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Old November 6th, 2008, 10:16 PM
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Physics Terminology puts Order Marker Activation in Context

Context:

This thread is designed to look into the basis for using terminology and definitions from physics to describe actions taken in Heroscape.

The game of Heroscape is complicated enough with its own terminology, and it isn't my intention to exacerbate this problem. My inspiration for starting this thread originated when reading Jexik's opinion on why he feels Marcu Essenwein costs too much:

Quote:
Productivity in economic terms is the amount of output you get from a unit of input. Turn productivity (or perhaps more accurately order marker productivity) in Heroscape terms is simply what you get out of a given turn. How many figures are activated and how many dice can they potentially roll on their attacks in the space of one order marker? That's turn productivity.
In the discussion that followed in the Book of Marcu Essenwein, Rev and Jexik delved into some physics analogies and terminology:

Quote:
Originally Posted by Revdyer View Post
Quote:
Originally Posted by Jexik View Post
Quote:
Originally Posted by Revdyer View Post
I appreciate the large issues of turn productivity (reminds me of the difference in physics between force and work) that you raise, Jexik. HERE.
I already posted a link to that in here.

The next one will be about efficiency, which I guess the nearest approximation for physics would be friction.
Or entropy. (My undergrad thesis was about entropy in Shakespearean language.)
The following is my attempt to establish some common terminology that we can all understand and agree upon when discussing Heroscape (in physics language).

A quick recap of some physics definitions:

Force = mass * acceleration [vector i.e. directional]
i.e. force is required to overcome an object's tendency to stay at rest or its tendency to remain in motion in the same direction with the same speed (inertia)
Units: [kg*(m/s^2)] = [N]

Work = force causing motion [scalar i.e. non-directional]
Units: [kg*(m^2/s^2)] = [N*m] = [J]

Energy = the ability to do work [scalar]
Units: [kg*(m^2/s^2)] = [N*m] = [J]

Friction = reactionary force directed in the opposite direction of the force causing motion; occurs between opposing surfaces [vector]
Units: [kg*(m/s^2)] = [N]

Power = rate of doing work [scalar]
Units: [kg*(m^2/s^3)] = = [N*m/s] = [J/s] = [W]
aka [Work/time] aka [Energy/time]

Productivity = output per unit of input [scalar]
i.e. Productivity = output divided by input = output/input

Efficiency = actual output compared to the ideal/perfect output; unitless [scalar]
i.e. Efficiency = actual divided by ideal = actual/ideal

Applying physics definitions to Heroscape:

In Heroscape, I would define work as removing points from the opposing player's army and cards (i.e. killing units or applying wounds).

i.e. HS Work = (wounds and/or kills)

Work cannot be achieved without applying a force.

In Heroscape, you apply force by attacking i.e. rolling a set number of attack dice (d6, d20, or auto-wound/kill depending on the army card you are using). I will return to the subject of HS force when discussing whether work is done or not.

i.e. HS Force = attack dice rolls

In Heroscape, time units (increments of time) are broken down into the opportunities we are given to impose force. That is, time is represented by the order marker (which represents the turn, but is not stictly speaking the same thing).

i.e. HS Time = order marker ~= turn

A round is a specific bundle of lesser time units, the same way that an hour is a specific bundle of minutes (e.g. 1 hour = 60 minutes)

i.e. 1 round = 3 order markers ~= 3 turns

In Heroscape, power is the amount of work (i.e. kills) you accomplish in a unit of time (i.e. order marker).

i.e. HS Power = (wounds and/or kills) / (order marker)
i.e. HS Power = (wounds and/or kills) per order marker

This is where the definition of "turn productivity" fits best. In order to optimize your turn productivity as Jexik suggested, you would seek to get the most kills possible (output) in a single order marker (input), all other things being equal. As stated, optimal Heroscape play includes maximizing the power of your order markers (increments of time in HS).

