for gameplay purposes very similar to ordinary [[Aim & Shoot]].
 +
 +
Already the first [[:Category:Console Games|Console Games]] included ''light guns''<ref name="light_gun"/> to allow players to aim physical gun props at their TVs. [[Duck Hunt]] is a later example of this type of games.
 +
 
[[Aim & Shoot]] is more or less a defining trait in [[:Category:FPS Games|first-person shooters]] such as the [[Quake series|Quake]], [[Doom series|Doom]], [[Half-Life series|Half-Life]], [[Left 4 Dead series|Left 4 Dead]], and [[Crysis series]]. It is also important in many other games with first-person views, e.g. the [[Deus Ex series]] and the [[Thief series]] as well as the latter installments of the [[Elder Scrolls series]] and the [[Fallout series]].
 
[[Aim & Shoot]] is more or less a defining trait in [[:Category:FPS Games|first-person shooters]] such as the [[Quake series|Quake]], [[Doom series|Doom]], [[Half-Life series|Half-Life]], [[Left 4 Dead series|Left 4 Dead]], and [[Crysis series]]. It is also important in many other games with first-person views, e.g. the [[Deus Ex series]] and the [[Thief series]] as well as the latter installments of the [[Elder Scrolls series]] and the [[Fallout series]].
  
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== Using the pattern ==
 
== Using the pattern ==
Making [[Aim & Shoot]] actions possible primarily depend on enabling players to complete [[Alignment]] goals of two points by having [[Line of Sight]]. For [[First-Person Views]] this is trivial, as one point is the player's view point unless either of the two points is moving. Somewhat more difficult are [[Third-Person Views]], as more movement of the player's [[Focus Loci]] is usually necessary. [[God Views]] are in most cases too difficult, as it is too hard to get the [[Spatial Engrossment]] required in order to line up the two points accurately. The possibility of [[Aim & Shoot]] actions can be restricted by requiring [[Tools]] or [[Weapons]], or the use of [[Resources]] such as [[Ammunition]]. The latter can introduce [[Tension]] to the activity and require [[Risk/Reward]] choices between shooting now or waiting for a possible better situation to shoot.
+
The normal use of [[Aim & Shoot]] actions requires that players are able to complete [[Alignment]] goals of two points by having [[Line of Sight]]. [[Crosshairs]] are very often used to support this [[Alignment]], and this makes [[Aim & Shoot]] nearly trivial in [[First-Person Views]] in unstressed conditions, as one aim point is simply the player's view point unless either of the two points is moving. Somewhat more difficult are [[Third-Person Views]], as more movement of the player's [[Focus Loci]] is usually necessary. [[God Views]] are in most cases too difficult, as it is too hard to get the [[Spatial Engrossment]] required in order to line up the two points accurately. However, an option to requiring [[Line of Sight]] is to require the judgement that shooting will create a suitable trajectory: either those close to parabolas simulating indirect fire (as in [[Scorched Earth]] and the [[Worms series]]), or those requiring bounces against other game elements (e.g. "kick shots"<ref name="kickshot"/> in [[Eight-ball]]). The possibility of [[Aim & Shoot]] actions can be restricted by requiring [[Tools]] or [[Weapons]], or the use of [[Resources]] such as [[Ammunition]]. The latter can introduce [[Tension]] to the activity and require [[Risk/Reward]] choices between shooting now or waiting for a possible better situation to shoot.
  
