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So what does this all mean, you ask?  Aren't the chances of winning the white ball jackpot still low?  Of course they are!  

But if you're going to play anyway, you might as well pick from the pool of numbers that have a higher probability of occurring.  I have calculated the actual percentages of all drawings since October 9, 2002 when they added 4 numbers.

-------------------------------------------------
Combination   Expected   Actual    Difference
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0odd/5even      2.29%     1.91%     -0.90%  
1odd/4even     14.07%    15.79%     -0.11%
2odd/3even     31.80%    31.58%     -1.55%
3odd/2even     33.13%    31.10%     -0.70%
4odd/1even     15.90%    16.75%     +2.68%
5odd/0even      2.81%     2.87%     +0.58%
 

 

We can then use the binomial coefficient (aka "n choose k") to determine ways of picking k unordered outcomes from n possibilities.  The formula is n!/(n-k)!k!.  We will abbreviate this as nck( n, k ).