Now, you are probably wondering where an opponent's defense fits into the picture, right? Well, here we go...

In Heroscape, friction (drag, resistance, etc.) is the defense of defending figures. That is, friction is the number of defense dice rolled (and includes all of the special statuses that prevent figures from being victims of auto-wounds/kills i.e. Soulborg status, Large status)

Without overcomplicating this analogy, friction (i.e. defense dice) is the reactionary force that opposes the force trying to do work (i.e. attack dice to get kills/wounds).

i.e. HS Friction = defense dice rolls + sum of status defensive bonuses

An object will remain stationary (that is not move and thereby resist the force applied to it to with the intention of doing work) so long as the (static) force of friction exceeds the force directed towards doing work.

An object is stationary when:
Friction > Force

Work is done when:
Friction < Force

Similarly in Heroscape, we have (over a large enough sample size i.e. where the number of rolls approaches infinity):

Defensive unit survival occurs when:
(Expected value of) Defense dice > (Expected value of) Attack dice
or
Shields > Skulls
i.e. Friction > Force

Defensive unit wounding/death and associated point loss for defending player occurs when:
(Expected value of) Defense dice < (Expected value of) Attack dice
or
Shields < Skulls
i.e. Friction < Force

Another way of saying this (that we all understand) is that wounds/kills happen when the number of skulls rolled exceed the number of shields rolled.

So far so good.

Exploring efficiency in the context of Heroscape:

So far, the above terminology only introduces complication to an already terminology/jargon-laden game.

It is in the examination of Heroscape efficiency via physics terminology that some benefit is gleaned.

Heroscape is set up so that all players are given an equal number of time intervals (i.e. order markers) each round.
*Special consideration will be given later to order markers lost from abilities like Dund et al. and/or army cards lost in battle*

Likewise, players are given an equal number of points (e.g. 500).

How then, can any player hope to win a game of Heroscape?

(If you are inclined to say "pure luck" in response to this rhetorical question, then please stop reading now and contribute your opinion to the discussion here).

Intuitively, we all know how a player can win at Heroscape.

Victory in Heroscape is achieved by applying more force to do more work over a shorter time period (i.e. more power) than an opponent while simultaneously attempting to apply greater resistance to the opponent's attempts to do work...

This is the same as saying:

Quote:
"I usually roll more dice than my opponents in most games." -Spider_Poison
I have heard many other skilled players attest to the same thing as Spider_Poison.

Both the physics analogy for winning by applying more power and the "roll more dice to win" statement are gross oversimplifications. Nonetheless, they are fairly accurate in my opinion.

How, then, do we roll more dice or apply more power in Heroscape? This is where Turn Productivity and Efficiency come in.

Maximizing turn productivity demands that we maximize the number of attack dice rolled and the number of activations granted by a single order marker (the base unit of time in Heroscape). To maximize attack dice from a single order marker, we seize Attack glyphs, take height, and take advantage of other bonuses. Likewise, multiple activations may be attained through multiple normal attacks; multiple special attacks; multiple target special attacks; special powers in addition to normal attacks; multiple target special powers; and/or squad figures.

As a rule of thumb, you will be using more activations, as an attacker, the more times that the defender must roll defense dice and the more times that you roll attack dice. These things are obvious, right?

The concept of maximizing both activations and attack dice may seem obvious, but it is often overlooked by players when placing order markers. As Jexik pointed out, a turn spent on Marcu (a single activation unit) represents an opportunity cost of the activations that are forfeit by doing so. The opportunity cost in this case is the difference between the number of activations enabled by an order marker on Marcu as compared with the number of activations enabled by other cards in your army.

So now that we have covered the concept of turn productivity, how does this relate to efficiency?

Being 100% efficient stipulates that actions are conducted so as to achieve a result that is as close as possible to the ideal result.