The difficulty of [[Aim & Shoot]] actions can be due to the [[Movement]] either of the game elements aimed at or the game element aiming. For [[Agents]], the intentional [[Movement]] due to [[Traverse]] or [[Evade]] goals can make aiming at them more difficult. For [[Moveable Tiles]] or other game elements, the mechanical [[Movement]] due to [[The Show Must Go On]] can likewise make aiming more difficult. The aiming can be further complicated by the players' own [[Movement]] of their [[Focus Loci]] or by a swaying of the aim to simulate the difficulty of real-world aiming. While performing [[No-Ops]] to slightly reduce the swaying is a common design feature, the use of [[Skills] and [[Tools]] can also motivate reducing the swaying; this instantiates the pattern [[Player/Character Skill Composites]]. In contrast, aiming can be made more difficult by introducing [[Tension]], for example through [[Competition]] or [[Time Limits]].
+
The difficulty of [[Aim & Shoot]] actions can be due to the [[Movement]] either of the game elements aimed at or the game element aiming. For [[Agents]], the intentional [[Movement]] due to [[Traverse]] or [[Evade]] goals can make aiming at them more difficult, especially if the [[Movement]] is actually [[Maneuvering]]. For [[Moveable Tiles]] or other game elements, the mechanical [[Movement]] due to [[The Show Must Go On]] can likewise make aiming more difficult. The aiming can be further complicated by the players' own [[Movement]] of their [[Focus Loci]] or by a swaying of the aim to simulate the difficulty of real-world aiming. While performing [[No-Ops]] to slightly reduce the swaying is a common design feature, the use of [[Skills]], [[Tools]] or [[Weapons]] can also motivate reducing the swaying; this [[Variable Accuracy]] is one way [[Player/Character Skill Composites]] can modulate [[Aim & Shoot]]. Various [[Auto-Aim]] solutions can also make [[Aim & Shoot]] actions easier through providing [[Player/Character Skill Composites]]. In contrast, aiming can be made more difficult by introducing [[Tension]], for example through [[Competition]] or [[Time Limits]].
  
 
The design of [[Game Worlds]] and [[Levels]] that makes players have a bad overview of the game state, for example the inclusions of [[Obstacles]], makes it difficult to [[Aim & Shoot]]. This means shots will not be well aimed and that potential targets likely are [[Surprises]] and they are in turn [[Surprises]] by being shot at. Other forms of [[Surprises]] likely cause a [[Disruption of Focused Attention]] for players and make players lose their aim.  
 
The design of [[Game Worlds]] and [[Levels]] that makes players have a bad overview of the game state, for example the inclusions of [[Obstacles]], makes it difficult to [[Aim & Shoot]]. This means shots will not be well aimed and that potential targets likely are [[Surprises]] and they are in turn [[Surprises]] by being shot at. Other forms of [[Surprises]] likely cause a [[Disruption of Focused Attention]] for players and make players lose their aim.  
  
Although [[Aim & Shoot]] is often applied to [[Combat]] with the goals of [[Capture]] or [[Eliminate]] of [[Enemies]], other goals and reasons are possible. [[Delivery]] of game elements can be done by throwing or shooting the game elements to the receiver and [[Capture]] can be the capturing of information rather than game elements. Shooting spider webs, throwing grappling hooks (as done in [[The Legend of Zelda series]] and [[Just Cause 2]]), or even firing cannons with oneself inside it (e.g. the [[Super Mario series]]) can give explanations for how [[Privileged Movement]] can be performed by [[Aim & Shoot]].
+
Although [[Aim & Shoot]] is often used to enable [[Combat]] with goals to [[Capture]] or [[Eliminate]] visible [[Enemies]] or destroy [[Destructible Objects]], other goals and reasons are possible. [[Deliver]] goals connected to game elements can be done by throwing or shooting the game elements to the receiver and [[Capture]] can be the capturing of information rather than game elements. Shooting spider webs, throwing grappling hooks (as done in [[The Legend of Zelda series]] and [[Just Cause 2]]), or even firing cannons with oneself inside it (e.g. the [[Super Mario series]]) can give explanations for how [[Privileged Movement]] can be performed by [[Aim & Shoot]]. When [[Aim & Shoot]] is done for [[Combat]] purposes, the typical effect of successfully perform the action is either [[Damage]] or instant [[Game Element Removal]]. An alternative for [[Aim & Shoot]] in [[Combat]] is to make [[Friendly Fire]] possible - this is typically done to provide more [[Challenging Gameplay]]. The presence of [[Achilles' Heels]] in some [[Enemies]] can increase the difficulty of [[Aim & Shoot]] for some battles.
  
