bookies odds vs real odds

**QUESTION 1**

I have a brother who plays the irish lottery every week , he picks 3 numbers and if he matches

them in the 6 drawn he wins £600 . so the bookies odds are **600 to 1** to match 3 numbers.

have i calculated the **real odds** correctly?

total numbers in draw** = 47**

numbers drawn per draw** = 6**

my brother picks **3 numbers only** for a £1

47*46*45 / 1*2*3 = 16215 . total number of 3 number combinations out of 47 numbers

6*5*4 / 1*2*3 = 20 . total number of 3 number combinations from 6 numbers drawn

16215/20 = 810 , so are the real odds are **810 to 1 ?**

**not sure if my workings are correct **

**QUESTION 2 **

__expected value for this game__

bookies odds **600 to 1**

real odds **810 to 1**

**210 / 810 = -0.25 **

so on average my brother loses **25 pence** every time he plays?