Board Game Designers Forum - Comments for "dice statistics help"
https://www.bgdf.com/forum/game-creation/mechanics/dice-statistics-help
Comments for "dice statistics help"enHard to share if copy paste fails...
https://www.bgdf.com/forum/game-creation/mechanics/dice-statistics-help#comment-109162
<p>I corrected some mistakes I made. Just to give you an idea on how difficult keeping an overview might be.<br />
My claim about 3 rolls above wasn't right. But after correction, I am more sure. I got to compare with your results. And we have almost the same now. I could even spot the differences. I coloured these red for you and put in my list right next to it. </p>
<p>I copied both sheets that I have into your file.<br />
But the copy paste makes no sense...<br />
Can you PM me your email? Then I simply send the file.<br />
That should help more.<br />
And things like, colours, formula's etc would be in there.</p>
<p>The file is rather complex for new eye's. (Especially when only the text is visible) But I might update it another time to answer questions.<br />
But you can ask me in PM, through email or here.</p>
<p>Maybe I should make some sort of tutorial on how I do things in a spreadsheet. But Excel is copyright. So no video's on that. </p>
<p>And you are free to ask me to calculate different things.</p>
<p>Cheers, X3M</p>
Sat, 19 Jun 2021 12:11:57 +0000X3Mcomment 109162 at https://www.bgdf.comI have updated the
https://www.bgdf.com/forum/game-creation/mechanics/dice-statistics-help#comment-109159
<p>I have updated the permissions in the above link, if you want to show me the kind of thing you were talking about. </p>
<p>Feel free to edit it. Or make a new tab etc</p>
Fri, 18 Jun 2021 20:56:18 +0000Juzekcomment 109159 at https://www.bgdf.comI think you made a mistake
https://www.bgdf.com/forum/game-creation/mechanics/dice-statistics-help#comment-109158
<p>Which happens when you don't let the system correct you.</p>
<p>3<br />
Chance<br />
23,36% 0<br />
37,38% 1<br />
26,17% 2<br />
10,47% 3<br />
2,62% 4<br />
1,31588785 </p>
<p>I copied this from my sheet. I prepared the 4d6 from a sheet that has ALL number of dice.</p>
<p>I expanded the sheet for 4d6 from 1 to 12 rolls.</p>
<p>I have 1,32 while you have 1,75? something ain't right there. I know that I made no mistake. Because the 2nd roll again gives 0,67.</p>
<p>With infinite rolls, you get at an average good result of 4. My table goes towards the 4, with 3,43 at the 12th roll.</p>
<p>Now, making the tables for less or more dice will be easy. It is simply copy pasting the stuff. And then change the size. Perhaps.... I could make one up to 12 dice. Which would simply be used for <12 dice as well. Because if we build up. Some calculations have to be re applied. And a field of 12*12 is a bit much to re-apply per sheet.</p>
<p>So, if you want to see it. I want to know 2 things:<br />
- How to share it anyway? PM me on this one.<br />
- Would you like me to prepare for other number of dice as well?</p>
Fri, 18 Jun 2021 19:12:01 +0000X3Mcomment 109158 at https://www.bgdf.comYou modified later on, right?
https://www.bgdf.com/forum/game-creation/mechanics/dice-statistics-help#comment-109157
<p>I see you got it for 98% complete now. The little percentages differences are the key here for the missing parts.</p>
<p>I will see, if I got some time this weekend. And make the table like I intended. This table should be able to be expanded and stuff. Merely by copy pasting. Then you will see what I meant. </p>
<p>But yours is good too. It is just more specific for the described situation of 4d6 that have 3 rolls.</p>
<p>You had to sort it out, the ways of how a player can roll, didn't you? My original method helps in this.</p>
Fri, 18 Jun 2021 18:31:58 +0000X3Mcomment 109157 at https://www.bgdf.comI tried a table
https://www.bgdf.com/forum/game-creation/mechanics/dice-statistics-help#comment-109156
<p>I tried a table method<br />
Table:<br />
<a href="https://docs.google.com/spreadsheets/d/1JezJXtFfTZ2qurpfmQkqG41_F5LAqRXgiFHzVPr6Q5k/edit?usp=sharing" title="https://docs.google.com/spreadsheets/d/1JezJXtFfTZ2qurpfmQkqG41_F5LAqRXgiFHzVPr6Q5k/edit?usp=sharing">https://docs.google.com/spreadsheets/d/1JezJXtFfTZ2qurpfmQkqG41_F5LAqRXg...</a></p>
<p>I broke down all the possible ways to get 4 good dice, 3 good, 2 good 1 good 0 good, and filled in with the chances from Anydice what the likelihood for each roll is.</p>
<p>But I must have a mistake somewhere! The total for all the chances for all the scenarios is only 55%, and it should be 100.</p>
<p>@X3M<br />
How does my table look?</p>
<p>@anyone else<br />
There has got to be a formula out there for something like this.</p>
<p>Thanks</p>
Fri, 18 Jun 2021 11:00:56 +0000Juzekcomment 109156 at https://www.bgdf.comMy attempt
https://www.bgdf.com/forum/game-creation/mechanics/dice-statistics-help#comment-109149
<p>There are much better people out there, who can help you with this. But I get the feeling you are stuck with me and my own kind of logic. I can't give you a formula. I am too stupid for that. I can only guide you into how I would calculate these things.</p>
