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The magical hammer of theoryhammer 
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Corsair

Joined: Thu Sep 26, 2013 6:24 pm
Posts: 89
Location: netherlands
You could do it differently though, you could calculate against what kind of units your particular unit has a good success rate (say 60%). for example, if you like playing MSU, including a unit of 14 witches, you could calculate what other units it can beat solo without buffs. this in turn can help you make the decisions on the battlefield. Well it would help someone like me who cannot do any math at all inside my head :-p. For me it would be easier to memorize all the units that your program says i have a 60% win chance against haha.

But you are probably right that the costs of making such a program don't outweigh the benefits :-P. Unless u can start a crowd funding and all warhammer players like me who cannot count can fund u to create such a program :-D


Wed Mar 11, 2015 3:44 pm
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Malekith's Best Friend
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Joined: Fri Oct 03, 2003 7:36 pm
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Location: Belgium, Brussels
Okay, but that's a different request. There you move in the opposite direction: given a situation, what are my outcomes? You narrowed down the search considerably and that can be done.
While it would take some time, given enough knowledge of the rules would enable us to work out such things for various circumstances, including magical buffs and debuffs. That is actually something I strive for in the future, but it needs a solid basis... Like the one presented in this topic ;)

One of the reasons I'm throwing in so much code in my theory posts is because I feel our community deserves a bigger knowledge base and more free open source support.

_________________
I love me a bowl of numbers to crunch for breakfast. If you need anything theoryhammered, I gladly take requests.

Furnace of Arcana, a warhammer blog with delusional grandeur.

"I move unseen. I hide in light and shadow. I move faster than a bird. No plate of armour ever stopped me. I strike recruits and veterans with equal ease. And all shiver at my coldest of whispers."
- The stiff breeze


Wed Mar 11, 2015 3:52 pm
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Corsair

Joined: Thu Sep 26, 2013 6:24 pm
Posts: 89
Location: netherlands
Isnt it essentially the same? You say known unit, known unit size, beats unknown unit and unkown unit size by fixed odd.

Is u can run that with chosen unit size 14 of witches, you can also do it with 10 and 40 and everything in between. Then you should be able to compare all the outcomes from this and see what the smallest unit size of witches is with the most successes controlled for a fixed succesrate (say 60%).

And if you can adjust the units to beat, say for instance, i want to use my witches only vs infantery and monsters, then you can use the program to select the smallest unit size to be effective for the purpose you want.

Instead of seeing what units your fixed unit (14 witvhes) can beat, you can find out what unit size you need for your fixed purpose (slay infantery and monsters).

Maybe its to much work to realize, i think this wil give valuable info


Wed Mar 11, 2015 6:19 pm
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Corsair

Joined: Thu Sep 26, 2013 6:24 pm
Posts: 89
Location: netherlands
Like you say: given the situation, what is my outcome?
But what i find more interesting by far is: I want this outcome, what situation am i minimally required to create.

In extension, this could eventialy mean that you could insert an opponants list, and you get counter units with minimum sizes.

Of course i am well aware that this is a computer program and it doesnt take human factors into acount. So the better list can still fail to the better general. And like you say, magic, msu, tactics, etc cannot be included


Wed Mar 11, 2015 6:26 pm
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Malekith's Best Friend
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Joined: Fri Oct 03, 2003 7:36 pm
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I took some time to think about this. It's an interesting point of discussion for sure :)
It is possible to build such a program, and it is possible to get numbers. The problem isn't getting numbers, but getting meaning out of these numbers. You juggle a lot of questions and ideas. A lot of them have potential, but some of them don't... and the difference is often subtle.

Quote:
Is u can run that with chosen unit size 14 of witches, you can also do it with 10 and 40 and everything in between. Then you should be able to compare all the outcomes from this and see what the smallest unit size of witches is with the most successes controlled for a fixed succesrate (say 60%).


Well, it is interesting to pit different sizes of a unit against a set of opponents. From 10 to 40. But what isn't interesting is having the algorithm tell you "X is the optimal size", even less so if it doesn't show the intermediate results. The reason is, that you simply can't capture "optimal" size based on the calculations I presented here.
There are too many aspects of a unit to capture its potential in a game. It's like replacing knights in chess by rooks because they are more powerful. You'll also be locked behind your peons for several rounds and more vulnerable to an opponent who knows how to use that against you.

So what lacks, here, is a perspective of that unit within the whole: the role of the unit within an army.

Quote:
And if you can adjust the units to beat, say for instance, i want to use my witches only vs infantery and monsters, then you can use the program to select the smallest unit size to be effective for the purpose you want.


This is interesting, because you're narrowing down the search to a specific role and purpose. This can help to explore potential roles of units. But you need to pay great care in how you formulate that role. Infantry and monsters come in so many shapes that you really need to be more specific. So much, in fact, that it becomes error prone which points me to this:

Quote:
Maybe its to much work to realize, i think this wil give valuable info


It can give valuable info in the hands of an experienced player who knows how to formulate the question with great care. It will be less usable for an inexperienced player who, unfortunately, may need a broader exploration to learn the ropes.

Quote:
But what i find more interesting by far is: I want this outcome, what situation am i minimally required to create.


