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Weight of sorting

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X3M
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Me and my dice...just wanted to share some new findings.
What happens when I sort the rolled dice in a different way in my game?

I roll 12d6. And remove all 5 and 6 for this one.

I wanted to know the difference in weight of my dice rolls, in terms of killing soldiers. Each soldier has 5 health.

My options:
-1; would be a complete random distribution of the damage. Which was done in the good old days.

0; is the damage added up and split if nesesary for killing soldiers. We have 2 flavours here, an injury counts partly as a kill or not.

1; the dice are sorted in the most optimal way in order to kill as much soldiers as possible. 1+4=5, 2+3=5, 1+1+3=5 etc.
This is the current mechanic but we want to get rid of it mostly due to analysis paralysis.

2; the dice are sorted from low to high. The last dice that don't kill are an injury on the next target.

3; the dice are sorted from high to low. The last dice that don't kill are an injury on the next target.

***

I won't bother you with my math. Even I resorted to simulations now. Time for only the results.

My list now:

6.0 Kills, a maximum from all dice rolling high enough to have 2 dice killing a soldier.

4.0 Kills; option 0, a super average and super optimal roll.

??? Kills; option 1??? Not even sure if it will end up here.

3.6 Kills; option 0, removing injury from the equation.

??? Kills; option 1??? Not even sure if it will end up here.

3.3 Kills; option -1.

2.8 Kills; option 2 and 3.

***

It turns out that option 2 and 3 have an exact same killcount. However, there is a choice in which one deals more damage as injury to the next soldier. The weight in this seems to be almost 2 damage difference, on average. This choice occurs 60% of the time!
When comparing however, the low to high seems to have a very small higher advantage in injury damage. And this matters most with the 3 damage difference as well.

***

My goal so far is to find out where option 1 will end up.
I want it to be an Event Card. And/Or a weapon attribute (owww yes!). The weight in terms of kills would then be compared to option 2 and 3.

Another decision I need to make is if I allow option 2 and 3 to be a choice for the player? This choice is really, what the last damage will be as injury. Higher is better, dûhhh. But figuring this out for 12 dice with each roll seems a bit silly.
My decision should be "from low to high"

Having damage split up can also be introduced as an attribute. The weight would be 42% on top according to the kills. Since it is annoying to the enemy. I might turn this into 50% on top.
And the sorting would simply NOT be an attribute. Since it is annoying to the player.

***

But this effect is 42% with 5 health. I tested the rest and this followed:

It is +150% with 1 health. (The highest effect)
It is +48% with 2 health.
It is +23% with 3 health.
It is +21% with 4 health.
It is +42% with 5 health. (Uhm...wut?!)
It is +30% with 6 health.
It is +29% with 7 health.
It is +29% with 8 health.
It is +42% with 9 health.
It is +39% with 10 health.

Going higher will yield weird results. Since 12d6 results in 20 damage on average. And comparing kills turns out in comparing a chance to kill just 1 target instead. Which follows a different patern.

In the past, I had a concussive attack. This was always 1 damage, in contrairy to the 0,0,1,2,3,4 that I am working with.

I need to review that one. And also determine a good weight for splitting the damage.

Cheers, X3M

X3M
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Review of concussive attacks

A normal die deals 10/6 damage on average.
Relative durability on 5 health is 3.662.
Relative durability on 1 health is 1.500.

Concussive dice don't exist.
The always deal 1 damage.
A concussive attack deals 6/6 damage on average.
Durability on 5 health is 5.000.
Durability on 1 health is 1.000.

What are the factors of advantage?
Normal die versus concussive attack.
5.000/3.662 = 1.36 versus 1.
1.000/1.500 = 0.67 versus 1.
Thus concussive attack versus a normal die.
0.73 versus 1.
1.50 versus 1.

A normal die has a 36% advantage against 5 health targets.
A concussive attack has a 50% advantage against 1 health targets.

I have no clue as of why I also assigned a weight factor of 67% to a concussive attack. Probably the fact that 5 and 6 are removed? This would only make them more usefull against any target if 5 and 6 remain.

X3M
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Yeah, that was it...

Turns out, my old concussive weapons are 10% better overall than normal weapons when facing 1 or 5 health. But 10% worse overall than normal weapons against very high health.
Their weight factor remains 100%.

***

As for the normal dice being implemented as yet another concussive attack... let's call this splash damage, hmmmm? :)

With +150% more efficiency in dealing with 1 health targets. Or a factor of 2.5. I need a square root in this?

Result: 1.58 is the weight factor that I need in order to balance the weapon between complete distribution versus losses in overkill.

But I need to know for certain I do this right.
Note; yes, 1 health needs 1 dice.

If we apply splash damage:
We kill 1.67 targets of 1 health with only 1 die.
We kill 4.00 targets of 5 health with 12 dice.
We kill 1.00 targets of lots of health.

If we apply normal damage:
We kill 0.67 targets of 1 health with only 1 die.
We kill 2.82 targets of 5 health with 12 dice.
We kill 1.00 targets of lots of health.

