Nope. it’s just that no matter what you roll on the first die, there’s always SOMETHING you can roll on the second die to get a 7, so the chances are 1/6.
If you want to roll a 2, you have to roll a 1 on both rolls, so the chance is 1/36. Same chance for rolling 12.
To roll a 3, you have a 1/3 chance to roll the required 1 or 2, then 1/6 to pick up whichever you missed on the second roll, so the total is 1/18.
The reason that the most likely sum of two 6-sided dice is 7 is that it’s the most common value that comes up when you make a list of all the sums of two numbers between 1 and 6. 7 can result from 1+6, 2+5, 3+4, 4+3, 5+2, and 6 +1, which makes up 6 out of the 36 possible combinations. Every other number in that range has a smaller number of possible combinations. It’s not that the first dice is magically influencing the second, it’s just that statistics says that 7 has to come up the most because it’s got the most entries on the list.
The fact says: if you roll two dice, the most probable outcome is 7. This is true, there are simply more combinations of two dice that give 7 than give any other number.
If you are roll a 2 with one dice and then make that result a fact, and then judge the probability of rolling a 5 afterwards, that is no longer the outcome of two dice rolls! That is the outcome of the second dice GIVEN THAT the first dice rolling 2.
In other words you are only most likely to get 7 if you roll the two dice together over and over. If you roll a 2 and then only roll ONE dice after that over and over, there is no one result that is more likely than any others.
Different roles of different or the same die have no connection with each other.
Each new roll has the same chance of outcome as the last. There is no memory involved.
Rolling a 6 two times in a row does not make the next roll anymore or less likely to be a 6.
If you roll a die twice (or two dies once) the possible outcome average out to 7 and make 7 the most likely sum you will get.
If you roll a die once, all six different outcomes are equally likely and they will average out to 3.5.
If you roll two die you will have 36 potential outcomes.
1st die | 2nd die | Sum
—|—|—-
⚀ | ⚀ | 2
⚀| ⚁ | 3
⚀|⚂| 4
⚀|⚃ |5
⚀|⚄ |6
⚀| ⚅|7
⚁| ⚀ | 3
⚁| ⚁ | 4
⚁ |⚂ | 5
⚁ |⚃ |6
⚁ |⚄ |7
⚁ |⚅ |8
⚂| ⚀ | 4
⚂| ⚁ | 5
⚂|⚂ | 6
⚂|⚃ |7
⚂|⚄ |8
⚂| ⚅ |9
⚃ |⚀ | 5
⚃ |⚁ | 6
⚃ |⚂ | 7
⚃ |⚃ |8
⚃ |⚄ |9
⚃ |⚀ |6
⚄ |⚁ | 7
⚄ | ⚂| 8
⚄ |⚃ |9
⚄ |⚄ | 10
⚄ |⚅ | 11
⚅|⚀ | 7
⚅|⚁ | 8
⚅|⚂ | 9
⚅|⚃ | 10
⚅|⚄ | 11
⚅|⚅| 12
As you can see, you have 6 out of 36 chances of having sum of 7, 5 out of 36 chance for having a sum 8 or 6 each, 4 chances each of having 9 and 5 and so on and just one chance for having a 2 or 12.
So 7 is not just the result that everything else averages out to it is also the result that you are most likely to get.
Once you have thrown a die and wait for the result of the 2nd die you can throw 30 of the 36 entries in the table above away. you will still have a 1 in 6 chance of both dies adding up to 7 but there will be 5 other equally likely results that are not 7.
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