Monday, 5 November 2012

Playing the lottery - Is it your ticket to dream?

I have never been much of a gambler.  Went I went to Macau for a weekend I was content to stop playing the tables when I had won enough to cover my boat ride back to Hong Kong.  It came as somewhat of a surprise to me, when I found myself entering (for only the second time in my life) the lottery for tomorrow's draw (Oz Lotto).

The amount of ordinarily rational people that play the lotteries astounds me - one investment banker repeated that old catch line of 'you have to be in it to win it' while explaining that he bought a ticket every week.  While strictly speaking this is true everyone knows that the odds are truly stacked against you.  However the more I thought about it, the more I realised that in big draws your expected value may actually be greater than 1.

That is for every dollar you invest in the lottery, purely statistically speaking you should expect to receive something greater than one in return.  Below are the calculations:

  • For every entry you have a 1 in 45,379,620 chance of winning
  • The cost per entry is $1.20
  • To buy up every single possible combination it would cost you $54,455,544
  • The jackpot is $100 million (you will see soon why this only works for the big prizes)
  • Therefore your expected return is
    • Sum of the probabilities * expected outcomes
    • 1 / 45,379,620 * $100,000,000 
    • $2.20036
  • If you then subtract the cost of entry you get your expected winning
    • $2.20036 - $1.20
    • $1.00036
However before you rush out and buy all the tickets remember that your potential winnings are diluted the more people enter the game.  You need to reduce this expected return by the proportion of people that are expected to win the jackpot.  To know this you need to know the number of tickets sold which they do not disclose.

Also you need to remember that this is a purely theoretical exercise - your chances of actually winning are still only 1 in 45 million.  As an exercise while writing this post I got the ticket I had bought which had 36 different entries.  I then went to last weeks draw to see how many of my combinations even got close to the winning combination - in none of my picks did I get more than 2 of the drawn numbers.  People who play expecting to win the lottery should keep track of how successful they are every week and then perhaps spend less money on it.

However having bought a ticket this time around I realised that the advertising folks may have got it right - I know I'm not going to win but I keep imagining what I would do if I won the $100m.  It most definitely is your ticket to dream - though what the advertising people do not include is that after you dream you have to wake up and get back to your normal life and finances.

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  1. What would happen to your blog if you were to win though, would be a bit redundant haha (couldn't resist but post about that one). I'm going in a syndicate @ work.
    Coincidently there's also another big gambling event (the Melbourne cup tomorrow.

  2. I briefly considered what I would do with my blog if I won the $100m and then realised that I was dreaming once again.

    I ended up winning $21.10 which gave me a return of ~50c on the dollar. I guess there will not be too much a disruption to this blog on that winning!