The lottery  an order statistics paradox?
Suppose 6 balls are drawn uniformly from 49 balls (numbered 1 to 49), without replacement.
Sort the balls by the value of their numeric label and let x_{i} be the value of the ith ranked ball for i from 1 to 6.
Then, for k = 1,2,3,...,49:
(Proof: homework exercise.)
These distributions look like this for i = 1,2,3,4,5,6; and
have the mean and mode as in the table. (Proof: another homework exercise.)

i  mean  mode 
1  50/7  1 
2  100/7  10 
3  150/7  20 
4  200/7  30 
5  250/7  40 
6  300/7  49 

In other words, the most likely value for the smallest numbered ball is 1,
the most likely value for the second smallest numbered ball is 10, and so on.
Everything I have claimed so far is correct.
Therefore, you should put your money on balls 1,10,20,30,40, and 49.