Was at work today thinking about ICM (independent chip modeling), when someone mentioned something about winning the lottery.

So i got to thinking about why people play the lottery. Take this situation:

its the end of the month and you have to pay your rent, we'll say its $1000.
problem is you only have $1. You come across a Lottery that pays out 1000:1
with odds of 1/2000. A very obvious -EV situation that you should never take.
But your $1 is pretty much useless to you and $1000 will save you from sleeping in the street.
so you should take the bet? because your $1 is the same as $.50 or $.25 to you.

just something interesting to me today. Dont know if Math can be applied to it, i guess you could give a value, (not monetary value) for each dollar depending on how many you have.

ok, this probably makes no sense.

http://en.wikipedia.org/wiki/Utility

people play the lottery because... YOU HAVE TO BE IN IT TO WIN IT.
it's a simple as that.

What you are talking about makes perfect sense (and the wiki page on utility posted previously is helpful). But just because your utility for anything less than $1000 is essentially zero doesn’t imply that you should optimally play that lottery you described. For instance, if you had access to a roulette game at a casino, you could bet red or black and if you started by betting your $1 and kept betting everything each time you win, you would have to win 10 straight bets to make enough to pay the rent (I’m assuming that the roulette game would let you bet any amount from $1 up to $512 here). Since your win probability is 18/38, your probability of winning 10x in a row is (18/38)^10 =0.000569 or about 1 in 1758 - a little better than the 1 in 2000 offered by the lottery.

Actually what I described is simpler to calculate mathematically, but not the actual optimal strategy for this bet. It is unless you win 9 straight. For the 10th bet you would bet $500 rather than $512, leaving you with $12 and some hope if you lose the 10th bet. That obviously gives you some nonzero probability of still getting the money in those cases where you win 9 in a row, but lose the 10th that you don’t have when you just go all in for that last bet.

That’s not really the point, though. The point is that even in situations like you described, EV still matters. The roulette bet is still -EV, but less so than the lottery. If you could get a zero EV bet (regardless of odds), you would have a 1/1000 probability of getting your money. If you could get a +EV bet, your probability of success would be even greater than 1/1000.