Putting a price on ‘long’ odds

December 03, 2007 5:05 AM
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I couldn’t help but chuckle as I read an article in The Motley Fool. It talked about the outrageous odds to win a Lotto drawing and the atrocious paybacks of these drawings — frequently at around 50% or worse.

In the end, it concluded that you’d be better off buying stock in some of the gaming companies rather than playing Lotto.

I’m not really sure how most gaming stocks have been performing, although beating a negative 50% return shouldn’t be too hard. I just found it ironic because I remember my dad always telling me that the world’s largest casino wasn’t in Las Vegas, it was in lower Manhattan (New York City), meaning the New York Stock Exchange. It is where more people go to gamble with their money than any other place I can think of!

It really is no surprise to most that the odds of winning a Lotto drawing are very long odds. The exact odds depend on the number of possible numbers, the numbers you need to get correctly and whether or not the order of the numbers have any significance (as is the case with Powerball, where the final number must be in specific order).

Generally speaking, the odds of winning the jackpot range from a low of 15 million to 1, all the way up to 100 million to 1 and then some.

Calculating the payback is a bit more difficult as the top prize is essentially some form of progressive with the contribution rate not fully known. Further complicating the matter is that you never know how many tickets have been sold which can affect the likelihood of you sharing the top prize.

So, in cases where the game might have appeared to go positive because the jackpot is $150 million, this is not necessarily an accurate picture of what is happening. As the jackpot grows, the number of tickets sold grows. As this grows, the likelihood that you’ll win the entire jackpot by yourself is diminished.

The odds that you at least share the jackpot does not change based on the number of tickets sold, but the probability that someone else picked the same numbers you did does grow.

The lower prizes in Lotto can almost be insulting. If you get 6 out of 6 numbers, you might win $10 million, $20 million or even $100 million. Get 5 out of 6, and perhaps you get a couple thousand. With 4 out of 5, you might win only a few dollars.

While the odds of hitting 4 out of 6 is greatly higher than hitting 6 out of 6, the percent contribution to the payback of each winning combination tends to have a much different distribution than the casino games we are more familiar with.

So, the paybacks are bad, the odds of winning are ridiculously low — why do people bother to play Lotto? I think it is the size of the jackpot. People are willing to accept these conditions when the prize is a life altering jackpot.

If they were to revamp Lotto and have it pay the same 50% payback but with a top prize of $100,000, I think the game would just sit there — some might say that this is basically what has happened with keno.

Keno is essentially a lot like Lotto, but you have some flexibility on how to pick numbers. Also, keno may have $50,000-$100,000 top prizes, but this is a far cry from $100 million.

People are also willing to throw a few dollars at something like Lotto because it might mean a few dollars lost one to two times a week. If you could somehow play Lotto the way we play video poker, we may find too many people losing so much so fast that the game would never succeed.

However, the risk of a few dollars twice a week for the chance to become a multi-millionaire is just too compelling for people.

I wonder whether Wall Street or Lotto has turned more people into millionaires? Even if it’s the former, there will be plenty of Lotto players who will be content to chase the weekly dream.