In the field of computational optimization, (close) approximations to the true solution are achieved by relying on vast computing power and sophisticated algorithms (e.g. hill climbing, annealing, genetic programming, etc.). In Heroscape, we don't have access to (or chose not to have access to) the solution resolving power of computational optimization. Nonetheless, we are always trying to determine what is the best move for any given situation.

For any board position, I suppose that their is an optimal move (or moves) that would maximize the game-long pursuit of victory. However, I would contend that this move does not always coincide with maximizing order marker productivity or order marker power.

Certainly, in a straight-up battle, the player who deploys more attack activatations with more attack dice on a more consistent basis will have the greatest likelihood of winning. Nonetheless, relying strictly on turn productivity discounts the concepts of time/opportunities and friction.

In Heroscape, we not only have to worry about maximizing our power for any one order marker. We must also contend with the actions of our opponent and try as best as possible to prevent them from depriving us of opportunities to apply force.

We can be denied of oppotunities to apply force by losing units in threat range and by losing unspent/unrevealed order markers. Both of these setbacks may contribute to our defeat.

The converse is also true. By targeting our application of force so as to deny the opponent opportunities to apply force we improve our chances for victory.

Therefore, the most efficient use of an order marker in Heroscape is the move that maximizes our power (i.e. kills per order marker) while balancing the needs to both deny our opponent opportunities to apply force (i.e. target acquisition of army cards with unrevealed order markers in threat range) meanwhile applying as much resistance as possible to our opponent's application of force (i.e. maximize defense dice and status immunities of our own units in threat range).

Essentially, I'm not saying anything that hasn't been said elsewhere in discussions of In-Game Point Value, Order Markers (UPC) or What's in an order marker?.

However, I think I have demonstrated what many of us know intuitively: Heroscape does not come down to merely maximizing the output of an order marker but also encompasses defensive considerations and the importance of seizing time-scale advantages by denying opponents of their turns through appropriate target acquisition and prioritization.

This has been my attempt to apply physics terminology to the language of Heroscape. I think the analogy of using physics is appropriate, given the importance of order markers in Heroscape (i.e. time) and the special distinction physics pays to the absolute value of applying energy (i.e. work) as compared with the rate at which energy is applied (i.e. power = work/time).

Last edited by mccombju; November 10th, 2008 at 11:00 PM.
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  #2  
Old November 6th, 2008, 10:28 PM
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Re: Physics Terminology puts Order Marker Activation in Cont

Well said!

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Old November 6th, 2008, 10:34 PM
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Re: Physics Terminology puts Order Marker Activation in Cont

Quote:
Originally Posted by mccombju View Post
Therefore, the most efficient use of an order marker in Heroscape is the move the maximizes our power (i.e. kills per order marker) while balancing the needs to both deny our opponent opportunities to apply force (i.e. target acquisition of army cards with unrevealed order markers in threat range) meanwhile applying as much resistance as possible to our opponent's application of force (i.e. maximize defense dice and status immunities of our own units in threat range).
This is a key point when playing most superheroes. Where you end your turn-- and especially end your round-- is as important as who you attack and when. Often, you have to resist the temptation to land the hardest hit you can if that would allow the enemy to get in a full turn of attacks on you. A less damaging attack, if answered by little or no enemy fire, is better than your full attack on him followed by his full attack on you.
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Old November 6th, 2008, 10:39 PM
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Re: Physics Terminology puts Order Marker Activation in Cont

Makes sense... I don't know what to say to this...

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Old November 6th, 2008, 10:46 PM
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Re: Physics Terminology puts Order Marker Activation in Cont

Nice article! How do you relate counterstrike though?

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Old November 6th, 2008, 10:47 PM
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Re: Physics Terminology puts Order Marker Activation in Cont

Hmm, is there something in there about overkill?

Marvelscape vs Heroscape has that a lot.

Maybe add "Maximizing force on the opponents close but slightly less friction."

Very good though. I think I know what I want to study now, because it seems very interesting.

