I would like to find the probabilities of rolling a result using different numbers of six-sided dice. I am looking for the best way to figure out the probability for each number of dice. I have found information that explains finding the probability of rolling specific numbers or for the sum of all the dice rolled, but I am looking for the result of rolling two numbers or any numbers higher than the target numbers.
It is easy enough for me to draw out the 36 possibilities of 2d6 to find these odds, but I would like to know what method can be used to calculate these odds for 2d6, 3d6, and 4d6. I have been banging my head against the wall with this problem for several days and I still fail to get a firm grasp of the proper concepts. I have not worked with probability calculations for many years and I would appreciate any guidance for this personal project of mine.
Below is a table that I would like to complete. For example, what is the probability of rolling at least 3 AND at least 5 using 2d6? Initially I had wanted to calculate odds with re-rolls added in, but I am having a hard enough time with just the flat rolls.
_______|2d6|3d6|4d6|
3+ & 3+ |___|___|___|
4+ & 3+ |___|___|___|
5+ & 3+ |___|___|___|
6+ & 3+ |___|___|___|
4+ & 4+ |___|___|___|
5+ & 4+ |___|___|___|
6+ & 4+ |___|___|___|
5+ & 5+ |___|___|___|
6+ & 5+ |___|___|___|
6+ & 6+ |___|___|___|
Thank you anyone who takes the time to help with my request.
It is easy enough for me to draw out the 36 possibilities of 2d6 to find these odds, but I would like to know what method can be used to calculate these odds for 2d6, 3d6, and 4d6. I have been banging my head against the wall with this problem for several days and I still fail to get a firm grasp of the proper concepts. I have not worked with probability calculations for many years and I would appreciate any guidance for this personal project of mine.
Below is a table that I would like to complete. For example, what is the probability of rolling at least 3 AND at least 5 using 2d6? Initially I had wanted to calculate odds with re-rolls added in, but I am having a hard enough time with just the flat rolls.
_______|2d6|3d6|4d6|
3+ & 3+ |___|___|___|
4+ & 3+ |___|___|___|
5+ & 3+ |___|___|___|
6+ & 3+ |___|___|___|
4+ & 4+ |___|___|___|
5+ & 4+ |___|___|___|
6+ & 4+ |___|___|___|
5+ & 5+ |___|___|___|
6+ & 5+ |___|___|___|
6+ & 6+ |___|___|___|
Thank you anyone who takes the time to help with my request.