[[Aim & Shoot]] may most often be used in [[Real-Time Games]] but can be found in [[Turn-Based Games]] such as [[Scorched Earth]], the [[Worms series]], and the pool game [[Eight-ball]]. The pattern can also be said to occur in some war games (e.g. [[Warhammer 40K]]) where one first declares attacks and then checks if one has [[Line-of-Sight]].
+
[[Aim & Shoot]] may most often be used in [[Real-Time Games]] but can be found in [[Turn-Based Games]] such as [[Scorched Earth]], the [[Worms series]], and the pool game [[Eight-ball]]. The pattern can also be said to occur in some war games (e.g. [[Warhammer 40K]]) where one first declares attacks and then checks if one has [[Line of Sight]].
 
+
 
+
[[Exaggerated Perception of Influence]]
+
[[Freedom of Choice]]
+
 
+
[[Avatars]]
+
  
 
Interestingly enough, most sports games due not make use of [[Aim & Shoot]] even though this is one of the primary activities in sports they simulate. The cause for this is probably the lack of overview of the game state that players would have if they had perspectives that allowed [[Aim & Shoot]].
 
Interestingly enough, most sports games due not make use of [[Aim & Shoot]] even though this is one of the primary activities in sports they simulate. The cause for this is probably the lack of overview of the game state that players would have if they had perspectives that allowed [[Aim & Shoot]].
 
[[Damage]]
 
[[Game Element Removal]]
 
  
 
=== Interface Aspects ===
 
=== Interface Aspects ===
Line 43: Line 34:
  
 
== Consequences ==
 
== Consequences ==
[[Aim & Shoot]] requires [[Dexterity-Based Actions]] in [[Real-Time Games]]. This often also requires players to engage in [[Extended Actions]] and [[Timing]], and when this is done from an [[Avatars|Avatar's]] (or other game element's) point of view, [[Aim & Shoot]] promotes [[Spatial Engrossment]]. While less common in [[Turn-Based Games]], the pattern promotes [[Puzzle Solving]] in these.
+
As an activity that in most cases require skill, [[Aim & Shoot]] typically adds [[Performance Uncertainty]] to a game (the use of [[Aim & Shoot]] in [[Advanced Squad Leader]] being a counter-example). It is often used to make [[Combat]] possible, or to make [[Destructible Objects]] possible to destroy. [[Aim & Shoot]] requires [[Dexterity-Based Actions]]  and [[Timing]] in [[Real-Time Games]], and since players can see and imagine hitting or activating what the aim at the pattern can provide an [[Exaggerated Perception of Influence]]. As soon as there is more than one target for the action, [[Aim & Shoot]] instantiates [[Freedom of Choice]]. As soon as [[Aim & Shoot]] is made possible through an action of a diegetic [[Agents|Agent]], it is an [[Abilities|Ability]]. The action often requires players to engage in [[Extended Actions]] (mainly consisting of [[No-Ops]]), and when this is done from an [[Avatars|Avatar's]] (or other game element's) point of view, [[Aim & Shoot]] promotes [[Spatial Engrossment]]. While less common in [[Turn-Based Games]], the pattern promotes [[Puzzle Solving]] in these. [[Puzzle Solving]] is also promoted when the aiming is not directly to the target through [[Line of Sight]] but requires a more complex trajectory.
  
[[Aim & Shoot]] actions from [[Enemies]] naturally increase and present [[Evade]] goals.
+
[[Enemies]] that can [[Aim & Shoot]] rather than just shoot make [[Evade]] goals. While [[Maneuvering]] of [[Enemies]] can make [[Aim & Shoot]] more difficult, the opposite also applies: [[Enemies]] shooting at one makes [[Maneuvering]] more difficult.
 +
 
 +
[[Aim & Shoot]] can easily be appropriated by players to engage in [[Beat the Leader]] activities.
  
