Confused about EV

[Colombo]

I'm planning on doing a project on why playing the lottery is futile in my calculus class. I'm going to outline EV and explain how it is calculated. However, I am having a difficult time trying to figure out how to calculate the EV of a lotto ticket.



That is a picture of the payout structure for the mega millions. Now, how would I calculate the eV of a $1 bet?

[jay_shark]

E(X) = x*p(x) {sum of all x [img]/images/graemlins/tongue.gif[/img](x)>0}

If you purchase one line , your expectation for a 1$ bet is :

2*1/75 + 3*1/141 + 10*1/844 + ... + jackpot*1/175 711 536

Add all these numbers up which should give you your EV for a $1 bet .I'm assuming you get the purchase lines of numbers and the correct line wins . For this particular case , you're purchasing one line of numbers .

[jay_shark]

lol that happy face shouldn't be there .

It should be { sum of all x for p(x) >0}

X is a random variable which in this case is the dollar value for each prize .

[Kerth]

If the jackpot's around $143 million it's ev neutral!

[T50_Omaha8]

Note further, however, that "jackpot" is not simply stated as a dollar amount. If, say, 25 million people play the lotto that day, you'll have to decrease the jackpot accordingly since there is a decent chance it'll get split.

[Tom1975]

The main problem with the lottery isn't the EV (although it almost always is negative), it's the variance.