Probability – A fair die is rolled 100 times if the value is summed up

A fair die is rolled 100 times and the value on top of the die is summed (we'll call that sum X – note that X is between 100 and 600, inclusive). Calculate the mean and variance of X.

I am not looking for a complete solution, but looking for clues as to how to approach this question. I want to know how to get the value of X.

dnd 5e – What is the probability that certain abilities will be rolled in D & D?

I'm about to start a new game in 5e, and I hate every opportunity to determine the ability values.

I have always felt that we play role-playing games at least in part, pretending that we are more than we do in real life and nobody wants to play a character that is just average. In my opinion, characters in some areas should have the ability to become world class.

If you are using either a standard array or a point-buy mode, you will not be able to start with any level 1 skill greater than 15 in any skill. This means that with racial modifications you can not reach values ​​higher than 17. To reach the highest possible level of 20, you need to have at least two talent opportunities to improve to 20, and you have essentially no chance of improving a secondary ability to something significant if you do not want to be able to perform capable talents at all.

And with dice, you may have a chance to start in a better position, but you have a significant chance of starting in a much worse position. If the consequences of such a disaster were a few difficult sessions, that would be one thing, but the ability to play a character for months or even years, whose negative modifiers outweigh the positives, seems unacceptable to me.

For this reason, I think some DMs (including Criterion Role's Matt Mercer) set lower limits on the dice and say, for example, that you can roll again if their total is below 70 for all six of them.

I like this idea, but I'm not sure if it's enough for what I want (to give my players a chance to be extraordinary).

I know that there are 1296 possible results for rolling 4D6, and I know that the average result of rolling 4D6 and dropping the lowest number is 12,2446, which means (I think) that the average score for these six Male is 73.46759.

I'm thinking of turning 73 into the "floor" for my players (so they have at least hero average, so to speak), but I'm not sure I understand the math well enough to know that's the right one is decision.

What I would like to know is "What is the likelihood that these rolls will be under 70 in total?" So, if you roll 4D6 and drop the lowest score six times and add the six results, what's the probability that it's below 70?

I would also like to know that for 71, 72, etc … up to 78. And I would like to know what the probability is to get over 80, and 81, 82, and so on up to 90.

I am not a mathematician and I do not know how to find out. I do not even know how to formulate the question. I hope that was clear enough to get an answer.

Dice – What's the name of the tool that makes it less likely that the same number will be rolled consecutively?

I'm looking for an online tool that a friend once used in an RPG and that has adjusted the probabilities of an otherwise fair dice roll so that it's less likely to roll the same number multiple times. So, if you roll a 1d6 and get a 4, it's less likely that your next roll of 1d6 will be a 4 than roll 1, 2, 3, 5, and 6.

This was a pretty interesting game as it forced a wider value distribution for dice that we would not have seen otherwise. We still diced the same number on average, but the distribution was wider.

Does anyone know where I could find this tool?

Barack Obama would have gone into a third term! He should not have rolled up his sleeves. That destroyed all his chances?

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