Age of Simulation

[Drib]

Hey everyone,

I just came back to Warhammer and did start a  fast growing Tzeentch army (about 3300 pts ins raw minatures (where did all my money go? )).

As I was a more or less professional MMORPG-Player, I was realy into simulations, and did them from time to time on my own. So that's how I came up with my new simulation project for my AoS battles too wich I'd like to present to you. For now, I only included all Tzeentch Units/spells, including the option to "dice" a spellcast to have a 100% chance to be cast,  and Kurnoth Hunters ( a friend of mine needed help to decide swords vs. scythe). All simulations are done using LabView (a system-design platform and development environment for a visual programming language from National Instruments)

 

I run 100k iterations for every saveroll the enemy has, from 0 to 2+ to determin the influence of any rend characteristics and every circumstances (as in the example - for Tzaangor Enlightened - whether there is a shaman nearby and/or an enemy unit in 3" already attacked). The wounds are then evaluated statistically and shown in a neat graph with the number of wounds on the abscissa and the associated probability on the ordinate. Most statistical values are shown ontop, their mean, standard deviation, max values, mode and the badluck probability to score 0 wounds.

The spells are cast in the same manner, 100k iterations. For my Tzeentch spells I can included Blue Scribes Buff and/or the Lord of Change bonus,

I also did some more specific simulations, like Ogroid Thaumaturge with combinations of Soulburn (trait) and spell enhancements (Infusion Arcanum and Arcane Transformation).

 

Any questions, thoughts, ideas (or maybe requests) are welcome.

[Tittliewinks22]

I don't think there's a whole lot of weight to simulations. Probability can be calculated pretty easily without running 100k "simulations"

Example, why run 100k simulations on scythe vs swords for hunters when you can easily math out their averages vs 2+/3+/4+/5+/6+/- save and curve off of that?

Sword: 4/3+/3+/-1/2

Scythe: 3/3+/3+/-2/d3

Before doing any math you can tell that at save 6+ or worse swords will do better on average 

At 5+: swords: 2.96 wounds avg; scythes: 1.33-4, 2.66 avg.

At 4+: swords: 2.37 avg; scythes: 1.11-3.33, avg 2.22.

Basically... I don't really get the point in simulations when probability works just as well...

Side question: what is a "professional MMORPG player?"

[Drib]

For your example it sure is  easy. But can you do it with rerolls and/or mortal wounds at 6+ or stuff like that. If so, sure simulations would be redundant and I'd better check my math. ?

Side answer: I played World of Warcraft for some bonus income during my Bechelor's degree and went on with it for about one year, before I got bored.

 

[Gotrek]

9 hours ago, Tittliewinks22 said:

</snip>

Side question: what is a "professional MMORPG player?"

People who use screen capture software to record themselves playing games, streaming the video on twitch and/or uploading chunks of the video to youtube. Twitch, youtube, and similar sites give content creators a cut of the ad revenue (and most are typically also supported via patreon). Viewers typically will tune in to learn how to best certain bosses, look for tricks to help with quests or getting to hidden areas, and simply to listen to the player for their views on the game. 

8 hours ago, Drib said:

For your example it sure is  easy. But can you do it with rerolls and/or mortal wounds at 6+ or stuff like that. If so, sure simulations would be redundant and I'd better check my math. ?

Side answer: I played World of Warcraft for some bonus income during my Bechelor's degree and went on with it for about one year, before I got bored.

 

Yes you can, thats typically how i do it because its a lot easier and faster than learning how to code the probabilities into a simulator. Basically you just need to keep in mind that any particular number on a d6 has a 16.6 (repeating) % chance of being rolled.

For example, skyfires (without shaman):

Unit leader (note he has a hit value of 3+, NOT +1 to hit): 1×0.5(1,2,&6 are off the table)= 0.5×0.66 (wound on 3)= 0.33

1×0.167=0.167

Other 2 schlubs: 2×0.33 (1,2,3, & 6 are off the table)= 0.66×0.66=0.44

2×0.167(rolling that 6)=0.33

(Going to go with a stock 4+ save for this comparison)

Leader: 0.33×0.66=0.22 (chance to get past save)

Peasants: 0.44×0.66=0.29

Leader: 0.22×2 (average damage on a d3)= 0.44

Commoners: 0.29×2= 0.58

Total normal damage: 0.87

Mortal wounds: 0.99

Total damage overall: 1.86

[Drib]

Okay, that's quite obvious and easy .. never thought of it. How do you calculate the rerolls of e.g. Guided by the Future Tzaangor Enlightened?