 
== Relations ==
 
== Relations ==
 
=== Can Instantiate ===
 
=== Can Instantiate ===
[[Evade]]
+
[[Abilities]],
 +
[[Beat the Leader]],
 +
[[Destructible Objects]],
 +
[[Capture]],
 +
[[Combat]],
 +
[[Eliminate]],
 +
[[Exaggerated Perception of Influence]],
 +
[[Freedom of Choice]],
 +
[[Line of Sight]],
 +
[[Performance Uncertainty]],
 +
[[Risk/Reward]],
 +
[[Tension]]
 +
 
 +
[[Puzzle Solving]] when not [[Line of Sight]] is sufficient
  
 
==== with [[Obstacles]] ====
 
==== with [[Obstacles]] ====
 
[[Surprises]]
 
[[Surprises]]
 
==== with [[Skills]] or [[Tools]] ====
 
[[Player/Character Skill Composites]]
 
  
 
==== with [[Real-Time Games]] ====
 
==== with [[Real-Time Games]] ====
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=== Can Modulate ===
 
=== Can Modulate ===
[[Enemies]],  
+
[[Achilles' Heels]],  
[[Combat]]
+
[[Combat]], 
 +
[[Evade]],
 +
[[Maneuvering]]
  
 
=== Can Be Instantiated By ===
 
=== Can Be Instantiated By ===
 
[[Alignment]],  
 
[[Alignment]],  
[[Capture]],  
+
[[Deliver]],  
[[Delivery]],
+
[[Enemies]],  
[[Eliminate]],
+
[[Privileged Movement]]
[[Line of Sight]],  
+
[[Tools]],
[[Privileged Movement]]  
+
[[Weapons]]
 
+
[[Tools]]
+
[[Weapons]], or the use of [[Resources]] such as [[Ammunition]]. The latter can introduce [[Tension]] to the activity and require [[Risk/Reward]] choices between shooting now or waiting for a possible better situation to shoot.
+
 
+
  
 
=== Can Be Modulated By ===
 
=== Can Be Modulated By ===
 +
[[Auto-Aim]],
 +
[[Ammunition]],
 
[[Competition]],  
 
[[Competition]],  
 +
[[Crosshairs]],
 
[[Evade]],  
 
[[Evade]],  
 
[[First-Person Views]],  
 
[[First-Person Views]],  
 +
[[Friendly Fire]],
 
[[HUD Interfaces]],  
 
[[HUD Interfaces]],  
[[Line-of-Sight]],  
+
[[Line of Sight]],
 +
[[Maneuvering]],  
 
[[Moveable Tiles]],  
 
[[Moveable Tiles]],  
 
[[Movement]],  
 
[[Movement]],  
 
[[No-Ops]],  
 
[[No-Ops]],  
 
[[Obstacles]],  
 
[[Obstacles]],  
[[Third-Person Views]],  
+
[[Player/Character Skill Composites]],  
[[Time Limits]],  
+
[[Resources]],  
 
[[Skills]],  
 
[[Skills]],  
 
[[Surprises]],  
 
[[Surprises]],  
 
[[Tension]],  
 
[[Tension]],  
 +
[[Third-Person Views]],
 +
[[Time Limits]],
 
[[Tools]],  
 
[[Tools]],  
[[Traverse]]
+
[[Traverse]],
 +
[[Variable Accuracy]],
 +
[[Weapons]]
  
 
=== Possible Closure Effects ===
 
=== Possible Closure Effects ===
Line 105: Line 115:
  
 
=== Potentially Conflicting With ===
 
=== Potentially Conflicting With ===
-
+
[[God Views]]
  
 
== History ==
 
== History ==
Line 113: Line 123:
 
<references>
 
<references>
 
<ref name="Bjork & Holopainen 2004">Björk, S. & Holopainen, J. (2004) Patterns in Game Design. Charles River Media. ISBN1-58450-354-8.</ref>
 
<ref name="Bjork & Holopainen 2004">Björk, S. & Holopainen, J. (2004) Patterns in Game Design. Charles River Media. ISBN1-58450-354-8.</ref>
 +
<ref name="kickshot">Wikipedia [http://en.wikipedia.org/wiki/Glossary_of_cue_sports_terms#Kick_shot section] for kick shots under cue sports terms.</ref>
 +
<ref name="light_gun">Wikipedia [http://en.wikipedia.org/wiki/Video_game_light_gun entry] for light guns.</ref>
 
</references>
 
</references>
 +
 +
== Acknowledgements ==
 +
Johan Wingård for the [[Duck Hunt]] example.

