Fred Zed said:
I don't know what wheels you are using but your analysis is definitely incorrect as
can be demonstrated with a simple wheel for 5 numbers
where 4 / 4 is required. The wheel is like this:
1-2 -3-4
1-2-3-5
1-2-4-5
2-3-4-5
Now, if 4/5 in above are correct, I am guaranteed 4/4.
Now if you extend this principle to larger wheels the same principle applies.
What counts is that the chosen sample contains the correct numbers.
It is much easier to pick a sample of 18 numbers that contains 6 correct numbers than it is to guess 6 numbers correctly.
Try not to get bogged down in complicated statiscal analysis, look at it at a simple level, wheels definitely work.
The trick here is the statement 'IF 4/5 in above are correct, then....'
When you account for the uncertainty whether the 4/5 are correct, you're no further ahead. If you are correct on the 4/5, you'll win more of the small prizes. If you are wrong on the 4/5, you'll win less of them. These circumstances balance each other out exactly, when it comes to your expected payback.
Simpler example:
If I roll a die, it can come up 1 to 6. I have 1/6 chance of guessing.
If I guess correctly in advance that it will turn up an odd number, it looks like I reduce my odds to 1/3 (there are three odds.) However, I'm only guessing, I don't know. And most definitely, the die can turn up an odd just as often as an even.
So, since there's a 1/2 chance of being odd or even (3 each), the real odds of winning is still 1/6 -- 1/2 x 1/3.
Same kind of math works for your example. This kind of stuff is hammered out on the internet. They basically conclude that there's no overall expected return for using wheels. There may be some taxation benefits, etc in some cases, but the basic lottery math is unchanged by using wheels.
Here's an example. Check out the stuff by Duncan Smith at the bottom.
http://groups.google.ca/group/alt.lotto.players/browse_thread/thread/af8789992fecd637
Anyway, believe me or not, I'm outta here.