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Those Colored German Dice

Discuss other HeroQuest expansion topics that do not fit into the above categories.

Re: Those Colored German Dice

Postby lestodante » Wednesday August 28th, 2019 8:53am

I am not sure you calculated them correctly, for example rolling 2 original combat dice the probability to obtain 2 skulls is 50%, not 25%;
On 3 black dice the probability to get a result of 3 skulls is 4/6 for each die so it should be 12/18 = 66%.
I am not sure if we are doing the same calculation, but anyway I agree that I need only 3 or 4 for each type and not even all types.


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Re: Those Colored German Dice

Postby arch8ngel » Wednesday August 28th, 2019 9:30am

lestodante wrote:I am not sure you calculated them correctly, for example rolling 2 original combat dice the probability to obtain 2 skulls is 50%, not 25%;
On 3 black dice the probability to get a result of 3 skulls is 4/6 for each die so it should be 12/18 = 66%.
I am not sure if we are doing the same calculation, but anyway I agree that I need only 3 or 4 for each type and not even all types.


His calculations are correct.

For 2 skulls on 2 dice the math looks like this:

1 die -- skulls 3 out of 6 faces = 1/2 = 50% probability

It gets slightly less intuitive once you start looking at outcomes involving multiples.

Probability = Number of desired outcomes / Number of possible outcomes

With 2 dice, there are 36 possible outcomes (i.e. 6 faces on each die -- 6*6 = a grid of 36 ways the rolls can match up)

There are 3 ways of each die to generate a skull -- providing 9 possible rolls that match two skulls.

The hypothetical grid looks like this

Die 1 --- Skull -- Skull -- Skull -- B Sh -- W Sh -- W Sh
Die 2
Skull X X X
Skull X X X
Skull X X X
BSh
WSh
WSh


So you can see that there are only 9 out of 36 possible roll combinations that give "2 skulls".

In direct calculation it looks like this:

Probability of the same outcome on 2 dice = (Probability of outcome on die 1) * (Probability of outcome on die 2)
or simply
1/4 = (1/2)*(1/2)




This is similarly why rolling 2 dice with 50% probability of an outcome doesn't just add together to give you 100% chance of 1 skull.
Instead if you look at the grid, you will see 9 ways that you DON'T get a skull (i.e. double shields of some kind).

That math looks like this:

Probability of outcome = 1 - (Probability of NOT outcome)
or
3/4 = 1 - (1/2)*(1/2) = 1 - 1/4
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Re: Those Colored German Dice

Postby ShadowHawk » Wednesday August 28th, 2019 1:12pm

lestodante wrote:I am not sure you calculated them correctly, for example rolling 2 original combat dice the probability to obtain 2 skulls is 50%, not 25%;
On 3 black dice the probability to get a result of 3 skulls is 4/6 for each die so it should be 12/18 = 66%.
I am not sure if we are doing the same calculation, but anyway I agree that I need only 3 or 4 for each type and not even all types.


I just edited the post as I realized I was missing "or more Skulls" for anything less than the max result. This is why the numbers don't reflect a bell curve but instead show a exponential curve.

As to 3 black dice the probability to get a result of 3 skulls is 4^3/6^3 = 64/216 = 8/27 (29.6%) You multiply, not add, to produce every combination.
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Re: Those Colored German Dice

Postby lestodante » Wednesday August 28th, 2019 7:31pm

Thanks for the explanation, but I guess I need the Talismane of Lore to understand this better...!


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Re: Those Colored German Dice

Postby Anderas » Thursday August 29th, 2019 5:01am

Nice discussion starting here.

In fact I am calculating this in life, each time, for each monster, when I start the Questimator. I should really find a way to publish it in a nice looking way.

For Heroquest, by the way, also the probs for Master and Guardian defense is interesting. :P

Or the difference if you attack with yellow instead white dice. :lol:

And displaying the results not as list of numbers but as YeOldeInn Smileys. :lol:


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Re: Those Colored German Dice

Postby Maurice76 » Sunday September 1st, 2019 12:07pm

You could of course try my Excel sheet, which has some macro code (which can be inspected, there's no password on it) to calculate it - and you can add up to 10 dice of any kind combined to determine the various odds.


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Re: Those Colored German Dice

Postby ShadowHawk » Sunday September 1st, 2019 5:20pm

The math is not that complicated, but you need to think it through (and possibly draw it out to wrap your head around it).

If you have 4 dice, 3 being white (3 sides with skulls) and 1 being black (4 sides with skulls), you can calculate what you need if you think it through a little bit.

For a result of 3 skulls or more, you have the following:

3 (1st die skull sides) x 3 (2nd) x 3 (3rd) x 4 (4th, blk die) = 108 This is the total possibility of 4 skulls being rolled
+ 3 x 3 x 3 x 2 (non-skull sides on the blk die) = 108 + 54 = 162 This is the total possibility of 3 skulls being rolled if the blk die fails to have a skull result
+ 3 x 3 x 3 (non-skull sides on the wht die) x 4 = 162 + 108 = 270 This is the total possiblity of 3 skulls being rolled if the 3rd white die fails to have a skull result
+ 3 x 3 (non-skull sides on the wht die) x 3 x 4 = 270 + 108 = 378 2nd white die fails to have a skull result
+ 3 (non-skull sides on the wht die) x 3 x 3 x 4 = 378 + 108 = 486 1st white die fails to have a skull result

And divide that total by the total possible sides available for a roll, which with 4d6 = 6^4 = 1296
486/1296 = 31/81 = 38.27%

Adjust accordingly to other dice. Hope that helps.
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