Aren't the odds just based on how many tickets you buy? The odds aren't
affected by different people buying more tickets. If only one person
buys a ticket in the entire lottery system, his odds of winning are the
same as if two people play, and the same as if 20 million play.
According to the wikipedia: "In probability theory and statistics the odds in favor of an event or a proposition are the quantity p / (1-p), where p is the probability of the event or proposition." If you assign equal probability of winning to each ticket then odds are how many tickets you buy relative to how many tickets everyone else has bought.
The probability of a ticket winning is 1 / m**n where m is the highest number possible and n is the number of numbers. If a lottery uses 6 numbers each in the range 1..42 then the probability of a ticket winning is 1/5489031744.
All of this is mathematics. Sometimes one or more tickets win. Is that "luck"?
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