stats question. If you play the same 4 digit lotto every day, how often (in yrs) would you win, average luck.

Question

Assuming the “Big 4” must be matched straight to be considered a win, the probability of winning would be (10^4) 10,000 to 1 (or 1 in 10,000).

If the bet $100, the payoff is $5,000:
The expected value of winning is:
Winlose
Gain X$4900-$100
P(X)100/10,0009900/10,000

E(X)=$4900*100/10,000 + (-$100)* 9900/10,000
=49+(-99)
= -50

Because the expected value of winning the game is negative, it is in favor of not winning (in favor of the house). Meaning that for every $100 spent, the player will lose $50. I don’t think it is worth taking the chance.

Winlose
Gain X$4900-$100
P(X)100/10,0009900/10,000

Answer 1

Correct, the payout would have to be $10,000 for every $1 played to break even.