# Deal or No Deal – Part 3 – Reader Poll

Late last year, I asked you (a number of times … just like Howie Mandel) …

…. Deal or No Deal?!

What would you have done [AJC: if you haven’t yet ‘cast your vote’, please go back to this post and drop a comment]?

We know that Ms Tomorrow Rodriguez (sounds like a character out of a James Bond movie)  said “No Deal!” to the miserly Banker’s’ offer that only paid out 1-in-3 for a 50/50 chance …

… Vote 1 for the ‘math kings’!

But, look at the situation that she’s faced with right now (in the photo above):

4 suitcases left: 3 of them contain ONE MILLION DOLLARS and 1 contains only \$300!!

Ms Rodriguez – with the odds clearly stacked in her favor – has two choices:

1. Take the Banker’s Offer of \$677,000

OR

2. Say “No Deal” and select just one more suitcase (then she will be presented with another offer)

Deal or No Deal?

Let’s examine the options:

1. Take the \$677k and run!

OK, the banker has offered \$677,000 but there are 4 suitcases left of which three contain \$1 Million and one is a (virtual) blank.

That smells like a 75% chance of \$1 Million to me … ‘worth’ \$750,000 (any maths whizzes out there to counter this?) … seems to me that the Banker is short-changing Tomorrow Rodriguez by \$73,000 buckaroos!

2. Select just one more suitcase and see what happens next (after all, she can’t lose on the next turn)

Well, here is the problem … unlike any of the lead-up turns, this time there is only ONE non-million case left; so, there are actually two possible outcomes here:

i) Tomorrow selects the one suitcase containing the blank (i.e. \$300) which means that she automatically wins (there are only 3 suitcases left … since each would then have to contain \$1 Mill. she can’t lose)

OR

ii) Three times more likely, Tomorrow selects one of the three suitcases that contain \$1 Million and the chance of winning on the next round drops from 75% to 67% (3 suitcases left: 2 contain \$1 Million and 1 contains \$300 only)

The significance?

From this round on, the Banker Deals can only get worse, because the next round after this one would leave just 2 suitcases (assuming that she hadn’t won by then) … or, a 50/50 chance (and, we’ve already seen how much the Banker will rip her off on that)

In fact, Tomorrow is effectively paying for each ‘roll of the dice’ from here on in … whether she realizes it or not …

So, if she turns down \$677,000, Tomorrow is really saying: “\$1 Million or Bust … I’m going all the way, Baby!” … because she will surely turn down the later, much lower offers (been there, done that!) as well.

So, Ms Rodriguez really has just two practical alternatives:

1. A guaranteed \$677,000 if she walks away right now

OR

2. A 75% chance of winning \$1 Million AND a 25% chance of walking away virtually empty-handed

Deal or No Deal?

Just like last time, make a vote & drop your vote into the comment section below (I’d love to hear your reasons) … next week, we’ll check out what our readers had to say … it should be interesting!

In the meantime, do you want to know what Ms Rodriguez chose? Do you agree?

# Deal or No Deal – Part 2 – Reader Poll

Gotta love a show that dangles a \$1 Million ‘carrot’ in front of people’s noses and all they need to do is make some sensible life choices – on the spot, and in front of millions of people 😉

Tomorrow Rodriguez (that’s her name … really!) is a sensible girl: married, been in the army, put herself through school, has a Master’s degree in something-or-other (obviously, not math).

And, she’s made it on to one of those ‘special episodes’ – you know, the ones where they put up 9 suitcases with \$1 Million in each of them, rather than the usual single suitcase: that’s 9 chances in 26 … 35% or roughly a 2-to-1 chance of walking away with \$1 Million.

Deal or No Deal?

OK, but there’s a twist … first you get to pick some suitcases and the ‘Banker’ makes you a take it or leave it offer:

He’ll give you \$43,000 to walk away right now! In fact, that’s exactly what he offered Tomorrow very early on in the show …

Deal or No Deal?

You say “No Deal!” (do you?) and pick a few more suitcases … the offer goes up and up, but you keep turning the Banker down, down, down, until the money gets serious.

Now, more than half the suitcases are gone (and 3 or 4 of the ones with \$1 Million in them, as well) but you still have a few ‘million dollar suitcases’ as well as a few lemons left … but, you have chosen well (birthdays, tarot readings, and horoscopes are really working well for you today).

The Banker offers you \$134,000 to walk away, right now!

Deal or No Deal?

Of course, you say “No Deal!” (are you sure that you do?) and Howie asks you to pick just two more suitcases … the offer goes up to …

… the amount in the photo above!

Deal or No Deal?

If you haven’t dipped out already, here’s something interesting to note; it may or may not change your mind, but it’s interesting nonetheless:

There are 6 suitcases left [AJC: one suitcase, also containing ONE MILLION in the bottom right has been cropped in the photo at the top of this post]:

3 suitcases containing virtually nothing (max. of \$400) AND

3 suitcases containing \$1 Million

So, the odds are exactly 50/50 that’s you’ll pick one of the suitcases that guarantees you \$1,000,000 so the banker should offer you \$500,000 (give or take a few bucks) …

… BUT, the Banker’s Offer is only \$349,000

Deal or No Deal?

Let me know where you stopped … click on one of the options in the poll … if you’re up for it, you can also drop the reason for your vote into the Comments section below … this should be fun!

In the meantime, do you want to know what Ms Rodriguez did? We’ll talk a little more about that next week 🙂

# What's the probability that you'll even read this post?

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.

In practice:

1. You should understand basic probability because it is so important in life,

BUT

2. You should first make the Life Decision then look at the odds …

Deal or No Deal?!