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Will....this die roll work?

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X3M's picture
Joined: 10/28/2013

If the army requires to many dice.

We replace every 4 dice with 1.
Make the same rolls as previously intended.
Then we roll a d6 as multiplier.

For 5 dice to 1. We have d6 +1.
For 6 dice to 1. We have d6 +2.

I still need to test this. Like literly drawing the results that anydice can't reach.
But the results so far are promising.

- Average outcome goes down.
- Chance on 0 goes up.
- Maximum outcome goes up.

But all are within a respectable range.


1 challenge remains.

36 dice can now easily be reduced to 6 dice.
As for sorting then.
A damage roll happens, before the multiplier roll.
This needs to be tracked somehow.

I CANNOT work with coloured dice here.
What else could I do?
Take note of the numbers of the damage roll?
Then sort them from low to high.
And roll in a box. Without watching, putting tyen in a row.???

larienna's picture
Joined: 07/28/2008
If you are using a binomial

If you are using a binomial distributions, like rolling X dices and counting successes, you could use the law of average.

if you hit on 5+, then every 3 dices scores a hit. So if you rolled 36 dices, 36 dices / 3 = 12 hits.

If you had 38 dices, then it's 12 hits + roll a die at 2/3 chances for the extra 13th hit.

Else, why do you need to roll 36 dices. The stats that gives you 36, can be applied to another variable than the number of dices. For example: roll a d20 + 36.

So just apply your value to another variable in your die roll than the number of dices.

X3M's picture
Joined: 10/28/2013
X3M wrote:If the army

X3M wrote:
If the army requires to many dice.

We replace every 4 dice with 1.
Make the same rolls as previously intended.
Then we roll a d6 as multiplier.

For 5 dice to 1. We have d6 +1.
For 6 dice to 1. We have d6 +2.

Law of average, right there.

d6 +2 has an average of 5.5.
So, replacement does punish the player a bit.
But the chance to roll lower and higher also increases.

X3M's picture
Joined: 10/28/2013
Also, I want to keep the...

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.

X3M's picture
Joined: 10/28/2013
I really like the replacement

I have never ever seen a distribution like this before. The averare is lower. And the Standard Definition is higher.

Make sure you pick the graph.

Remember, this weird result is done with only 6 dice.

X3M's picture
Joined: 10/28/2013
I will log my testing here, plus analysis

I made a mistake with the program. Here is a new one:
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)

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.

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.
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.

- 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.

X3M's picture
Joined: 10/28/2013
2 questions

1. What would be the rule of replacement? At how many dice do we go for a replacement? Since, well.... analysis paralysis will happen for certain. So.... make a list for the players to go by? Or some easy rule to go by? Not sure how the easy rule should look like though. I bet they need the list to skip all the calculations instead. So, just the roll.

2. How to sort the multipliers?
Have a tracking sheet for every die? Meaning, I count the projectiles per possible damage? And then sort the next roll. Then go back to the tracker and multiply accordingly???

X3M's picture
Joined: 10/28/2013
Rule of replacement?

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.

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.

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.

X3M's picture
Joined: 10/28/2013
I have made a decision

6 dice per set.
There will be....only 1 set.
The roll will be for only one group of projectiles fired. So the players need to make choices here too.

4 normal colours.
1 light and 1 dark.

1 to 6 dice will remain 1 to 6.
At 7 dice. The light and dark die will represent 4 dice, and only 3 normals are needed. The dark die as factor will have no modification.
At 8 dice. We have the same as 7 dice, but 1 extra normal die.
At 9 dice. We have the same as 8 dice, but the dark die will have a +1 modifier.

Not sure how to explain this all to players. But I think the best way is simply saying: Number of projectiles minus 8 is the modifier on the dark die.


Should I keep 7 projectiles as an exception?
Or should I have a negative modifier join?
Only minus 1 would allow a decent punishment.

larienna's picture
Joined: 07/28/2008
If you don't want to

If you don't want to substitute dices, that is fine. Simplify your rolling system. Use the KISS philosophy.

Get back to the basics, what are the objectives. EX: determine the winner and the amount of casualties.

Sometimes a single D6 can solve most solution. You could have in my example above 1D6 for winning, and 1D6 for casualties. One or two D6 CRT can also do a great job.

X3M's picture
Joined: 10/28/2013
I must substitute dices

Or else players end up with more than 12 dices. And by now it is bothersome.

I tried the CRT. Too much looking up, while it was also good in theory.

So, practically speaking, substituting dices. However, I didn't know what the best way was. But now I think I do.
And the way to get to it was taking some advice from someone I know in private life.
I went back to basics. And "added" a roll. And suddenly this worked.

