Will....this die roll work?

Subtle overkill on certain dice.

And this new mechanic increases the chance on this effect.
The overkill adds more balance to the fodder too.
I am winning in 2 ways already.

36 dice would be 6 dice with +2.
38 dice could be 4 dice with +2 and 2 dice with +3.

Stil 6 dice at most.

***

Law of average:
d6+0 has 3.5 used for 4.
d6+1 has 4.5 used for 5.
d6+2 has 5.5 used for 6.
...
d6+17 has 20.5 used for 21.
d6+18 has 21.5 used for 22.

I also have a 2x 64 dice moment.
This is a rare moment.
Each bucket is a different roll.
So each bucket needs a reduction.

If I want my goal to be 6 in total. I allow only 3 dice per group.
The value's are 21+21+22.
So, we need 2d6 +17 and d6 +18.

Maybe, I should tell you that the roll here. Can still end up as 0. Because the other rolls will discard the dice. And also act as a factor.

Gona cook up the biggest and rarest option. To see, how it translates to the 6 dice.

I made a mistake with the program. Here is a new one:
https://anydice.com/program/34ba9
It slightly changed. More gaps. But it changed only slighlty.

As for the rest of this post. It is all math and analysis. Sorry, but I simply track it here ;)

Current test
Slow increase of basic soldiers. And their dice replacements.
The riflemen have an accuracy of 5. And a damage die of d6-2.
I brainstormed on a distance with one of my most experienced players.

This test showed me, that the factor die will not get a subtraction. It seems that the risk has to be spread out.
So, 1 to 8 dice were kept as is.
Only at the ninth, my testing buddy wanted to start replacing the dice with a factor die.
Not sure how to put this in a formula here...

But the main reasons are:
1. To spread the risk as much as possible. And therefor getting a stronger average.
2. To get a percentage penalty to be as low as possible.
6 to 1 has a 5% penalty (5.5/6)

Original
9 dice, roll 5 or less for hit, roll d6 -2 for damage per projectile.
With replacement
3 dice, roll 5 or less for hit, roll d6 -2 for damage per projectile.
1 die, roll 5 or less for hit, roll d6 -2 for damage per projectile, roll d6 -0 for a factor.

Note
As for what is the best option?
I made a comparison of all ONE optional replacements.
Meaning, you keep the normal dice. But get alterating ammounts of replacements.
And I think, I need to set up a rule for getting replacements. After all, players will at least keep the normal rolls too at certain ammounts. So, what should be the replacements then?

The overkill is not included here yet.
Either way, I replace more and more dice into 1.
Just read is as the output number is the number of dice that are replaced by the 1 replacement die.

https://anydice.com/program/34baa
Best observed by using "graph"+"at least". And it looks like 9 outputs is a bit too much already.
If you want to observe the normal. Perhaps removing the last 2 outputs will make the graph easier to see.

What I see is:
- The average drops down. But somehow halts at 10.42.
Why this happens? Probably because the multiplier roll will not have a 0.
- The Standard Definition drops 1 time. Then starts to slowly increase. Until it even exceeds the average at the last 2 outputs. Either way, replacement dice give much more risk to the roll. Which makes the game, more of a game.
- The last output shows gaps now. This is due to that the multipliers minimum is high. And there is only a replacement die here. All replacement dice will show a gap if there are no normal dice present.
- The more we get the replacement die, the higher the chance we get to roll 0. High risk, high reward? It seems this doesn't hold true? The maximum damage increases only with 4.
On which the chance to roll this is...A little over 2%.
- The replacements maximum 4's, start at 3, while the fodder dice are at 7. We want a fodder die to complete the maximum die. Then we got 4 and 6, 5 and 5. Assuming that the chance on having an average number of hits on the fodder dice is 56%. Thus almost half. We know that the best chances to complete are roughly at output 2 or 3.
- Further analysis shows me that if we look at the chance on 20 damage. Also slowly increases after a little dip. 20 damage is enough to defeat 1 trooper. The chance on doing this goes as following:
6.5% 5.5% 7.1% 9.5% 12.2% 15.1% 18.0% 21.1% and 25.5%.
As for defeating 2 troopers. Only the last 2 outputs show a chance... 0.3% and then 2.3%. Which is almost nothing though.
- Final analysis. Where I consider killing an X ammount of soldiers. Assuming, we roll "4's". And thus every 8 damage, we defeat an infantry unit. We look at 8 damage, and the chance to defeat 1 soldier here is:
87% 76% 70% 64% 59% 54% 50% 49.5% 49%
This seems to....decrease. And the chance is even only half, eventually. So, if you want to deal with fodder. Seems having more dice is indeed the way to go.

