> Is that a reference my inscrutable habit of jumping from thread to thread?
> If so, it's a good one. I don't know if I can explain it any more clearly
> than I have, but I'll try again: you are no more likely to win in any
> individual (if I knew HTML, I would've italicized that) drawing by
> participating more often. Collectively, though, you are more likely to
> eventually win. However, if you're unlucky enough to go through 999,999
> lotterys without a win, the millionth time is no more likely to be a charm.
Hmmm, I'm not sure what you mean by the distinction between "individual" and "collective" lottery play. Collective play would be a pool, where you and 11 mates pick 500 numbers and split the cost of the tickets. That is the same as you picking 500 numbers as far as probability is concerned. Whether it is worth it to do that depends on your disposable cash and the reward and the number of mates in your collective, things that are orthogonal to the probability of winning.
Anyway, look at it this way. Each play of the lottery has two variables. First, the number of outcomes which are favorable. Second, the total number of possible outcomes.
But forget about lotteries for a second, and consider coin tosses. For a coin toss, if we want to probability of heads, we divide the total favorable outcomes, 1 (there is only 1 way for a coin to come up heads) by the total number of outcomes, 2 (either heads or tails). The probability of getting a heads is 1/2.
If we do 5 coin tosses, there are now 5 favorable outcomes (a heads on any toss), but there are also 10 possible outcomes (a head or tail on any toss). The probability of heads is 5/10, or 1/2. Still the same.
Do you follow this with coin tosses? Each coin toss, no matter how many times you do it, has a 1/2 probability of coming up heads. It doesn't matter if your previous 500 coin toss where heads (See Stoppard's play _Rosenkrantz and Guidenstern are Dead_...), the next coin toss still has the same probability.
The probability works exactly the same way for lotteries, even though the fraction is more like 1/10^8. The way which probabilities work doesn't change when you are dealing with astronomical odds.
Many folks believe that coin tosses and lotteries have memories; that each play somehow "remembers" what it did previously, and that if a certain outcome hasn't yet occurred, the toss or lottery will adjust it through some unknown means so that the unoccurred outcome becomes more likely. But that is silly; lotteries have no memory, nor do coin tosses.
Hence lotteries are taxes on people that are bad at math. :)
> Even better than playing a million times would be purchasing every
> combination (discounting the fact that doing so generally results in a net
> loss of money on the purchaser's part).
As I've shown above playing a million times does not help. But the latter method WOULD help, as you are increasing the number of favorable outcomes (different numbers you've purchased) and keeping the total possible outcomes the same. But that isn't practical, as you indicate.
If lottery systems included some kind of memory in the system (which they do not), then your claim would be true. For example, if the lottery only allowed a number to be chosen once, and then any time that number came up again there would be a re-draw until a new number came up, then playing more would change your odds (playing later rather than more often would be a better pay-off, though). This is because the total number of possible outcomes would be slowly getting lower. The denominator of the fraction would be shrinking, increasing odds.
But there is a reason lotteries don't work that way. :)
When it comes to probabilities, don't trust your intuition. If it can't be expressed in mathematics, it is just an opinion.
Matt
-- Matt Cramer <cramer at voicenet.com> http://www.voicenet.com/~cramer/ PGP Key ID: 0x1F6A4471 aim: beyondzero123 yahoo msg: beyondzero123 icq: 120941588
"Hold your fire" - that's what I told the FBI.
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