A common solution to any tricks involving a named/thought-of number that needs to be within a certain range is to usually through some presentational angle. I think it’s much easier to limit the range through process than to justify it through patter. If their range is limited without them knowing it’s limited, it’s probably going to feel less limiting than focusing on their “free” but limited choice.
So ACAANs for example, instead of telling them the range with whatever justification, use the process of adding single digits. Let’s say your range is between 10 and 20. Well, we know adding the two highest single digit numbers (9 + 9) is 18. So the total of any high 2-digit numbers is going to hit that range. Something like you’d ask them to name a random 2-digit number and make it a high one, and they say 55. Have them add the two digits together: 5+5, which would get you to 10. Although if you ask for a high 2-digit number, they will probably name one higher than 55.
Similar case goes for larger ranges. Let’s say you’re now aiming for between 10 and 30. 9 + 9 + 9 is 27. So the sum of the numbers in a high 3-digit number will likely land. You do have to account for what people would consider a high 3 digit number, though. technically 711 can be considered high but that would only add up to 9. So to account for that, any 4-digit number might be better- since 9x9 is 36, which is not far from 30.
Another way to approach this is to have single digits named by different people. You’d get one person to pull out a calculator to add up some numbers. You get three others to name numbers and if you need one more number, then the person with the calculator becomes the fourth and names and add their number to the rest. If not, then the calculator person just hits equals.
So how do we get the numbers to have more weight? Yes, you can just ask them to name some random ones, and I do think that having this simple process already improves on generating random numbers. But if whatever you’re doing needs a bit more to connect with audience members might I suggest Jerx’s Unknown Personal approach.
Still working on my ACAAN notes. Have a couple more things to share before that. But this post and this one are related. :)