If a lottery has 300 tickets, shouldn't I win every 300 times I play?

Question

Suppose I play a lottery that has 300 tickets. I can only buy one ticket per draw. Statistically speaking, shouldn't I win once every 300 draws? Is it more complicated than this? **Edit** This question has generated much more response than I had imagined. Thank you all, for your input and your great explanations. To go into further details: The lottery has 300 tickets. You can buy 1 ticket per draw. Every draw, is all new tickets, so in essence, you can hold 1 out of 300 numbers, at each draw. **Edit** Just to give some funny (not really funny) side info. I have now played 1,104 times, and still have not won anything. I suppose I am EXTREMELY unlucky.

Answer 1

And if you continue the experiment , you will get two wins within 300 trials. So it all averages out per the LAW OF LAW NUMBERS a.k.a Law of Averages.

You can simulate this experiment in excel. Use the formula =RandBetween(1,300)

Now choose any integer number you wish to designate as the "winning" number, say 77.

So if you generate 1000 random such integers between 1 and 300, you can see how many times

the designated number (77 in this case) appears as the winner.

I did just that and got 20 wins out of 4500 trials which is 0.004 while 1/300 = 0.003

The cell containing the # of wins is located in cell J234 just below the table of data.

Cells A1:T225 contain random integers between 1 and 300. That's 4500 random integers.

THe name of the spreadsheet is lottery 300, and I uploaded it in the resources section for your perusal.

You can simulate it , so as to convince yourself.