Conclusion
- The normal 9 dice seems to be preferred for the fodder.
- The 1 replacement seems to be preferred when dealing with the next tier of units.
- The first realistic replacement seems to be at 4 to 1. But here the optimal completion will be incomplete.

***

One more thing. Once all the rolls are done with the coloured dice. The "damage" should be tracked.
Then the dice are rolled again. But have to be sorted for the multiplier. I think that this should be my main focus for now.

Then, I need to see what happens if I only use replacement dice. For this. I could start with 12 riflemen. Or even 36.
12x1, 6x2, 4x3, 3x4, 2x6 and then 1x12. Or even starting with 36x1, which would only include a 6x6 in the whole list.

And ehm.... I think that my previous AnyDice example would be done differently in the game by other players.

I think I need to combine the 2 challenges.

Each roll for a set of projectiles should contain 3 variants of colour. For example: Light blue, blue and dark blue.

The light and dark variant would serve as a team. Where the dark would be a multiplier die to the light one.

As for the normal variants. I need at least 1.

This way, I can roll the dice for penalty. Then once the damage roll is needed. If the light die is still present. I can add the dark die. There is now, no need for sorting.

***

I have 2 options now for expanding this mechanic.

1.
I add more of the normal variant. Not exceeding a total of 6 dice. This means there are 4 normal ones. And this will allow for a better distribution of the damage dealt.
However, with each type of projectile, the player will be rolling 1 to 6 dice. With the current mechanics, this is doable.

2.
I allow only 3 dice per colour. And I add more sets of different colours. Where they double as extra projectiles of the same kind. Just like option 1. Or they are a separate set. But making a roll distribution bad.

I prefer option 1.

I suspect I need a new form of tracking damage for the projectiles.

But I am going to rewalk the path again of all the tweaks I did for going for a public game.

- No damage rolls, just hits.
- No multiple health, just armor.
- Less units.

Heck, even miniatures can be on the menu again.
Thus damage tracking can be done with cubes or pins, probably cubes.

***

Picturing 6 riflemen now. Oh, no need for the factor dice...
Picturing 4 flamethrowers now... I forgot their multipliers...4 per unit I think.
Ok, 16 projectiles.
The factor die is +8.
So 9 to 14 is the factor here.... IF the other die is a hit.
And the other 4 dice are 0 to 4. Each a 1/3rd chance for a hit.

It makes no sense.
The squad either kills 0 to 4 riflemen.
Or all 6 are fried at a 33% chance.

Only 3 flamethrowers are also still wacky.
The factor die is +4.
No gaps in kills. But clearly, killing 4 is rare.
And the chance to fry the whole riflemen squad is still 32%. Yes, you read that right.

Ok, lets consider 2 flamethrowers.
This time, we have only a 13% to fry them all. The kills also seem to be better distributed.

At least i know that the original way had a better distribution. Average/Standard definition
1.33/0.94
2.67/1.33 2% to fry all 6.
4.00/1.63 18% to fry all 6.
5.33/1.89 45% to fry all 6.

This new mechanic is better with damage dice. But has been rather dissapointing with hit=kill mechanics.

Perhaps I should have the "factor die" act per unit here. Then we get only 4 dice per flamethrower squad.

Going to look into that.