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What are the odds?

May 21, 2008 at 22:20
filed under rant

Odds are a funny thing, we wish for them to work for us in most cases but in other instances, such as the lottery, we want them to prove us wrong by defying the logic and making us the exception.

Not a lottery player myself, the 6/49 draw of March 19th nonetheless was quite surprising. The winning numbers were 23, 40, 41, 42, 44, 45 and the bonus was 43! Here are some interesting facts about the odds, as noted by Prof. Schwartz of SFU:

There were:

0 winners of the 6/6
239 winners of the 5/6 + bonus;
106 winners of the 5/6
5245 winners of the 4/6
91935 winners of the 3/6
65843 winners of the 2/6+ bonus.

The odds of winning are 1 to:

13,983,816 for 6/6
2,330,636 for 5/6 + bonus
55,492 for 5/6
1,033 for 4/6
56 for 3/6
81 for 2/6 + bonus

If you multiply the number of winners x odds you should get approximate number of tickets sold (assuming a uniform random distribution).

13,983,816 x 0 = 0
2330636 x 239 = 557,022,004
55492 x 106= 5,882,152
1033 x5245= 5,418,085
56.7 x91935= 5,212,714
81.2 x65843= 5,346,451

So for the first 4 prize levels, it shows that about 6,000,000 tickets were sold. Clearly the result for 5/6 +bonus are very unusual as there is no way 557,000,000 tickets were sold!

With no explanation possible, this is another case which we simply must learn to accept the exception confirming the rule, which is much easier when you’re on the winning side of the odds.

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