Latest revision as of 10:03, 13 May 2022

The action of taking aim at something and then shooting at it.

Combat is a common occurrence in games, and then many times through players having to Aim & Shoot. However, one of the most natural ways of showing attention to something is to look or point at it, and the action of Aim & Shoot can be generalized to describe any action where one indicates what one wants to affect through pointing.

Examples

The wargames Advanced Squad Leader and Warhammer Fantasy Battle requires that shooters have a clear line of sight to fire. They do also include indirect fire, but since this does not require calculations of trajectories it is for gameplay purposes very similar to ordinary Aim & Shoot.

Already the first Console Games included light guns[1] to allow players to aim physical gun props at their TVs. Duck Hunt is a later example of this type of games.

Aim & Shoot is more or less a defining trait in first-person shooters such as the Quake, Doom, Half-Life, Left 4 Dead, and Crysis series. It is also important in many other games with first-person views, e.g. the Deus Ex series and the Thief series as well as the latter installments of the Elder Scrolls series and the Fallout series.

Examples of non-violent applications of Aim & Shoot include taking photos in Dead Rising and Pokémon Snap, and using the grappling hook in The Legend of Zelda: The Wind Waker and Just Cause 2 (although the latter may be used to kill enemies even so).

The turn-based games Scorched Earth and the Worms series require players to aim their tanks and worms respectively before shooting, in some cases having to take into consideration wind effects.

Using the pattern

The normal use of Aim & Shoot actions requires that players are able to complete Alignment goals of two points by having Line of Sight. Crosshairs are very often used to support this Alignment, and this makes Aim & Shoot nearly trivial in First-Person Views in unstressed conditions, as one aim point is simply the player's view point unless either of the two points is moving. Somewhat more difficult are Third-Person Views, as more movement of the player's Focus Loci is usually necessary. God Views are in most cases too difficult, as it is too hard to get the Spatial Engrossment required in order to line up the two points accurately. However, an option to requiring Line of Sight is to require the judgement that shooting will create a suitable trajectory: either those close to parabolas simulating indirect fire (as in Scorched Earth and the Worms series), or those requiring bounces against other game elements (e.g. "kick shots"[2] in Eight-ball). The possibility of Aim & Shoot actions can be restricted by requiring Tools or Weapons, or the use of Resources such as Ammunition. The latter can introduce Tension to the activity and require Risk/Reward choices between shooting now or waiting for a possible better situation to shoot.

The difficulty of Aim & Shoot actions can be due to the Movement either of the game elements aimed at or the game element aiming. For Agents, the intentional Movement due to Traverse or Evade goals can make aiming at them more difficult, especially if the Movement is actually Maneuvering. For Moveable Tiles or other game elements, the mechanical Movement due to The Show Must Go On can likewise make aiming more difficult. The aiming can be further complicated by the players' own Movement of their Focus Loci or by a swaying of the aim to simulate the difficulty of real-world aiming. While performing No-Ops to slightly reduce the swaying is a common design feature, the use of Skills, Tools or Weapons can also motivate reducing the swaying; this Variable Accuracy is one way Player/Character Skill Composites can modulate Aim & Shoot. Various Auto-Aim solutions can also make Aim & Shoot actions easier through providing Player/Character Skill Composites. In contrast, aiming can be made more difficult by introducing Tension, for example through Competition or Time Limits.

The design of Game Worlds and Levels that makes players have a bad overview of the game state, for example the inclusions of Obstacles, makes it difficult to Aim & Shoot. This means shots will not be well aimed and that potential targets likely are Surprises and they are in turn Surprises by being shot at. Other forms of Surprises likely cause a Disruption of Focused Attention for players and make players lose their aim.

