A better lottery analogy would be evey one in China (1 billion people) slecting a number between 1 and 1 trillion, and then each month comparing these numbers with 10 "winning" numbers within this range (thus no pre-necessity of a winner each month as in the previous example).
Since a trillion is 1,000 billion and there are a billion persons in China the odds would be 1000 to 1 against any one of the numbers being hit upon in any month. However this would be offset by the fact that there are 10 possible winning numbers - hense the odds drop to 100 to 1 of there being a winner in any month (thus on average there should be 1 winner every 8.5 years ).
However, the odds of getting 12 winners in any single year would be 1 in 10 to the 24th (100 times 100 times 100 times etc.- twelve times), which if it occured (even if within a 1,000,000 year period of lotterys) would be strong evidence of fraud .
Furthermore, if in the resulting fraud trial an indicted lottery officials defense was that: "Unprobable things happen all the time judge !- why take this deck of cards judge and randonly shuffle it. Now that you are done here is the sequence (7of clubs, 6 of diamond, etc.). Do you know judge that the odds of getting the specific combination of playing cards that you just got from random shuffling?- Why it is less than 1 in 10 to the 67th! yet it still happened! and there certainly was no fraud on your part in such an unlikely event occurring. Therfore, why should anyone be charged with fraud in the lottery case of 12 winners in the past year with its much more likely odds of occurring!"
Of course a wise judge would recognize the fallacy in the mans defense argument, in that (similar to as Dr. Batten wrote in another AiG arcticle) that any arrangement of cards is as ‘good’ as any other and there will be of necessity (with 100% probability) an arrangement of cards within the period of time that the judge shuffled them. However, within the time period of the lottery (even if 1,000,000 years) the odds against twelve winners in any year are in contrast a very low probability (so low that intelligently directed fraud within that year would be very well substantiated).