I guess for now, I will stick to the simulations, as I have a running template where I only have to input hit and wound values. To go straight to Simulations might have been a bit overkill. Maybe I will still find a use for it, like simulating a clash of two units or even an Age of Sigmar minigame.?

[Gotrek]

27 minutes ago, Drib said:

Okay, that's quite obvious and easy .. never thought of it. How do you calculate the rerolls of e.g. Guided by the Future Tzaangor Enlightened?

</snip>

Just doing the spears as an example 

7 attacks at 4+/3+ rend 1, damage 2 vs a unit with a 4+ base save.

7×0.5= 3.5 hits and 3.5 misses

3.5 misses × 0.5 (reroll) = 1.75 converted into hits. 

3.5+1.75= 5.25 hits

5.25×0.66 = 3.47 wounds.

1.78 (failed wounds) × 0.66 = 1.17 converted into wounds. 

3.47+1.17= 4.64 wounds

4.64×0.66 (4+ base w/ rend 1 means saves on 5s)= 3 go through × 2 damage each is 6 damage inflicted.

 

Now, if you want you can actually derive a set of..."reroll constants" (I guess that's a good word? I'm sure actual math nerds have a real term for it). Basically, if you need 4s and a rerolling everything then you can just multiply by 0.75 instead of 0.5 and the failures by 0.5 and adding them together. For 3s it's 0.88 (0.33 failures × 0.66 for the reroll is 0.22. 0.22+0.66 for the initial success is 0.88). 

 

 

Don't judge me.

[Drib]

Won't judge! Thanks for your reply it realy lightened up alot.

But as I said, having a runing template makes it a lot easier for me and I am too interested in the standard derivation so I will stick with it.

Again, thanks for your insights!

[Twitch of Izalith]

Thats possibly the most nerdy thing I have ever seen I congratulate you sir!

[daedalus81]

On 5/29/2018 at 3:17 PM, Tittliewinks22 said:

I don't think there's a whole lot of weight to simulations. Probability can be calculated pretty easily without running 100k "simulations"

Example, why run 100k simulations on scythe vs swords for hunters when you can easily math out their averages vs 2+/3+/4+/5+/6+/- save and curve off of that?

Sword: 4/3+/3+/-1/2

Scythe: 3/3+/3+/-2/d3

Before doing any math you can tell that at save 6+ or worse swords will do better on average 

At 5+: swords: 2.96 wounds avg; scythes: 1.33-4, 2.66 avg.

At 4+: swords: 2.37 avg; scythes: 1.11-3.33, avg 2.22.

Basically... I don't really get the point in simulations when probability works just as well...

Side question: what is a "professional MMORPG player?"

Probability doesn't cover everything.

12 * .666 * .666 * .5 * 2 = 5.3
9 * .666 * .666 * .666 * 2 = 5.3

Both of these things come to the same number, but both behave very differently in terms of randomness and potential.

Below is a more complex dice rolling simulation.
As you can see the difference between the weapons is pretty small with the scythe being a bit worse, but then again the scythe has extra range so if that ever matters it might be a better choice.

In 40K the variable damage can be a liability especially since you can't overkill models, but in AOS the lines are a lot clearer.

 

 

[amysrevenge]

If you have a computer, brute force (ie. simulation) can be easier than calculating probabilities.  Especially if there are conditional rerolls.  To get simple average damage it can still be easiest to just do the math, but to see the spread of the curve, simulation is probably much easier.    And sometimes knowing the spread is useful.

This isn't anything that has been unsaid in the thread, I just felt like chiming in hahahaha.

[MOMUS]

This wouldn't really work for me as I tend to always roll 6s.

Nice job tho :)

[Gotrek]

3 hours ago, MOMUS said:

This wouldn't really work for me as I tend to always roll 6s.

Nice job tho

BURN THE WITCH!!!!