And it comes with a bonus of "overkill" effect being more present. Something that dissappeared with lots of dice.
Now I am trying to see, how much I can cut into this mechanic for it to be working.

And if I can substitute dice while keeping it to 1 roll (not including the penalty rolls). That would be awesome.
I feel I am close. I have yet to test my new idea. Which is gona happen now.


The rule at the minimum (riflemen)

The following is all math and analysis again. I don't mind if you skip.

I will start at looking at 7 dice and the 2+3 dice substitute, but also the 2+4 dice substitute with the minus 1 on the factor die. This for my 7 riflemen.
And ehm... decided to look at 6 riflemen too, where the dice are always "normal".

They will be shooting at a tank so all damage counts.
Output 1: 7 riflemen, old rules
Output 2: 7 riflemen, 2+3 dice, +0 on factor
Output 3: 7 riflemen, 2+4 dice, -1 on factor
Output 4: 6 riflemen

Now to discuss. I look at the graphs for a better view.
Normal view shows me the averages

Group 1 clearly does more damage than group 4, on average.
And if it comes to kills, they are almost equals. Yet group 1 has 1 more soldier. And this will matter in round 4.

Group 1 also does more damage than group 2 and 3, again on average. But the maximum damage did go up. 28 to 36. But since I use so many dice in total (6, hahaaha) the chance on this is minimal. Let's see the damage needed to kill a trooper then (20 damage). 1% versus 10% and 7%. Group 2 wins this.

When killing at least 1 soldier (5 damage). We got 91%, 70% and 77%. Not sure if this difference is important...oooh, would you look at that. Group 4 has 84% here... So, the chance to kill at least 1 soldier goes down when you go from 6 to 7 riflemen. No matter which of the 2 are chosen.

The chance to kill 2 soldier. Thus 10 damage. 51% for group 1. But roughly 37% for all other groups. Rounding is sometimes a Bch.

Alright, let's observe 3 dead soldiers. Yeah, they keep silent...
Alright, killing 3 soldiers then. 15 damage.
12% 20% 17% 5%
Clearly group 4 is out of the picture here. Group 2 has the best score now.

Oh, silly me. Could have done this:

Apparently, there is even a decent chance in killing 5 soldiers with the new mechanic. I mean 4% is pretty big if you have these gamble's, right?
Well, I need to remind myself that getting to 25 damage with the mechanic in mind has overkill rolls.

I did all this testing to see which 7 I even wanted in the first place. I think I go for the modifier anyway. The difference is small enough. And the top isn't that much of a mess.


The rule at the maximum (riflemen)

Before I continue. I need to look at something awefull first. After all, I got only 1 substitute, as suggested by several.
What the F?!

Seems this is.... well awefull indeed.
The "6" substitutes looked much more refined in results.
But now we got an incomplete rollercoaster. Litterly. The player is launched into the ground. I knew there would be gaps in the graph. But as I feared, this is ridiculous.

When I look at the 75%, 50% and 25% markers. And consider how many might die....
9, 10 or 11 compared to 1, 7 or 19...
And that second list doesn't even happen due to the overkill effect...

Considering the overkill?

With 36 dice, I don't know how to do it. So, the fodder dice don't get this effect. Only the 1 substitute die.
If you still want to know something, the maximum number of kills with the original way is only 18. Chances on this is (5/6)^36*(1/3)^36.
I hope I did it right...(i edited a bit)
Seems 4 kills is impossible.
But the maximum number of kills goes down for the new mechanic.

Where the original makes 6 kills for certain. The new mechanic drops down immidiately. It's at 0...
The expected average of 10 kills is at 52% with the original. The new mechanic drops this to 41%.
It seems that 14 kills is the limit for the original. The new mechanic goes up to 18.
And the lists at the 25-50-75% markers are:
9-10-11 compared to 1-7-15. Ok, the upper limit dropped as expected. The calculation is more correct now.

The average and SD are also important.
9.6/1.8 compared to 7.4/6.7

X3M's picture
Joined: 10/28/2013
I suspect I need a new form

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
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.

X3M's picture
Joined: 10/28/2013

I only recently returned.
And it will be temporary.
And I will actually quit today, knowing my own past on boardgaming discussions.

But it is absolutely sure that this mechanic described in this topic doens't work well.

1. I didn't understand it myself after reading the topic.
I had to re-read again to make sure. ( I do tend to write to much )

2. I worked on a new balance method. But this one cannot be combined with the new dice replacement mechanic. The new balance method doesn't work for all my games. But the dice replacement seems to work for none.

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