You or the computer pick random positions on the playslip by throwing a dart at a random spot on it (if you hit a spot that you've already picked, toss that and repeat). Or another way is to have your own set of Chinese character balls at home, and reach in and grab one at random and mark off the corresponding spot on your playslip and repeat (without replacement) until you have the 5 (or whatever # needed) symbols.
In other words, lottery numbers have no special mathematical meaning to them. Another example is to have 69 irrational numbers and play powerball with it -- pi, e, √2, √3, √5, 2pi, 10e, etc. No Chinese characters, and they are all numbers, so they could be summed, but what would be the point?
Another example: after each drawing, Powerball burns the 69 balls and they take 69 blank balls and paint numbers on them that range from -100 to +100, selecting 69 of the 201 possibilities at random. For example, they could pick:
-99,-96,-92,-90,-86,-81,-80,-79,-77,-75,-57,-55,-50,-49,-45,-43,-39,-38,-35,-34,-32,-26,-22,-21,-20,-19,-13,-4, -3,3,8,9,12,15,17,18,25,26,29,32,33,35,36,37,40,43,46,47,48,49,55,57,59,62,64,65,66,67,68,69,72,86,88,89,91,92,93,95,100
They tell everyone what the 69 numbers to choose from are, the retailers print out blank playslips with those numbers, and then people can pick them or do QP.
Then after the next drawing (which had winning numbers -92, -77, 3, 65, 88), they toss those balls and pick 69 numbers again, this time getting:
-97,-94,-92,-87,-83,-82,-78,-77,-75,-74,-73,-72,-67,-61,-55,-50,-49,-46,-45,-44,-43,-40,-39,-29,-28,-26,-20,-18,-14,-12,-10,-6, -2,1,10,12,17,18,20,23,27,29,31,32,36,37,38,42,44,45,50,51,53,54,56,59,62,69,70,72,74,75,79,81,85,88,91,97,98
The logistics of doing this are possible, but pretty silly, and more importantly, many people would stop playing because they don't understand this and think that Powerball is up to no good when in fact the probabilities of winning are unchanged.
My point is that with this system, you don't have Chinese characters and you don't have irrational numbers, just those easy integers. Yet by changing them for every drawing and widening the choices from 1-69 to 69 of -100 to +100, the concept of sum is hard to use (and useless anyway), and consecutive winning numbers are suddenly far less likely, yet the probabilities of winning are UNCHANGED.
Another one is to pick an integer at random (-52, 112, 0, anything), call that n, and then say that for the next drawing, the available numbers will be from n to n+68. The probability of consecutive winning numbers is the same as it is today. Trying to sum them is a waste of time because the range constantly changes.
btw I used Excel to generate the 69 numbers in my two examples above. 201 rows going from -100 to +100, in the next column is =RAND(), then sort the 201x2 cells in order of the second column. What you get is the same 201 numbers but arranged in a random order. Then I selected the first 69 (could be any range of 69, still just as random) to be the 69 available numbers to choose from. Then I just picked 5 of those at random to be the winning numbers.
