Well, if we look at all the billions of people on this planet [AJC: is it 6 billion or 8 billion now … damn, I lost count] … the chances are minuscule.
If we take all the people who use the Internet daily … still microscopic.
If we take all the people who read Personal Finance blog … not much chance.
If we pick all people who read the self-prophesying headline to this post …. bloody great! You see, it WAS a trick question of sorts …
… all to lead me on to the subject of Probability … as in “it’s probable that your eyes will glaze over just about now, and you’ll click back to Pamela Anderson’s home page” … brought to my attention by a recent post from an excellent blog by All Financial Matters, appropriately titled Probability 101.
Even if you hated math [AJC: in other countries, known as: maths] and statistics, stick with me past this excerpt:
I’m in the process of reading Peter Bevelin’s awesome book, Seeking Wisdom – From Darwin to Munger (Not an Affiliate Link). I HIGHLY recommend this book for anyone interested in investing and behavioral finance. As boring as that sounds, this book is a page-turner. One of the sections of the book that I found most interesting was this illustration of probability on page 151:
A lottery has 100 tickets. Each ticket costs $10. The cash prize is $500. Is it worthwhile for Mary to buy a lottery ticket?
The expected value of this game is the probability of winning (1 in 100) multiplied with the prize ($500) less the probability of losing (99 our of 100) multiplied with the cost of playing ($10). For each outcome we take the probability and multiply the consequence (a reward or a cost) and then add the figures. This means that Mary’s expected value of buying a lottery ticket is a loss of about $5 (0.01 × $500 – 0.99 × $10).
The first comment that I would make is that whilst you need to understand the basics of a ‘good decision’ against a ‘bad decision’ in probability/statistical terms, simply running your eye over the key line “A lottery has 100 tickets. Each ticket costs $10. The cash prize is $500” should do the trick:
If you bought all 100 tickets, at $10 each, you would spend $1,000. But you would only win the cash prize of $500 … are YOU smarter than a 3rd Grader?
But, as one of the comments on that post pointed, out not all decision that SEEM to be mathematical ARE simply mathematical:
Unfortunately, probability doesn’t always translate directly into real-life situations.
Let’s take your example of the lottery, except we’ll change things up a little.
Mary is 50 years old and approaching retirement. She’s been financially savvy for her entire life and has accumulated $1M in cash.
Donald Trump decides to hold a lottery for only Mary. One ticket costs $1M, and she has a 50% chance of winning $10M.
If you looked at just probability, her EV is -(0.5 x $1M) + (0.5 X $10M), or +$4.5M. Does that mean she should buy the ticket? Obviously, no.
I think what this comment is saying is that EVEN THOUGH you have a 50/50 chance of winning 10 times your money, you shouldn’t invest your entire life savings into it … because you have an equal chance of ending up flat broke!
The concept is good, but I take issue with the “obviously no” bit …
The numbers in this example are ridiculously skewed for most people, so I tried to give some ‘closer to home’ examples in my post centred on that popular game show, Deal or No Deal.
It all boils down to this:
When a decision is potentially Life Changing … the numbers count less … the possible result counts more.
1. You should understand basic probability because it is so important in life,
2. You should first make the Life Decision then look at the odds …
Deal or No Deal?!
Whether you should take the gamble or not depends on how risk averse you are as we economists say. It’s a question of maximizing expected utility (happiness, wellbeing) rather than expected profit. Only someone who is “risk neutral” will maximize expected profit without paying attemtion to the downside. So there is no “obviously no” it all depends on how risk averse Mary is…
“Fooled by Randomness” is a good book about the inability of many individuals to logically apply an expected statistical outcome to situations where money is at risk (the author talks primarily about the stock market). The book echoes your same idea/point.
Just throwing that out there in case anyone was interested in more info on the topic
@ Moom – I wouldn’t risk $10 Mill. to have a 50/50 chance to win $100 Mill. … I will, however, chance many hours and some expense in blogging, writing a book etc. to have a miniscule chance of making a “Robert Kiyosaki-like” $26 Mill.
The $10 Mill. was just too damn hard to go through making again, and gives me everything that I need now (if I ‘needed’ $100 Mill. for my life to work, then I would go for it in a shot!).
On the other hand, I write for the enjoyment of sharing knowledge … if I make the ‘big bucks’, well, so be it … if I don’t, it’s no biggie.
@ Andrew – Haven’t read that particular book, but I am saying that even a logical person should ONCE IN A BLUE MOON make decisions AGAINST the odds when one of the possible outcomes is critically important.
This post reminds me about something I remember seeing in the headlines about a guy becoming a millionaire after winning at the races by betting on a horse for which the odds were literally 1Million-to-1.
oopss. forget to mention the obvious (for emphasis) that all he put at risk was $1
@ blogrdoc – You know where my facination with the Number 7 came from?
I went to the races on my 27th birthday (happens to be 7th July) and a horse named 7th Heaven was running in Race # 7 with odds of 700 to 1 … naturally, I bet all of my savings: $7,000 to win!!
… the horse came 7th :))
Read this….it is shocking….
The lottery is usually set very far against the players.
There was one exception. About 10 years ago there was a company that decided they could make money playing the lottery. It was a lottery in a smaller state with odds of about 1 in 4million. But the lottery had not paid out in months and the prize money was over 30million. This company had the money to buy 1 ticket of EVERY combination. So as soon as they could buy tickets they started, and were able to buy 2.5 million tickets. They wanted to get all 4M but there simply was not enough time, because they had to get printed paper tickets to make it work. Lucky for them they did win, unlucky for them so did one other guy. At the end of it they walked away with a profit of over 10M. The local people were very upset, they wanted the lottery to NOT pay them, the company won in court, but decided that to never do such a thing again.
@ Jason – ’tis sad but true: there are NO shortcuts to wealth … you need to learn the critical lessons of money on the way UP to stop you from falling back DOWN. Happens to lottery winners, sportsmen, celebrities … when the money stops flowing in the tide starts rushing out …
i need to know what the saying ‘once in a blue moon’ has to do with chance and probability, please help!
@ Laura – What’s the CHANCE that somebody reads this post nearly 18 months after it was first posted?! I mean, that’s like saying people read my posts ONCE IN A BLUE MOON 😛