marți, 1 februarie 2011

Final Lotto Post

Anon in my previous lotto post has been playing devil's advocate saying that he/she is still going to play the lotto. Here is the comment:

Well, if the choice is a dollar on the roulette wheel vs. a dollar on consumer goods, I say let the good times roll! or, as you suggest I could take my weekly dollar and put it in a savings account and at the end of 30 years at 4.0% (taxed) I'd have 2,300 dollars which with inflation will be worth less than 1,000. Since I will have saved 1560 dollars from a lifetime of avoiding the lottery and depriving myself of M&Ms, that doesn't seem like very good return. Even if the chance of winning the lottery is teeny-teeny tiny, it is still larger than my chance of getting great honking wads of cash with my dollar any other way. Hey, someone has to play devil advocate! I should mention here that the 2nd dollar that you spend on the lottery each week is completely wasted since it does not appreciably increase your odds. Guess I wont have to skip the diet Coke.

First, if you took that $1/week and invest it in the stock market for 30 years, assuming a 10% rate of return, you'd have almost $9,000. Take into account 3% inflation and you're looking at $4,000. True it's not "great honking wads of cash", but I'll take it.

Ironically, you touch on the second point I wanted to make: "the 2nd dollar that you spend on the lottery each week is completely wasted since it does not appreciably increase your odds". This is even more true over the entire 30 years. I took a look at the fictional lottery that I mentioned before, and here is what I found

After 30 years
Probability of matching 3 numbers 99.9999820851%
Probability of matching 4 numbers 48.7778006739%
Probability of matching 5 numbers 1.0045145272%
Probability of matching 6 numbers 0.0031159717%

After 30 years of playing the lottery, you have a 99.9999% probability of matching 3 numbers. So you'll definitely win that $3 dollars, but you'd have spent $1,560.

You have a 48.77% chance of matching 4 numbers, so then you'll win a couple hundred dollars.

Now it gets really bad, even after playing for 30 years, week after week, you would still only have a 1% chance of matching 5 numbers and a .003% chance of matching 6 numbers. Needless to say, your expected value is still quite negative. Plus remember, this is the cumulative probability, you're still very unliklely to win on each individual lottery game.

So there, that's it. No more lottery posts after this, I swear. :)

On another note, Anon, thanks for playing devil's advocate on this one. If you're going to forgo those M&Ms to play the lotto, that's fine. The sad part is when you have people that forgo food for their families to play the lotto.