powerball suppose you held a lottery ticket worth $10 million. i offer to trade you that ticket for a 10% chance to win $100 million. would you do it? of course not. how about a 1% chance to win $1 billion. that's billion with a b. again, of course not. the expectation of all three scenarios is the same. they are all of equal value. so either should be a fair trade. but you'd have to be insane or a serious gambling addict to make the trade. or i suppose ridiculously wealthy. okay what about a 10% chance for $1 billion? hrm. no. but at least you should think about it. how about 90% chance for $20 million? tempting but no. why not? economists call it utility. your utility for $10 million is high. your utility for $1 billion is higher. but only a little bit higher. so when you decline my kind offers, you are subconsciously maximizing the expected utility. which is what you should do for any game of chance. the dollar expectation for powerball is +$1.18 or so. ie $3.18 minus the $2 you paid for the ticket. it's also irrelevant. the relevant number is the utility expectation. most of that positive dollar expectation comes from the remote chance of winning huge sums. which means the utility expectation is significantly lower. and almost certainly negative. let's put it this way. winning $1000 is nice. but it's not a life changing event. like winning $1 billion dollars. or like winning $100 million. so as far as utility is concerned: utility($1b) and utility($100m) are nearly equal. so substitute $100m for $1b in the dollar expectation calculation. so that $3.18 becomes $0.32. and the reality based expectation becomes a $1.68 loss. which means 'go buy as many tickets as you can afford' is really very bad financial advice.  ¶ 8:00 AM