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Subject: Math behind the dice. rss

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Marcus Hultqvist
Sweden
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Hello everyone!

So I'm currently working on die-system using custom d6s.
I've tried the system using real dice and a dice app but I would like the math behind it all.

Anydice, which I use frequently, is very good but unfortunately my "programming" skills are not sufficient enough to get what I what.

The system contains two different dice.
The attack die with the layout:
Miss
1
1
1
2
Trigger


And the defense die with the layout:
Miss
Miss
1
1
1
2


Note: This one I actually did manage to figure out using Anydice. Code if anyone wants it:
output 5d{0,0,1,1,1,2} named "Defense".
Change the 5 in 5d to any number to change amount of dice.


The max amount of dice you'll have is five, and I'd like to see the percentage of rolling any given number including the trigger with 1d6 up to 5d6s.

I've only come as far as to set the trigger to 100 in anydice since I have no idea if you can actually name the face of a die with "trigger" (only get a syntax error if I do).
Since math isn't my strongest point I came here for some help to atleast point me in the right direction.

And one final thing.
I've been trying to figure out now for the past hour how big the chance is of rolling a pair using three dice with both of my custom dice.
Is it the same probability that you can use in Yahtzee, that is 90/216 (5/12)?

That's all for now!
 
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Hervan Rossi
Brazil
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I think you have to tell us what "trigger" means, and how it's different from 1s and 2s.
Actually you have to say what "miss" means as well - what you got from the defense dice in anydice was the sum of those numbers rolling 5 dice, and when the sum is 0 it means all of them were misses, but if it's 2-10, you can't tell how many misses you rolled. (or maybe you're using a lot of wargame terminology that I'm not aware of)
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Cheb
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When you are rolling 1d6-5d6, are these all "attack" or "defense" dice or could it be a mixture of the two?
 
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Marcus Hultqvist
Sweden
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Oh I'm so sorry!

On the attack die 1 and 2 only means the amount of damage you make. Miss is 0.

E.g
I roll 2d6 and get 1 and 2 my total amount of damage is equal to 3.

As for the trigger, it will "trigger" either a passive or active ability.

E.g
You roll 3d6 and get Miss, 1, Trigger.
Incase that your weapon or ability has a trigger this will now become active and you make 1 damage aswell.

On the defense die it's the amount of damage you block. 1 and 2 means you block 1 or 2 damage and Miss is you block no damage at all.

Hope that cleared it up to some extent.


 
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Marcus Hultqvist
Sweden
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@Cheb

You have one attacker and one defender.
So the attacker will only roll his Attack Dice whilst the defender will only roll his Defense Dice .
 
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Cheb
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With lots of dice it becomes a big problem very quickly.

The way I would do it is use Excel to write out the combinations - an example of 2 dice here:

d1 d2
0 0
0 1
0 1
0 1
0 2
0 T
1 0
1 1
1 1
1 1
1 2
1 T
1 0
1 1
1 1
1 1
1 2
1 T
1 0
1 1
1 1
1 1
1 2
1 T
2 0
2 1
2 1
2 1
2 2
2 T
T 0
T 1
T 1
T 1
T 2
T T

You can then count the combinations you are interested in.

I've done this with your attack dice up to 3 dice - the probability of throwing a pair of anything is ~72% if you include triples and ~ 58% if you don't include triples.
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Franz Kafka
United States
St. Charles
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Hjuhuhmer wrote:
And one final thing.
I've been trying to figure out now for the past hour how big the chance is of rolling a pair using three dice with both of my custom dice.
Is it the same probability that you can use in Yahtzee, that is 90/216 (5/12)?

You can find the chance of rolling a pair as one minus the chance of rolling no pairs.

For defense dice, that would be:
Chance of rolling a miss (2/6), times
Chance of rolling a 1 (3/6), times
Chance of rolling a 2 (1/6), times
The number of ways these three dice results could be ordered (6, like abc-acb-bac-bca-cab-cba)

The probability of zero pairs on three defense dice is 1/6.
The probability of at least a pair on three defense dice is 5/6.
It would be slightly lower (37/54) if you just want a pair, and not the result where you get three of a kind.

Edit: For the attack dice, I've come up with 26/36 for at least a pair on the attack dice, and 21/36 for strictly one pair on the attack dice. I might show my work later when I'm not typing on a phone.
 
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Mark Rickert
United States
Templeton
California
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Your 100 trick should work, but you'll have to massage the data just a bit. For example, any result greater than or equal to 300 and less than 400 will contain exactly 3 triggers. Subtract 300 to get the number of hits.
 
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Jeremy Lennert
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You may find this relevant:

Re: Calculating Probabilities for Dice with Symbols, not Numbers
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Marcus Hultqvist
Sweden
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@Cheb

Thank you for taking the time to do that, it's highly appreciated.
I actually made an excel document yesterday with the range of 1d6-5d6 with 30 rolls for each set.
I do feel that the system works depending on how I balance it.

I mostly wanted actual numbers because showing the odds of different rolls in percentage can be nice to have.
 
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Marcus Hultqvist
Sweden
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@Franz

Thank you for the slight number crunching. So the odds of getting a pair is quite high at least for the 1s on the attack die.

And also thank you for the explanation it helps a lot!
 
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Marcus Hultqvist
Sweden
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@Mark

I will most likely do it that way. Not that the data itself is useful for me since I've tried the system and it does seem to work well in my initial tests but having the percentage makes the tests seem more complete. Also it's quite interesting

 
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Marcus Hultqvist
Sweden
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Antistone wrote:


Cheers! I'll check it out right away
 
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