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April 27th, 2017, 04:30 PM   #1
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Probability - Game

Hello all, first time here.

I am not exactly an expert at maths (far from it), but I am working on making a dice based probability game for myself and my friends.

At its core, you roll between 1-5 10 sided dice (D10). You will add a flat number to that roll between 0 and 10. Giving a range of 1-20.

However, the kicker is if you roll a double you can take the number displayed on the double and add it to your total. However you can only add this extra from one set of doubles (so if you roll a double 10 and a double 6 you will only take the double 10 adding 10 to your total. )

What I'm trying to work out is the probability of reaching any given number with the varying range of dice and modifiers.

For example. I roll 5D10, and get 4,2,6,6,8. Which gives me a value of 14 (8 + the 6 from the double). If I have a flat modifier of +4, then my final total is 20.

Attached are some images of what I've been trying to work out so far. However, I could be completely wrong and ignorant already, so if anyone could possibly help me out in a way I can understand which will allow me to fill in the rest of the table (or a way of working out specific numbers like 13) I would really appreciate it.

Many thanks!
Attached Images
File Type: jpg Prob1.jpg (19.7 KB, 3 views)
File Type: jpg Prob2.jpg (22.7 KB, 2 views)

Last edited by skipjack; April 27th, 2017 at 04:52 PM.
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April 28th, 2017, 12:51 AM   #2
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Is the initial result (before a double is added) the highest of the dice rolled or the total? (your 4,2,6,6,8 example suggests it is the highest).

The easiest way to do this would be to brute-force all possible results, either with some code or with big tables (or some code which created tables).
I would ignore the modifier for now, it's simple to add on at the end.
If you go down the tables route and require help, would this be in Excel or Google Sheets (or something else)?
I'm sure there are equations which will give the answers, but that's too hard for me, I'm an engineer, easy route wins
The 1D10 results should be easy, I'd start with that table then progress to 2D10 etc...
3D10 gets trickier to find the doubles, I would break it down into columns for each possible double (1-10) and autocount how many of that number appear in the row, this gets especially useful with 4 and 5 D10 where there will be multiple doubles, the result then picks the highest number column (1-10) with >1 in the count result to add to the final result.
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April 28th, 2017, 03:27 AM   #3
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Yes the initial result is the highest number rolled.

I had a feeling I would have to resort to excel or google sheets.

As far as tables go, attached to the question are a couple of pictures of the tables that I've started working on. Although for those it was something I found on the internet where someone had posted answering 'what are the chances of rolling any double on XD10' and the answer was this;
Dice Odds of a double
1D10 0%
2D10 10%
3D10 28%
4D10 50%
5D10 70%
(so I am making the assumption this is correct)
So I then divided those percentages by 10, to work out the individual double.
(so the chances of rolling a double 10 on 5D10 is 7%, the chances of rolling a double that is 2-10 would be 63% etc)

Then I took the odds of rolling a 1 through 10 on each varying dice pool. And tried to work out the odds of rolling at least higher than the target number on any of the dice. (so for 9+ the odds of rolling a 9 or 10 on any of the dice rolled)

Target No 1D10 2D10 3D10 4D10 5D10
10 10% 20% 30% 40% 50%
9+ 20% 40% 60% 80% 100%
8+ 30% 60% 90% 100% 100%
7+ 40% 80% 100% 100% 100%
6+ 50% 100% 100% 100% 100%
5+ 60% 100% 100% 100% 100%
4+ 70% 100% 100% 100% 100%
3+ 80% 100% 100% 100% 100%
2+ 90% 100% 100% 100% 100%
1+ 100% 100% 100% 100% 100%


Assuming I have both of those tables correct (which is a big assume at the moment) then it's the part where I'm working out how the two variables interact that's got me stumped.

Last edited by skipjack; April 28th, 2017 at 08:21 AM.
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April 30th, 2017, 10:59 AM   #4
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Right so currently I'm at the stage where I think I need to make a big old matrix.

So if I'm right given my above system (ignoring the flat modifier bit completely) the range of possible outcomes goes from;
10 on a single d10 because the outcomes are 1-10
To
50 on 5d10. Rolling 10,10,10,10,10. And taking the duplicates gives 50.

So if I create a chart which goes 1-50 along the top and then 1d10-5d10 going down can anyone help me with what formula I would need to put in to fill that chart out?

I figure a chart like that is exactly what I need as I can then quickly see exactly what the probabilities of hitting any particular number will be. But I just need to know what the method is for working out these probabilities.

I really am drawing a blank right now so help would be appreciated.
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