Skip to Content

Reducing the number of dice

9 replies [Last post]
X3M
X3M's picture
Offline
Joined: 10/28/2013

I have found a neat way to reduce a certain number of die rolls for my game.

The 5/6th per roll, is used a lot. (Rolling 6 means a fail, and the sequence stops immidiately)
And it happens that the number of rolls can be a lot too.

This time, I don't want to alter the "exponential" effect into a "lineair" effect.

I did some calculations and thought of the following:

1 rolls of 5/6th equals 1 roll of 5/6th.
2 rolls of 5/6th equals 1 roll of 4/6th.
4 rolls of 5/6th equals 1 roll of 3/6th.
6 rolls of 5/6th equals 1 roll of 2/6th.
10 rolls of 5/6th equals 1 roll of 1/6th.

To compare the expected chances with the new chances:
0,833333333
0,694444444 is lowered with 4% to 4/6th.
0,482253086 is increased with 3,68% to 3/6th.
0,334897977 is lowered with 0,5% to 2/6th.
0,161505583 is increased with 3,2% to 1/6th.

***

I can allow "attacking" players to determine, which kind of rolls they use. But the bottomline is that 10 dice rolls will become 1 if they want to.
I bet that all players will combine the positiver outcomes with normal rolls. And that they will not use the negative rolls.

Chances grow exponential small, if players know that the target will make use of these rolls. So the high number of rolls, will be rare.

The only valid options now are 4 and 10 rolls. Since they have a slightly better outcome.
4 is an average situation.
And 10 is often the upper limit, caused by the new "slower projectile". Any chance on a higher number of rolls would mean that attacking players would not even take chances.

***

I can't imagine that no one has thought of this before: Is there a similar case with this?

Are there better ways to do this?

How do you guys feel about this approach?

pelle
pelle's picture
Offline
Joined: 08/11/2008
Did you consider a CRT? Do

Did you consider a CRT? Do anyone seriously consider using a CRT these days? Because I often see these systems using dice in ways that just seems to add complexity (and maths) that would be easier to do with just a small table, making the possible outcomes obvious and quick to calculate (and as a bonus they make it possible to completely tailor the probability distribution to what you want it to be, not being restricted by various tricks on looking for sides on combinations of dice).

I think CRTs (and tables) deserve to have a comeback sometime soon, because that would simplify many games and also allow them to have more interesting random outcomes without all the complexities and amount of stuff to remember with rolling dice with symbols or numbers on them and having to manually sort out what the results were.

X3M
X3M's picture
Offline
Joined: 10/28/2013
CRT

I don't see how CRT helps me with this.
I am already using it too. I didn't know it was called CRT though. I was calling it, "having 2 prints on each die side". (I actually got that idea from MtG, when I thought of rolling creatures)

Black numbers:1,2,3,4,5,6
Red numbers:0,1,1,2,3,3

Black is used for most, "roll this or less, then...", situations.
Red is used for damage out put.

So 2 numbers on each side. But there is room for a third. But in what way? Since the black numbers got it covered.

larienna
larienna's picture
Offline
Joined: 07/28/2008
I have an hard time

I have an hard time understanding your question.

- How many dice do you roll
- How much faces do they have
- What do you do with the results (Math or comparison)

Certain dice systems can have more variables than other systems. You might want to list the variables that you want to influence the system.

For example:

Roll X dice where the nb of dice greater or equal to Y must exceed Z

has much more variables than the roll

Roll 1 Die + X that must exceed Y

X3M
X3M's picture
Offline
Joined: 10/28/2013
The question was more of a

The question was more of a general one. If there are examples of other cases, where the die rolls could be sumarized to make it easier and simpler. Without discarding the balance of the game.

I want to know what is out there for examples, regarding simplifying dice rolls. Who knows how many dice rolls I can replace.

Maybe, the given example, can be done in even a better way?

***

In the given situation. I roll X times d6.
Any 6 rolled, and the entire pool is discarded.

I discovered that if I have to roll 10d6, with any 6 rolled is a miss. Equals 1d6 with any 2 to 6 rolled is a miss.

Is this a good approach?

larienna
larienna's picture
Offline
Joined: 07/28/2008
In a recent example, somebody

In a recent example, somebody triggered an event while rolling 2D6 with the same face. Which gives 1/6 chance of success, so rather simply roll a single D6 and trigger on any number you like.

You can look at some probability tables here can compare with your probabilities:

http://bgd.lariennalibrary.com/index.php?n=DesignMaterial.Material200907...

Rolling 10D6 is a lot, you can use the law of average if you want.

In average with 6D6 you would hit once (for 6+). So you could for example with 10D6 hit once + 4/6 chance to hit a second time ( 6 + 4 = 10). This is just an idea that could solve your problem.

gxnpt
Offline
Joined: 12/22/2015
percentage dice

Just calculate your tables rounded off to 2 (or 3 if you feel silly) digits and use a different colored d10 (numbered 0-9) for each digit.

pelle
pelle's picture
Offline
Joined: 08/11/2008
CRT = Combat Resolution

CRT = Combat Resolution Table. Very common in older war-games. Less common in recent war-games.

So instead of rolling some number of dice and using some algorithm to calculate what happens, you roll one or two dice and then just look in a table and get the answer in an instant.

And also the other way around, if the player wants to know what the possible outcomes are and how likely they are, they just need to look in the table. No need for maths. Or at least a lot less need.

CRTs can be printed on dice instead. Sort of. But I have not heard of anyone doing that since Reisswitz in his Kriegsspiel 1824. Lots of numbers on each side of those dice. Not sure how big they were, but probably a lot bigger than most common dice, or they had very small digits.

Desprez
Offline
Joined: 12/01/2008
pelle wrote:CRTs can be

pelle wrote:
CRTs can be printed on dice instead.

There are a number of ways to integrate CRT into dice, too. And dice have the advantage of faster resolution and less math than CRTs.

If you have a set of dice to pick from, you get a CRT but without lots of numbers or results per face.
Basically, the die you choose becomes the "row" and the faces become "columns" (or vice-versa.)

Alternately, you can get some CRT-like detail using symbol dice. You give the units symbols that correspond to attack and defense properties, where clever matching and distribution on die faces can result in complex behaviors.

X3M
X3M's picture
Offline
Joined: 10/28/2013
This is digged up? An update from my end.

The manual has been updated with the findings in the first post. Players have been given a table of suggested replacable rolls. With 1 to 4 for optimal and 1 to 10 for fastest. 20 is already ridiculous, but still valid. And the message for rinse and repeat has been given. Any more rolls would mean less than 1 hit on 36.

The whole thing is explained. And a most optimal table is given. Plus a table for a fastest resolution. Thus 2 tables.

There is no need for an extra CRT on the dice. Since the black numbers are sufficient.

I build up the tables like this:

Number of rolls needed - Replaced by rolls (optimal results)
1 - <6
2 - <6 <6
3 - <6 <6 <6
4 - <4
Rinse and repeat

Number of rolls needed - Replaced by rolls (fastest results)
1 - <6
2 - <5
3 - <5 <6
4 - <4
5 - <4 <6
6 - <3
7 - <3 <6
8 - <4 <4
9 - <4 <4 <6
10 - <2
Rinse and repeat

Syndicate content


forum | by Dr. Radut