Splash is 1.67/0.67=2.50 times more efficient against 1 health.
Splash is 4.00/2.82=1.42 times more efficient against 5 health.
Splash is 1.00/1.00=1.00 times more efficient against lots of health.

Splash needs a weight factor, such that 5 health becomes the norm for normal weapons. Although, there will be higher healths as well in the game.

***

I can go 2 ways, or a combination of the ways.

I either balance 1 versus lots of health.
Or, I balance 1 versus 5 health.

5 health is a basic factor. And those with "1" health with higher armor value's. Do have more than 5 health anyway. I know it sounds weird. So, I am going to calculate both ways to see how the weight works.

1 compared with lots of health has that square root of 2.5.
1 compared with 5 health has a square root of (2.5*1.42).

So, once more...
1.58
But this time we can go up to 1.88.
Let's see what happens here.

---

If we apply splash damage with a weight factor of 1.5:
We kill 1.11 targets of 1 health with only 1 die.
We kill 2.67 targets of 5 health with 12 dice.
We kill 0.67 targets of lots of health.

Splash is 1.11/0.67=1.67 times more efficient against 1 health.
Splash is 2.67/2.82=0.95 times more efficient against 5 health.
Splash is 0.67/1.00=0.67 times more efficient against lots of health.

Advantage factor is 1.67*0.95=1.58 over 5 health.
Advantage factor is 1.67*0.67=1.11 over lots of health.

---

If we apply splash damage with a weight factor of 1.67:
We kill 1.00 targets of 1 health with only 1 die.
We kill 2.40 targets of 5 health with 12 dice.
We kill 0.60 targets of lots of health.

Splash is 1.00/0.67=1.50 times more efficient against 1 health.
Splash is 2.40/2.82=0.85 times more efficient against 5 health.
Splash is 0.60/1.00=0.60 times more efficient against lots of health.

Advantage factor is 1.50*0.85=1.28 over 5 health.
Advantage factor is 1.50*0.60=0.90 over lots of health.

---

If we apply splash damage with a weight factor of 1.58:
We kill 1.05 targets of 1 health with only 1 die.
We kill 2.53 targets of 5 health with 12 dice.
We kill 0.63 targets of lots of health.

Splash is 1.05/0.67=1.58 times more efficient against 1 health.
Splash is 2.53/2.82=0.90 times more efficient against 5 health.
Splash is 0.63/1.00=0.63 times more efficient against lots of health.

Advantage factor is 1.58*0.90=1.42 over 5 health.
Advantage factor is 1.58*0.63=1.00 over lots of health.

---

If we apply splash damage with a weight factor of 1.88:
We kill 0.89 targets of 1 health with only 1 die.
We kill 2.13 targets of 5 health with 12 dice.
We kill 0.53 targets of lots of health.

Splash is 0.89/0.67=1.34 times more efficient against 1 health.
Splash is 2.13/2.82=0.76 times more efficient against 5 health.
Splash is 0.53/1.00=0.53 times more efficient against lots of health.

Advantage factor is 1.34*0.76=1.01 over 5 health.
Advantage factor is 1.34*0.53=0.71 over lots of health.

---

If we apply splash damage with a weight factor of 2:
We kill 0.83 targets of 1 health with only 1 die.
We kill 2.00 targets of 5 health with 12 dice.
We kill 0.50 targets of lots of health.

Splash is 0.83/0.67=1.25 times more efficient against 1 health.
Splash is 2.00/2.82=0.71 times more efficient against 5 health.
Splash is 0.50/1.00=0.50 times more efficient against lots of health.

Advantage factor is 1.25*0.71=0.89 over 5 health.
Advantage factor is 1.25*0.50=0.63 over lots of health.

***

I see a lot of numbers returning.
It is certain to me now that "splash damage" should have an advantage against <5 health.
No advantage against >5 health.

The weight factor of 1.88 is a bit silly though. And I am not sure if splash damage should have an advantage, disadvantage or be equal in effect against 5 health.

Please note; a concussive attack can never be combined with splash damage.
One is always 1 damage. The other is always the rolled damage distributed, which can go up to 4.

Concussive has a clear advantage against 1 health over 5 health. Against 5 health it clearly has a disadvantage. Concussive is going to be the chosen one in dealing with 1 health.

Thinking about how splash is supposed to be slightly more effective against infantry anyway. The weight factor should be such, that splash has an advantage factor > 1 over 5 health.
No, scrap that. It should be > 1 times more efficient.

And concussive should be an better option than splash against 1 health targets.

It has gotten late now. So I continue this with breakfast.

X3M
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Quick note

Concussive efficiency with weight factor 100% is:
1.500 vs 1 health
0.732 vs 5 health
0.600 vs ∞ health

That 1.500 should be higher than the efficiency of the splash damage.
That 0.732, idk yet.
That 0.600 should be preferably lower than the efficiency of the splash damage.

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