# FAQs

## Overall Odds of Winning

**If the overall odds of winning are 1 in 13 and I play once a week will I win 4 times a year?**

In short, no.

**Why not?**

To make the maths simpler lets look at the chances of rolling a six when rolling a single dice 6 times:

On the first roll the chance of rolling a six is 1 in 6

So on the first roll there is a ^{5}⁄_{6} chance we *didn't* roll a six and in that case we need to roll again.

On our second roll the chance of rolling a six is still 1 in 6, but our overall probability for the two rolls is:

^{1}⁄_{6} + ( ^{5}⁄_{6} x ^{1}⁄_{6} ) = ^{11}⁄_{36} which is slightly *less* than 2 in 6.

Why did we multiply the odds for the second roll by ^{5}⁄_{6}? We did this because we only need to consider the second roll if we didn't roll a six on the first roll, so only in the 5 of 6 occassions that we didn't roll a six.

On the third roll there is a ^{25}⁄_{36} chance that we didn't roll as six on the previous two rolls, therefore the chances are:

^{1}⁄_{6} + ( ^{5}⁄_{6} x ^{1}⁄_{6} ) + ( ^{25}⁄_{36} x ^{1}⁄_{6} ) = ^{91}⁄_{216} which, again, is slightly less than 3 in 6

Another way at looking at this is each time we roll, there is a ^{5}⁄_{6} chance it is *not* a six, so we can work out the chances of not rolling a six more easily:

^{5}⁄_{6} x ^{5}⁄_{6} x ^{5}⁄_{6} x ^{5}⁄_{6} x ^{5}⁄_{6} x ^{5}⁄_{6} which is just over ^{1}⁄_{3}

The general formula for rolling a six in *n* rolls is 1 - ^{5}⁄_{6}^{^}*n* which means the chances of rolling a six in 6 rolls is only about ^{2}⁄_{3}, in fact although the probability rises with each roll it will never be ^{1}⁄_{1} (i.e. you are never **guaranteed** to roll a six).

It works the same way for lottery numbers. Although the probability of a particular number appearing increases with each one drawn, it can never be guaranteed that it will appear within a certain number of draws.