Those Colored German Dice

[JCool]

My dice arrived yesterday - fast shipping as i only placed the order a week+ ago. I ordered 6 of the multi-colored packs so that I have some variety. Quality looks good. I'll post pics later tonight.


Wall of dice: roll 36 dice in defense!


Size comparison of German dice vs. originals

[ShadowHawk]

Has anyone worked out the probabilities for the dice and dice combos? Looking at the nice, the new distributions look random rather than thought out. Here is a quick skulls comparison using just the original white and the new black die:

2d6 Original
Roll 2 Skulls: 1/4 (25%)
1 or more Skulls: 3/4 (75%)

3d6 Original
Roll 3 Skulls: 1/8 (12.5%)
2 or more Skulls: 1/2 (50%)
1 or more Skulls: 7/8 (87.5%)

2 White + 1 Black
Roll 3 skulls: 1/6 (16.7%)
2 or more Skulls: 7/12 (58.3.7%)
1 or more Skulls: 11/12 (91.7%)

1 White + 2 Black
Roll 3 Skulls: 2/9 (22%)
2 or more Skulls: 2/3 (66.7%)
1 or more Skulls: 7/18 (94.4%)

3 Black
Roll 3 Skulls: 8/27 (29.6%)
2 or more Skulls: 20/27 (74%)
1 or more Skulls: 26/27 (96.3%)

4d6 Original
4 Skulls: 1/16 (6.25%)
3 or more Skulls: 5/16 (31.25%)
2 or more Skulls: 11/16 (68.75%)
1 or more Skulls: 15/16 (93.75%)

Looking at the percentages, I don't see a reason for needing more than 4 sets of dice.

Original Set
Skull Heavy Set: 3 x1, 1 x2, 1 x2, 1 x1
White Shield Heavy Set: 2 x1, 1 x2, 1 x2, 2 x1
Black Shield Heavy Set: 2 x1, 1 x2, 1 x1, 1 x2, 1 Special*

*Special can be a unique symbol used for rare effect determinations in the quest.

That should give plenty of variability without breaking the bank. Also, each heavy die offers a lower probability but stronger effect for a converse result, allowing for manipulations of lowering probability of success in exchange for a higher number.

[lestodante]

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.

[arch8ngel]

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

[ShadowHawk]

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.

[lestodante]

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

[Anderas]

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.

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

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

[Maurice76]

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.

[ShadowHawk]

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.

[BStewart80]

I recently went to http://spielwarensaloon.de/ to purchase these dice described here. Sadly, my experience has not been very good. I originally purchased the white, green, black, blue, purple and orange dice in July and waited for weeks. I attempted to contact the website, but response was very slow. By the first week of August, the seller refunded my money and explained that Germany was restricted from mailing to USA due to the pandemic. I later reordered the dice and communicated that he can hold my purchase until the restriction was lift. As of September 2, 2020 the restriction has been lifted. I have attempted to contact the seller by sending two emails, one in English and another in German. In addition, I have sent multiple communication requests through the website. I haven't received any response.

I'm sure that everyone enjoys the product, but I can tell you the lack of communication from the seller has made this a very frustrating experience for the past two-three months. I understand the pandemic, and mailing restrictions. I don't understand the lack of communication.

I really would like to get these dice. Their nice and affordable. I can gather the graphics and go to boardgamemakers.com but 36 custom dice cost $150. I would hate to spend that much...though I am getting there.

Has anyone had any issues?