"I deal you the 2 of spades, then the 3 of spades"
If multiple test draws had consecutive numbers you'd have a somewhat relevant analogy, if not an actual point. Since we didn't see consecutive numbers we're clearly not dealing with whether or not adjacent balls were adequately shuffled by the randomization process. The imaginary issue you're tilting at is the repeating of a few numbers in consecutive drawings.
"Now in a field of 59 numbers, if we draw 30 (about half) of them(because that's how many total white balls were drawn including allpractice draws and the real thing) and allow repeats, what would weexpect?"
I'd expect what probability suggests. How about you?
"We might see a repeat."
And here's our proof that you don't have a real grasp of the probability. Only having one or two repeats is quite unlikely.
"But to have 4 or 5different numbers repeat, and then have a certain number show up THREEtimes in our draw... that hints that the process is not as random asthey originally thought."
No, it only means that your concept of random is wrong. Having 3 to 6 repeats is what should be expected. Having one of those repeat a 3rd time should happen fairly often. That's based on the 5 regular balls. Incuding the power ball just makes repeats a bit more likely.
"I could type in 569283/9484 into my calculator, and I certainlywouldn't know what digit would be in the tens place of the answer, butdoes that mean it's random? No, it means that the factors involved areso complicated that I can't possibly know what the result will be. "
Of course you can know what the result will be (even if you can't do it in your head), because the "factors" aren't complicated at all. It's an exact process, and not subject to any randomization, whether perfect or not. The numbers are bigger, but it works exactly the same as dividing 1 by 2,and every time you do it you'll get the same result, to 1000 decimalplaces if your calculator is good enough. Again, the example isn't at all analagous to random probability.
If you pick *any* 6 PB drawings (or MM, since the number pool is similar) you should expect results that are similar to the ones from the last drawing. It can be a single drawing with the tests, or it can be any 6 official drawings, without the test drawings. If you look at the last 6 PB results you'll find a pattern that's essentialy identical to what you used. 5 of the numbers repeate twice and one repeats 3 times.
All that said, just because the results don't really suggest a trend doesn't mean there isn't one. There's no question that the system isn't perfect, and a ball being lighter or heavier, or less round by 1/1000 of 1% will have a very minor affect, making that ball the least bit more or less likely to be drawn. The problem is that even if a ball is a full 15 more or less likely, that's not very meaningful.
BTW, the number that came up 3 times in the previous 6 drawings? 17.