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Old November 7th, 2008, 12:02 AM
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Re: Physics Terminology puts Order Marker Activation in Cont

Quote:
Originally Posted by LongHeroscaper View Post
Nice article! How do you relate counterstrike though?
Thanks.

Counterstrike is very tricky... As far as I'm concerned, it could go either way.

I'm inclined to think that counterstrike would be considered an application of force (you are rolling attack dice... even if you are rewarded for shields as opposed to skulls) to achieve work (i.e. wounds/kills) that only triggers under special circumstances (against normal attacks; not even on your own turn!).

Alternatively, you could say that Counterstrike is resisting your opponent's application of force. This would be true especially in the event that your opponent neglects to use his/her own attack activations against the unit(s) with Counterstrike for fear of taking wounds and/or losing units.

All told, Counterstrike falls outside of the definitions supplied. It seems to be an exception to my contrived categories for applying physics terminology to the language of Heroscape.

Last edited by mccombju; November 7th, 2008 at 01:16 PM.
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Old November 7th, 2008, 12:14 AM
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Re: Physics Terminology puts Order Marker Activation in Cont

Counterstrike = Potential Energy, waiting for something else to act upon it. or something like that...
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Old November 7th, 2008, 12:22 AM
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Re: Physics Terminology puts Order Marker Activation in Cont

Quote:
Originally Posted by LongHeroscaper View Post
Nice article! How do you relate counterstrike though?
Counterstrike could be something like entropy. An inefficiency in attack. Or it could be a direct counter force that is applied in some situations.

I think a physics term that might connect all of this together in entahlpy, or flow work. It is actually the energy that can be harnessed from a moving fluid. Every fluid had an internal energy (defined as a Work element in the HS example) This energy is amplified by the velocity of the flow. A slow moving fluid with a lot of internal energy (High attack but few activations) has much less entalpy than a high speed fluid with low internal energy (low attack, but many activations (Q9 anyone)) Power plant engineers spend their whole lives playing with states of water to harness the most energy from it.

There has been a lot of work done in this particular area in the Battletech game. They mathematically related damage potential and surviveability into a factor called battle value. You could compare battle vaues and predict which unit would win a fight.

Using these physics relations it may be possible to calculate the battle value (enthalpy) of Heroscape units. Remember that energy and work are found by intigrating. If we can quantify the Force (attack dice) and the time, we shoud be able to calculate Energy, and by default entahlpy.

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Old November 7th, 2008, 12:52 AM
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Re: Physics Terminology puts Order Marker Activation in Cont

Another thing I would relate to: While force and work are all deterministic, Heroscape involves a lot of randomness. So, should we talk about quantum physics instead of classical physics?

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Old November 7th, 2008, 01:16 AM
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Re: Physics Terminology puts Order Marker Activation in Cont

Quote:
Originally Posted by LongHeroscaper View Post
Another thing I would relate to: While force and work are all deterministic, Heroscape involves a lot of randomness. So, should we talk about quantum physics instead of classical physics?
Heisenberg's theory of Heroscape Physics "One can not know the outcome of any attack until it actually takes place"

Schrodinger's Dund "If Dund was dead in the box, would he still be useless?"

You can actually quantify the uncertainty of randomness, actuaries do those types of calculations all the time. Attack potential cold be modified by statistics.

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Old November 7th, 2008, 01:21 AM
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Re: Physics Terminology puts Order Marker Activation in Cont

Quote:
Originally Posted by Ryougabot View Post
Quote:
Originally Posted by LongHeroscaper View Post
Another thing I would relate to: While force and work are all deterministic, Heroscape involves a lot of randomness. So, should we talk about quantum physics instead of classical physics?
Heisenberg's theory of Heroscape Physics "One can not know the outcome of any attack until it actually takes place"

Schrodinger's Dund "If Dund was dead in the box, would he still be useless?"

You can actually quantify the uncertainty of randomness, actuaries do those types of calculations all the time. Attack potential cold be modified by statistics.
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