What is interesting is that the program could return a set of situations and how they score/compare. It should be up to the user to interpret these results and evaluate what situations seem reasonable to achieve.
Without that layer of interpretation, mind razor will probably score top position in almost every comparison. But Shadow isn't always the best lore, and relying on mind razor isn't always the best tactic.

Quote:
In extension, this could eventialy mean that you could insert an opponants list, and you get counter units with minimum sizes.


Humm.. It could point at units effective against some match-ups. But I wouldn't take it so far that it gives you a counter list. Not based on these calculations anyhow.

What you could do, is feed both lists and have it automate every match-up, shot, damage and even combinations of these. This can help in building priority targets, revealing things to avoid or things worth the risk.

Quote:
Of course i am well aware that this is a computer program and it doesnt take human factors into acount. So the better list can still fail to the better general


Well... I sincerely doubt such calculations will give you the better list, because of those human factors. Numbers can only be followed to a point.

In particular these kind of calculations have their limitations:

1. There are too many factors that are not computable in the manner presented in this topic. Movement is a fine example in this. It's very valuable, but how would you take that into account in combat value? Dark Riders can not possibly match Black Guard in head-on combat. Yet everybody piles Dark Riders, and very few use Black Guards. Movement is but one of so many factors that influence the game, yet it is sufficient to show that you can not compute an optimal list based on combat value alone.

2. Comparing all units to reveal only the best sounds like a broad-perspective approach, but it's not. Some units simply won't come up because they don't have enough power individually. For example chariots, monsters, our Lords and Heroes while they are hardly ineffective. You may have to define what a good score is, for each unit individually :S

3. Like wise, comparing a unit's performance to all foes sounds like a broad-perspective approach but it offers only a very narrow perspective in its outcome. Let's say you want a unit that can beat 90% of the foes, and to illustrate the problem, let's assume there's 10 foes. So in this example you're looking for a unit size that can beat all but one foe. Then the "optimal" unit size is the unit size required to beat the second toughest foe. None of the lesser foes still matter. Even worse is that a cheap unit that can beat 80% of the foes will be trumped by an expensive unit that is tailored to handle that extra 10%. This isn't necessarily bad logic. You may want to tailor your list against tough opponents. But it is hardly a broad perspective on unit performance. Again, you may need to look at all the results and balance out what you consider a good return on investment.

4. There is an obscurity due to randomness. At some point numbers simply become unreliable. Take, for example, cannons. Its damage chart against most models looks something like this:
Image
Now that doesn't look so scary, does it? But once that cannon hits, it fits the textbook definition of a slaughter machine. The all-or-nothing "IF" at the start of the cannon's performance obscures the damage that follows. But given a shot or two, that hit will roll and heads will follow.
A similar effect occurs for impact hits, thunder stomps and combat resolution. For example, you may have a 40% chance to break your opponent in the first round of combat. That could be a 40% chance to win the game right there. But what happens if the opponent succeeds the break test? While it may prove computable to work out the second round of combat, you're already looking at such a different situation that the overall outcome becomes unreliable.

5. Trying to obtain guarantees can lead to over investment. As the previous point shows some numbers are unreliable, and investing more into a unit to get reliable scores isn't necessarily the answer. For example, Witch Elves vs 5-wide spearmen will have a very wide spread set of outcomes:
Image
In order:
  • Chance to do X wounds.
  • Chance to do at least X wounds.
  • Chance to do at most X wounds.
The difference between reliable top score and reliable low score is 7-ish wounds or 60%. Even with respect to the mean value, that's a 25%-ish increase. You'd be getting very big units in your results, that are far from optimal points wise.

6. Winning isn't always about a high chance of success but about creating opportunities. Sometimes, it pays off to pick a strategy with a small chance of success, but a great reward. I used to field units of 9 Shades a lot in our 7th edition book. And I would use them to shoot warmachines unless there was a higher priority target. The damage:
Image
Hardly a reliable tactic, but still a near 20% chance to delete a 3 wound warmachine outright, or 45% against a 2 wound machine. It pays off every once in a while, and that's always a sore blow to the opponent.

So... while you can get a calculated unit size with a given chance of success in several match-ups, I wouldn't dare to rely on a computed optimal number. It could very well be that the calculations steer you away from good unit sizes.

Now, a wholly different kind of approach is to make a set of units and pit it against a set of opponents with different parameters (magic, etc), then evaluate yourself how well they handle them. IMO this encourages more sensible questions such as:
- Is this viable? Can it work? Is it worth the shot?
- How can I (nearly) guarantee success, if needed? Can it be done?
- How can I block an enemy tactic, or create a window of opportunity?
- If I'm forced to stray from ideal match-ups, what are my odds and how I can improve them?
- What are the biggest factors? To Hit? To Wound? Number of attacks?

You need the human interpretation to take into account the factors that aren't computable. What is a good investment, after all?

_________________
I love me a bowl of numbers to crunch for breakfast. If you need anything theoryhammered, I gladly take requests.

Furnace of Arcana, a warhammer blog with delusional grandeur.

"I move unseen. I hide in light and shadow. I move faster than a bird. No plate of armour ever stopped me. I strike recruits and veterans with equal ease. And all shiver at my coldest of whispers."
- The stiff breeze


Mon Mar 16, 2015 5:48 pm
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