"Dice Probability question" Topic
7 Posts
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28 Apr 2014 5:21 p.m. PST
by Editor in Chief Bill
- Changed title from "Dice Probablity question" to "Dice Probability question"
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| Black Cavalier | 28 Apr 2014 4:01 p.m. PST |
Trying to help a friend change a dice mechanic & have a question if the probabilities of these 2 options are the same. 1) rolling 1d10, needing to roll equal to or under a certain number based on a stat. If your stat is 4, then you need a 4 or under. So each additional point in stat is an extra 10%. 2) rolling Xd10, needing a 10, where the X is the number of your stat. If your stat is 4, then you'd roll 4d10 & need a 10 on any of them to succeed. So each additional point in stat gives an extra d10 which has a 10% chance of being successful. Thanks |
| CraigH | 28 Apr 2014 4:12 p.m. PST |
A quick, intuitive response, so often wrong in probability, is no, they are not identical. Reason being, the chance of getting any specific number throwing 10d10 is clearly not 100%. |
| Happy Little Trees | 28 Apr 2014 4:13 p.m. PST |
No. In the first your chance is 40%. An extra point makes it 50%. In the second, your chance on 4d10 is 34%. With a 5th die it rises to 41%. |
 Mserafin  | 28 Apr 2014 4:14 p.m. PST |
Not the same. In case 2 you have to remove the probability of getting more than a single 10, which knocks it down to about 34% if my very quick math is correct. Adding more dice is not 10% additional per die – if you have 10 dice, the probability is not 100%, because you can roll all of them and not get a 10 on any. |
| CPBelt | 28 Apr 2014 4:27 p.m. PST |
Anydice is your best friend. Play with it for all sorts of fun. Here are the odds for your #2. I did 1 to 10 d10. You can change this to anything you like. anydice.com/program/3a89 |
| (Phil Dutre) | 29 Apr 2014 3:22 a.m. PST |
Probability in the first gase goes up by 10% for each additional status point. Probablity of rolling at least 1 ten on XD10 equals 1 – the chance to roll no 10 at all.
So: 1 – 0.9^X So, both cases are not identical. Intuitively, this might seem strange to those who are not well-versed in probabilty theory ;-)
But consider this: If you roll 2 D10, the first has 10% probability of showing a 10. So does the second. But there is also the event that they both show a 10, which you would count for twice when you would simply add up the individual probabilities. |
| Dynaman8789 | 29 Apr 2014 5:04 a.m. PST |
> Intuitively, this might seem strange to those who are not well-versed in probabilty theory ;-) I am well versed and I still get it wrong almost every time, till I work out the math. The Monty Haul problem had me baffled for days for example. |
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