0

I calculated the propabilites to get numbers 2 to 12 by throwing 3 dices and picken only 2 out of them.

If someone throws 3 times a 1 the event is [1, 1, 1]. There are 3 possible combinations to get a 2 out of the thrown dice.

I summarized all possible combinations for 2, 3, 4, 5, ..., 12. Eachs has his own sum. At the end i divided each counter by the sum of all counted combinations.

For throwing a 2 there exist in total 18 combination. If I divide 18 by the sum of all counted possible combinations, the propability is the same as I just throw 2 dices.

The results for 2 up to 12 are all equal. So apparently it does not matter if you throw 3 dices and pick 2 of them or just throw 2 dices. But it feels kinda wrong to me that they seam to be the same.

Am I doing a mistake or are the propabilites the same for throwing 2 dices and throwing 3 dices but pick 2 out of them?

Hopefully you can understand my explanation, I am no native speaker.

Aaron
  • 11
  • Related video and follow-up. – Arthur Jul 03 '23 at 08:15
  • 1
    Well, you need to explain how you select the two out of three. If, say, you always take the two highest rolls, then of course it is not the same. Presumably you meant to say that you select two uniformly at random (so that any two are equally likely to be chosen). In that case, of course each selected die is equally likely to come up on any given face independently of the others which is all you need. – lulu Jul 03 '23 at 10:08
  • The idea is to flatten the distribution, so it is less random. One throwes 3 dices at once instead of 2 and chooses 2 out the 3 which are benefitial.

    But apparently this procedure does not effect the distribution at all. Is this true?

     – Aaron Jul 03 '23 at 11:13
  • To answer your request. Yes the selection is kinda random. For example if one needs a 2. He throwes 3 dices and gets the results [1,2,1]. Obviously one would choose 1 and 1 to achieve the 2. How I understand the suspect this is not quit random. But I don't know how account this "decision" in the calculation. – Aaron Jul 03 '23 at 11:23
  • You need to say what is the "decision" about. For example, you can ask, if it is possible to choose 2 dice out of 3 to get given sum. And probability that it is possible is higher (if you want some result from 2 to 12) than just getting this sum on 2 dice. – mihaild Jul 03 '23 at 14:39
  • If the selection process is correlated to the values, then the distribution will generally not be the same. This is generally true in sampling....if your selection process is correlated to the thing you are trying to measure, you will get a biased result. If you conduct an internet survey to determine what percentage of the population are online, you will get too high an estimate...just as an example. – lulu Jul 03 '23 at 18:09
  • Ok. So I was thinking about "settlers of catan". My problem with the game is the big influence of luck on the outcome of the game. So my idea was, instead of throwing 2 dices use 3 and so on.

    For those unfamiliar with the game. In many cases you want roll a couple values to achieve some progress. For example you want to roll a 2 to get a card you need.

    Now if you roll with 3 dices and choose 2 out of them, which have the most benfitial outcome for your game. It should flatten the curve. Right?

    My whole question is about, how to model this decision to get the new distribution.

    thx

     – Aaron Jul 04 '23 at 07:02

0 Answers0