Are My Chances Of Winning Better If I Play Less Often..?

[Q] Your chances of winning the UK Lotto are normally about 1 in 13 million (as it's a 6 from 49 game). If you buy 4 lines in one draw then your chances are 4 times better, so about 4 in 13 million. I've heard it's better to play more entries in one draw, but if you buy 1 entry for 4 weeks, aren't your chances exactly the same 4 in 13 million?

[A] Your figures are not quite right. If you play once a week for 4 weeks the probability is not 4 in 13 million, it's actually slightly less than that.

Think of it this way. If you played the lottery once a week for 13 million weeks, would you be guaranteed to win the jackpot? The answer is of course no, because you still only have a 1 in 13 million chance in EACH draw. So it's perfectly possible to play 13 million times and never win. Alternatively if you played 13 million lines in one game, you would definitely win.

If you think in terms of dice it's much easier to get your head around. The prize is £1 million - which would you rather bet on:-
a) roll the dice 6 times and pick 1 number each time, or
b) pick 6 numbers and roll the dice once, or
c) are they the same thing..?

I think you'd probably take b)  :-)

Here's The More Complicated Explanation...

(...so you might want to just skip to the how to boost your chances of winning bit below!)

You're still reading..!  ;-)

Mathematically speaking, if you're calculating independent events you multiply, for dependent events you add. Lottery draws are of course independent events as the results of this weeks draw are not in any way affected by last weeks results.

So to work out the chances of winning in any of the 4 weekly draws, you need to work out the probability of winning in each draw and then add them together. At first glance this might seem like 1/13 million x 1/13 million x 1/13 million x 1/13 million - but it isn't because that would be the probability of winning in all 4 draws and you're interested in winning ANY of them!

So what you actually need to calculate are these 4 outcomes and add them together:-

Outcome 1 -> Draw 1 - Lose, Draw 2 - Lose, Draw 3 - Lose, Draw 4 - Win
Outcome 2 -> Draw 1 - Lose, Draw 2 - Lose, Draw 3 - Win, Draw 4 - Lose
Outcome 3 -> Draw 1 - Lose, Draw 2 - Win, Draw 3 - Lose, Draw 4 - Lose
Outcome 4 -> Draw 1 - Win, Draw 2 - Lose, Draw 3 - Lose, Draw 4 - Lose

Technically you would also be interested in adding on the chances of winning in more than 1 draw (i.e. lose, lose, win, win etc), but it doesn't make much difference to your chances (just to your bank balance!).

The Boost Your Chances Of Winning Bit!

The bottom line is that your chances are marginally better if you play the same total number of entries but play them in less draws. So for no extra outlay you get a better chance. The effect is greater the larger your number of entries.

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