<p><div class="quote-msg"><div class="quote-author"><em>X3M</em> wrote:</div>I consider % as a factor of 1/100. Percentage means per one hundred. Cent is an old roman word for one hundred.</div><br />
<a href="https://membean.com/wrotds/cent-hundred" title="https://membean.com/wrotds/cent-hundred">https://membean.com/wrotds/cent-hundred</a><br />
Ok, I hope my calculation at the end makes sense this way.</p>
<p>***</p>
<p>Either way. You need to cut your problem in smaller pieces.</p>
<p>After all, you say that you roll 4 dice. And you roll them 3 times as long as you roll something bad.</p>
<p>Your main question would be, how much is the chance on every number of successes. And for every roll.</p>
<p>Ok, so, you want a list that has something like this:</p>
<p>G: 1st 2nd 3th<br />
0: ##% ##% ##%<br />
1: ##% ##% ##%<br />
2: ##% ##% ##%<br />
3: ##% ##% ##%<br />
4: ##% ##% ##%</p>
<p>Right?</p>
<p>Or perhaps you want the average results of good rolls.<br />
Which would simply become a list:<br />
Rolls (of 4): Good<br />
1: ##<br />
2: ##<br />
3: ##</p>
<p>The main problem here is the number of re-rolls on the individual dice. When a die is good, it will not be re-rolled. Thus reducing the chance by the number of dice.</p>
<p>If I where to use tables. I could calculate this. But I can't show it too you. If only we had a Discord for BGDF.</p>
<p>Either way. We start with...</p>
<p>0</p>
<p>You have no good rolls. So your first roll commences with 4 dice. We are going to consider the number of successes. And we can use anydice for this.</p>
<p><a href="https://anydice.com/program/22ccb" title="https://anydice.com/program/22ccb">https://anydice.com/program/22ccb</a></p>
<p>The results:<br />
0,48.225308642<br />
1,38.5802469136<br />
2,11.5740740741<br />
3,1.54320987654<br />
4,0.0771604938272</p>
<p>Now, let's look at the 0. We got a 48.2% chance that you have 0 good results. This means that the 2nd roll is going to have 4 dice.<br />
If we look at for example the mentioned 4 good results. Then there is no 2nd roll.<br />
We need to consider how much dice the second roll is going to have. And multiply the results of that with the chance that we even need to do a 2nd roll.</p>
<p>So, the next step is to consider the results with less than 4 dice. But we still include the 4 dice.</p>
<p><a href="https://anydice.com/program/22ccc" title="https://anydice.com/program/22ccc">https://anydice.com/program/22ccc</a></p>
<p><strong>4 Dice</strong><br />
0,48.225308642<br />
1,38.5802469136<br />
2,11.5740740741<br />
3,1.54320987654<br />
4,0.0771604938272</p>
<p><strong>3 Dice</strong><br />
0,57.8703703704<br />
1,34.7222222222<br />
2,6.94444444444<br />
3,0.462962962963</p>
<p><strong>2 Dice</strong><br />
0,69.4444444444<br />
1,27.7777777778<br />
2,2.77777777778</p>
<p><strong>1 Die</strong><br />
0,83.3333333333<br />
1,16.6666666667</p>
<p>How to read this?<br />
When we roll the dice, we add a number of good results on the previous roll.<br />
So if the first roll yields 2 good results. The chance for this is 11.57%. The roll of 2 dice is also 11.57%.<br />
We look at 2 Dice. And an example of rolling 2 more good results is 2.78%.<br />
The true chance of this happening is 11.57% * 2.78% = 0.32%<br />
So a chance of 0.32% that we roll 2 good results in the first roll and get to 4 in the 2nd roll. This chance however can be added up to the 0.077% of rolling 4 good dice right away. After all, we want to know how big the chance is in getting 4 good dice. But we need to calculate other results as well. The 4 good dice in the second round include:<br />
4 in the first round +0 in the 2nd round<br />
3 in the first round +1 in the 2nd round<br />
2 in the first round +2 in the 2nd round<br />
1 in the first round +3 in the 2nd round<br />
0 in the first round +4 in the 2nd round</p>
<p>On a side note, +0 in the 2nd round with 0 dice is 100%. So the chance on the 4 good rolls in the first round is used again.</p>
<p>So you need to add up 5 percentages for a total chance on getting 4 in the 2nd round. Then you use this percentage and rinse and repeat. If you do this correctly. Every round of rolls will slowly shift the results from low to high.</p>
<p>In order to calculate the average per round. Simply have the result 0,1,2,3 or 4, multiplied by the chance it occurs. For example, the first round average is:</p>
<p>0 * 48.225308642%<br />
1 * 38.5802469136%<br />
2 * 11.5740740741%<br />
3 * 1.54320987654%<br />
4 * 0.0771604938272% +<br />
________________________<br />
0.6667</p>
<p>Yes, that's right, the average result in the first roll is 2/3th.</p>
<p>Now, perhaps you can make the table. Or show me a place where I can show it to you. Because then I would make the table in excel. And it would go...eventually simple and fast...<br />
I don't do much formula's anymore in calculating chances. I have fallen in love with my table method.</p>
<p>Good luck!</p>
Thu, 17 Jun 2021 20:41:28 +0000X3Mcomment 109149 at https://www.bgdf.com