I think: Here's my proof:


It can be: If:


The answer is quite simple when you know the concept of a derangement, since the only time this doesn't happen is if the first deck is a derangement of the second. In other words, we are looking for There are online calculators if you want the exact value, which is approximately


Starting off short before the end of this answer we take


You can't make it in a fair way, as JS1 answered. But given lateral thinking tag - you could have dice where one influences the other. Perhaps by magic or magnets. For example, first die is fair (1/6 chance of any number) and when it rolls 1, there is 6/11 chance of rolling 1 on the second one and 1/11 to roll any other number. Symmetry tells us 6 should ...


We can test this statement by the following: However I doubt this is the "lateral thinking" the OP has in mind.


From JS1's answer we already see that this is impossible for normal dice. But assuming the dice's result are dependent on each other as if they could communicate, This is how it works: Let's pick a "nice" solution: Actual numbers:

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