As far as I know, to decide either you should enter a bet or not, you should get the expected value of that bet
I was wondering if the lottery has a very high expected value, is it wise to join?
There is a real life lottery with this inputs
Choose 5 numbers out of 50
If you get 3 right you win 350
If you get 4 right you win 1000,000
If you get the 5 numbers right you win 10,000,000
Entry fee is 35
So Expected value is
so total of 112.5- 35(entry fees) = 77.5
This is a very high expected value, i wonder if i did the math wrong?
it was like simple probability
3 winning balls should be
(combin(5,3) * combin(45,2)) /combin (50,5)
And so on did I calculate it wrong? or it's just too good ? and if the expected value is more than double the entry fees, is wise mathematically to join for a long run?
Noting that for i know that for even wining 4 numbers, probability to lose is 99.989%
on the long run for 52 times for example, the probability to lose them all is 99.989%^52 = 99.449%
I'm just confused how the expected value is too high, yet by intuition it seems the right decision is not to join even for a long run Or how should I think about it?
Edit : I guess the point is the 1 Million prize will be shared between winners, but i don't know how should i calculate the expected value in that case?