Although Aim & Shoot is often used to enable Combat with goals to Capture or Eliminate visible Enemies or destroy Destructible Objects, other goals and reasons are possible. Deliver goals connected to game elements can be done by throwing or shooting the game elements to the receiver and Capture can be the capturing of information rather than game elements. Shooting spider webs, throwing grappling hooks (as done in The Legend of Zelda series and Just Cause 2), or even firing cannons with oneself inside it (e.g. the Super Mario series) can give explanations for how Privileged Movement can be performed by Aim & Shoot. When Aim & Shoot is done for Combat purposes, the typical effect of successfully perform the action is either Damage or instant Game Element Removal. An alternative for Aim & Shoot in Combat is to make Friendly Fire possible - this is typically done to provide more Challenging Gameplay. The presence of Achilles' Heels in some Enemies can increase the difficulty of Aim & Shoot for some battles.

Aim & Shoot may most often be used in Real-Time Games but can be found in Turn-Based Games such as Scorched Earth, the Worms series, and the pool game Eight-ball. The pattern can also be said to occur in some war games (e.g. Warhammer 40K) where one first declares attacks and then checks if one has Line of Sight.

Interestingly enough, most sports games due not make use of Aim & Shoot even though this is one of the primary activities in sports they simulate. The cause for this is probably the lack of overview of the game state that players would have if they had perspectives that allowed Aim & Shoot.

Interface Aspects

Games with Aim & Shoot and First-Person Views very often have reticles in HUD Interfaces while those with Third-Person Views have some other kind of support for making players have Alignment with their targets.

Consequences

As an activity that in most cases require skill, Aim & Shoot typically adds Performance Uncertainty to a game (the use of Aim & Shoot in Advanced Squad Leader being a counter-example). It is often used to make Combat possible, or to make Destructible Objects possible to destroy. Aim & Shoot requires Dexterity-Based Actions and Timing in Real-Time Games, and since players can see and imagine hitting or activating what the aim at the pattern can provide an Exaggerated Perception of Influence. As soon as there is more than one target for the action, Aim & Shoot instantiates Freedom of Choice. As soon as Aim & Shoot is made possible through an action of a diegetic Agent, it is an Ability. The action often requires players to engage in Extended Actions (mainly consisting of No-Ops), and when this is done from an Avatar's (or other game element's) point of view, Aim & Shoot promotes Spatial Engrossment. While less common in Turn-Based Games, the pattern promotes Puzzle Solving in these. Puzzle Solving is also promoted when the aiming is not directly to the target through Line of Sight but requires a more complex trajectory.

Enemies that can Aim & Shoot rather than just shoot make Evade goals. While Maneuvering of Enemies can make Aim & Shoot more difficult, the opposite also applies: Enemies shooting at one makes Maneuvering more difficult.

Aim & Shoot can easily be appropriated by players to engage in Beat the Leader activities.

Relations

Can Instantiate

Abilities, Beat the Leader, Destructible Objects, Capture, Combat, Eliminate, Exaggerated Perception of Influence, Freedom of Choice, Line of Sight, Performance Uncertainty, Risk/Reward, Tension

Puzzle Solving when not Line of Sight is sufficient

with Obstacles

Surprises

with Real-Time Games

Extended Actions, Dexterity-Based Actions, Spatial Engrossment, Timing

with Turn-Based Games

Puzzle Solving

Can Modulate

Achilles' Heels, Combat, Evade, Maneuvering

Can Be Instantiated By

Alignment, Deliver, Enemies, Privileged Movement Tools, Weapons

Can Be Modulated By

Auto-Aim, Ammunition, Competition, Crosshairs, Evade, First-Person Views, Friendly Fire, HUD Interfaces, Line of Sight, Maneuvering, Moveable Tiles, Movement, No-Ops, Obstacles, Player/Character Skill Composites, Resources, Skills, Surprises, Tension, Third-Person Views, Time Limits, Tools, Traverse, Variable Accuracy, Weapons

Possible Closure Effects

Damage, Game Element Removal

Potentially Conflicting With

God Views

History

An updated version of the pattern Aim & Shoot that was part of the original collection in the book Patterns in Game Design[3].

References

  1. Wikipedia entry for light guns.
  2. Wikipedia section for kick shots under cue sports terms.
  3. Björk, S. & Holopainen, J. (2004) Patterns in Game Design. Charles River Media. ISBN1-58450-354-8.

Acknowledgements

Johan Wingård for the Duck Hunt example.