The maths is complicated, but suffice to say it's nothing like 1 in 8000, because he is still only spending $20 each week, even if he is spending $1000 over the course of the year.
spunkrat said:
...I find it hard to believe you will win the Oregon lottery by buying 8000 tickets, though to be honest I don't know how the Oregon lottery works...
The math is not complicated if we make some reasonable assumptions, and based on your second quote you appear to have misunderstood the original poster in the first place.
Haltherrion said:
Interestingly, the odds of rolling 3 20s in a row is the same odds as winning the Oregon state lottery (average payout around $6M i think) during one year if you spent about $20 a week on the lottery.
The original post states that the odds of winning the Oregon state lottery
in a year are about 1 in 8000 if you spend $20 a week for that entire year. The number of tickets this buys isn't specified, and doesn't matter if every ticket has the same chance of winning over the course of a year. How frequently they select a winner is also not specified and doesn't matter, or at least doesn't matter very much. (Depending on the details of the lottery both of these may affect the expected number of winners per drawing, so there may be some effect depending on the pot sharing rules for multiple winners. Likewise, if the probability of a ticket winning depends on the number of people playing or if the pot size is not fixed, then some corrections would be necessary. But unless they do something really bizarre these are 2nd order effects that can be ignored in a back-of-the-napkin calculation, particularly one in which only information about the average results over the course of a year are provided).
What matters is that on average you would have to spend that kind of money (i.e. 20*52, or about $1000) 8000 times to expect to win the lottery once over the period of time specified. Well, 1000*8000 is 8 million, which is greater than the winnings of 6 million. And, of course, to the state it doesn't actually matter whether that money comes from one guy or from thousands, or if it is spent over 1 giant year long lottery or lots of daily ones. All that matters is the probability that someone who bought a ticket won. (If multiple prize winners don't split the pot, they also care about the probability of there being two or more prize winners each time there is a drawing or whatever, which will be minuscule in any case). In other words, for every 8 million dollars in lottery tickets the state takes in
from any source, it could expect to pay 6 million dollars to winners. If there are no other prizes and there is sufficient volume to account for fluctuations about this average, this is a perfectly sustainable lottery for the state. Assuming a single ticket costs no more than $20, and all tickets are equally likely to win, the best possible odds to win with a single ticket based on the given information would be 1 in 8000*52, or about 40000. If, instead, every ticket costs $1, then each ticket has about a 1 in 8 million chance to win 6 million dollars.
Whether the actual Oregon lottery uses these approximate odds is of no interest to me.
So as to marginally contribute to the thread's topic, I will chime in with a fun story involving somewhat implausible odds:
We were fighting some kind of demon or devil in 3.5, and the party was in rough shape. The cleric (of the god of death) perished, but was returned by his deity to finish the battle, with the understanding that whether he ended up succeeding or failing, he would permanently return to the higher planes immediately after the fight (if not during). In the end he struck the final blow against the last remaining enemy...which proceeded to explode in its death throes and knock him to precisely -10 hp. We never settled whether that was how the god chose to take his servant back, or if he was simply spared the trouble of needing to do it himself.