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"Probability on D6 (new,)" Topic

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511 hits since 20 Jan 2023
©1994-2023 Bill Armintrout
Comments or corrections?

Khazi Kwarteng20 Jan 2023 6:13 p.m. PST

Disorder is achieved by scoring two sixes.
This is done by using 4 d6 dice .

A small unit has only 2,dice but still needs two ,sixes to disorder.

What is the probality please?

I'm rubbish at maths.
Thank you

Personal logo Editor in Chief Bill The Editor of TMP Fezian20 Jan 2023 8:31 p.m. PST

Wouldn't that be 1/6 x 1/6 = 1/36 or 2.78% ?

Stryderg20 Jan 2023 9:08 p.m. PST

I brute forced it in Excel and came up with:
13.1944 % chance of rolling 2 or more 6s on 4d6
2.7778 % chance of rolling 2 or more 6s on 2d6

Personal logo Editor in Chief Bill The Editor of TMP Fezian20 Jan 2023 10:17 p.m. PST

2.7778 % chance of rolling 2 or more 6s on 2d6

not much chance of rolling more than 2, eh? grin

Khazi Kwarteng21 Jan 2023 12:58 a.m. PST

Cheers gents .

If you added a +1 modify for Elite units ,
How would that increase the probality?

Thank you

FourDJones21 Jan 2023 2:31 a.m. PST

"If you added a +1 modify for Elite units ,
How would that increase the probality?"

No wonder you were no good as a chancellor.

Khazi Kwarteng21 Jan 2023 3:43 a.m. PST

Sadly my economic groundbreaking philosophy was to radical but lm sure when history is looked back on people will realise how brilliant l was.

+1 for Elites.( They need 5/6 then)
So disorder is caused on two sixes thrown by 4 dice.
elites would need 5 or 6 score on 4 dices.
What is the probality?

Personal logo etotheipi Sponsoring Member of TMP21 Jan 2023 5:44 a.m. PST

Exactly two sixes or at least two sixes?


I just went ahead and worked it anyway. This is how I explain it for simulation designers:


This uses permutations, so you treat each die as a separate thing. The chart shows the ways you can get exactly two sixes in the top secion, then how you can get more in the bottom two sections.

The number is the number of rolls on each die that will give you the result you want. So in the first row you have 66XX, so only one roll on the first and second die will give you six, but five rolls on the other two dice will give you "not six".

When you walk the possible patterns from left to right, it is pretty easy to get all the possible patterns. Separating them into groups of different outcome also makes it easy to walk the pattern, and give you interim results that you might want. For example, it would be easy to use this chart to figure out probability for exactly two or an even number of sixes.

The separation pattern of this also gives you a good visual on how this actually works. For example, when I did this this first time, I accidentally put a "6" in for one of the fives. Easy to see and easy to fix.

Using combinations (outcomes) instead of permutations (exact rolls) is the more efficient way to do this, but there is no easy visual (if you find one, tell me) or simple way to check your work. You write out the formula and you get your answer.

I think there is value in working through this manually if you are designing the system.

Things like the bonus (is it for exactly sixes or sixes or greater) can be worked on a replicant of the chart and compared side by side to understand how you are affecting things.

Personal logo Mister Tibbles Supporting Member of TMP21 Jan 2023 6:28 a.m. PST

I've been using the website AnyDice for ages for calculating dice odds. Learning curve is not steep.

Personal logo Extra Crispy Sponsoring Member of TMP21 Jan 2023 8:17 a.m. PST

+1 Mr Tibbles

Cormac Mac Art21 Jan 2023 8:57 a.m. PST

This is a way to calculate dice probability


Cormac Mac Art21 Jan 2023 9:00 a.m. PST

Looks like 4D6 rolling exactly two 6's is a 11.5% chance, and rolling two 6's on two D6 is a 2.7% chance.

robert piepenbrink Supporting Member of TMP21 Jan 2023 9:31 a.m. PST

"So disorder is caused on two sixes thrown by 4 dice.
elites would need 5 or 6 score on 4 [dice].
What is the [probability]?

Vastly greater, Khazi. Well over double your chances. But if you need a probability and don't know how to calculate it, you might want to consider another mechanic. Consider also that doing it this way, a -1 for levies makes a successful roll mathematically impossible.

Stryderg21 Jan 2023 9:31 a.m. PST

not much chance of rolling more than 2, eh? grin

Oh, it can be done, just not in 3 dimensions.
{stupid copy/paste/then not paying attention}

Stryderg21 Jan 2023 9:45 a.m. PST

Chances of rolling a 5 or 6, on 2 or more dice, when rolling 4d6;
So Robert nailed it :)

robert piepenbrink Supporting Member of TMP21 Jan 2023 10:28 a.m. PST

Thank you, Stryderg. I'm glad someone could do the math, even if it wasn't me. I could see the shape of the thing, but couldn't for the life of me to the exact numbers without losing a BIG chunk of afternoon.

But my apologies, Khazi. That last comment of mine was more snide than it ought to have been. Still, dice are subtle things, and if you're putting together (or modifying) a rules set, the whole process goes faster when you don't need outside help with probabilities. For me, this means
1. Make a set total number, adding or subtracting from the dice total for tactics, terrain and elite status.
2. Require a certain number on the dice--usually "6"--to do damage, but give more dice (or take dice away) for terrain, tactical position or training.
3. Require a certain number to do something--inflict damage, pass morale or whatever--but give elite units dice with more sides.
4. Do everything with percentages--D10's carefully marked for tens and digits.

Using any of these methods, it's very easy to calculate what the odds of accomplishing something are, and then to decide if those are the odds you want. Opposed throws are a little hairier, but at least it's easy to see who has the advantage.

But it's good of you to ask the question. I've seen games get to conventions where it was not possible for one side to score a hit, or even march to the objective, and the game designer never realized this.

Khazi Kwarteng21 Jan 2023 1:10 p.m. PST

Thank you everyone

Zephyr121 Jan 2023 2:58 p.m. PST

If you want to increase the probabilities, consider using rolled doubles instead of 6's… ;-)

Bunkermeister Supporting Member of TMP21 Jan 2023 7:29 p.m. PST

That's why I use a d20 in marked in 5% increments. It makes life a lot easier.

None of this decimal nonsense, none of this rolling to find out if something has a 3% chance of happening. Not worth the bother unless it's at least 5%.

Mike Bunkermeister Creek

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