In the previous lecture, we saw that if 
you're going to bet, then you ought to 
pick a favorable bet over an unfavorable 
bet, and even over a neutral or fair bet. 
But the next question is, do you want to 
bet at all? 
And there we have to look at other values 
besides money. 
Let's consider this case. 
Suppose that you can't just bet a dollar. 
This game's not for fun. 
These are serious gamblers. 
Your minimum bet is $100,000. 
And now, if you draw a spade, you win 
$1,000,000 net. 
Cool. 
Well what's the expected financial value? 
One chance in four of picking a spade, 
the amount you win net is a $1,000,000. 
You have to subtract the probability of 
losing three out of four because you lose 
if you pick a heart a diamond or a club 
times the amount you bet which is 
100,000. 
Pretty neat, this bet's got an expected 
financial value of a $175,000. 
Now that sounds like a great bet, but is 
it really a great bet? 
It is favorable and it's only favorable 
financially. 
Imagine that a $100,000 is all the money 
you've got in the world. 
It's what you use to pay your rent with 
it's all your retirement money and if you 
lose it you're going to be out on the 
street with nothing. 
Then should you bet this money? 
No, absolutely not. 
It just doesn't make sense to take that 
kind of risk with this money if you're 
going to be out on the street if you lose 
because you've got three chances in four 
of losing. 
Sure you might win you might be better 
off but you've got an awful lot to lose 
and that's why you shouldn't make this 
bet because there's just too much to 
lose. 
And what does that mean? 
Think about what it means that there's 
too much to lose. 
It's not that there's too much money to 
lose, because you've just calculated the 
financial value of the bet. 
What really is the loss, is security. 
You're not going to have a place to live. 
You're not going to know. 
How to make ends meet, or buy your next 
meal. 
That's the problem, is there're lots of 
other values besides money. 
And, in these situations where we say 
you've got too much to lose. 
It's those other considerations in 
addition to money. 
That make it, a bad bet. 
Now let's look at the other side. 
In some cases, you don't have too much to 
lose, you got too much to win. 
That is, the amount that you win just 
might not add up in the way that you 
thought it would. 
This is the phenomenon called diminishing 
marginal utility and what that means is 
that each increment decreases as you get 
more and more and more of those 
increments. 
You just don't need that much. 
One example is hamburgers. 
If you're really hungry and you don't 
have anything to eat you might want a 
hamburger. 
But what about two hamburgers? 
Is two hamburgers twice as good as one 
hamburger? 
Not really, I mean, maybe you want two 
hamburgers, that would be nice but it's 
not twice as good. 
What about three hamburgers? 
Is that three times as good as one 
hamburger? 
And what about four or five or six or 
seven or eight or nine or ten? 
What about ten hamburgers? 
Are ten hamburgers ten times as valuable 
to a hungry person as one hamburger? 
No. 
because you're going to get full, before 
you ever eat that tenth hamburger. 
So the marginal utility of a hamburger 
goes down. 
The first one might be very valuable to a 
hungry person with nothing to eat. 
The second 1's a little less. 
The third 1's a little less. 
The fourth one's a little less, 
and the difference between nine and ten 
might be totally negligible, because 
they're all going to go bad before you 
eat all ten of them. 
The same thing happens in lotteries. 
Let's compare two lotteries. 
In the first lottery, if you buy one 
ticket for $100, then you have one chance 
in a million of winning $300,000,000. 
That sounds like a pretty good bet. 
I'll let you calculate the actual 
expected financial value of that bet in 
one of the exercises after this lecture. 
But I bet you can do it in your head 
pretty quickly and compare it to this 
lottery. 
If you buy one ticket for $200, then you 
have a one in 2,000,000 chance of winning 
billion dollars. 
Which of these lotteries has a higher 
expected financial value? 
Well, we'll leave the actual calculations 
of the expected financial values to the 
exercises, but you can probably tell, 
that the one with the larger expected 
financial value is lottery B. 
Does that mean that you ought to spend 
the extra money to play in lottery b 
instead of lottery A? 
Well, that depends, I suppose. 
How much more valuable is a billion 
dollars to you than 300 million? 
300 million is a lot of money. 
I could buy pretty much anything I ever 
wanted if I had 300 million dollars. 
I'm not sure why I would want all that 
extra money. 
It's like that tenth hamburger, I 
wouldn't really need it. 
So, which of these lotteries should you 
pick if that's the way you see the 
relationship between the winnings. 
Well even though the expected financial 
value is greater in lottery b you might 
reasonably pick lottery a cause you have 
a bigger chance of getting the 
$300,000,000. 
And the difference between 300 million 
and a billion doesn't matter that much to 
you. 
Not everybody's going to share that value 
judgement. 
But if it doesn't really matter much to 
you whether you have 300 million or a 
billion, then it makes sense to go for 
lottery A. 
And this shows, yet again, that there's 
more to life than expected financial 
value. 
The other values in life are captured in 
the notion of overall value. 
The actual overall value or sometimes 
called utility of an act is simply all of 
the good and bad effects that the act 
actually has, the values of those 
effects, positive values and negative 
values calculated together. 
And the, expected overall value. 
Of the bet, or of an action. 
Sometimes called the expected utility of 
the act is all the good and bad effects 
of the act multiplied by the probability 
of each of those effects. 
So you bring not just the values into 
play, but also. 
The probabilities. 
And if you're really going to decide what 
you ought to do, you shouldn't be looking 
just at money. 
You should be looking at all the 
different values, including security as 
we mentioned. 
Or how much good the money's really 
going to do you if you've going to have 
$300,000,000 anyway. 
There's lots of other things to consider. 
The problem is, how do you calculate 
that? 
How are you going to actually calculate 
overall value or expected overall value? 
Here's an example to show how hard it is, 
imagine that you have a friend that you 
love playin with after school and. 
You then get an offer, of a job. 
And you can make a bunch of money. 
By doing the job after school. 
But then you won't get to play with your 
friend. 
Well, 
how are we going to figure this out? 
Let's calculate the expected overall 
value. 
What's the probability that if you take 
the job you won't be such good friends 
with him anymore, because you won't be 
playing as much and then you'll lose your 
friend? 
And what's the value of that friend? 
You've got to multiply the probability of 
losing your friend by the value of that 
friend. 
Well, how are you going to do that? 
How do you put a dollar value on that 
friendship? 
How do you figure out the probability 
that your friend's going to leave you and 
not be as close anyway as he was before? 
Well, you just can't do that. 
You can't really put it into numbers like 
that. 
There are some economists have very 
sophisticated techniques for taking 
preferences and attaching values to those 
preferences and then multiplying 
probabilities and so I don't want to say 
it can not be done, but the point here is 
just it's a lot more difficult than 
figuring out whether you ought to make a 
bet in a simple little poker game or even 
whether you ought to put your money into 
the lottery. 
When we start talking about real 
decisions about friends and about other 
values in life, some of them cannot be 
reduced to money. 
And then it's hard to put a number on 
them, and it's hard to do the actual 
calculations. 
So I don't want to suggest that any of 
this decision theory regarding expected 
utility is going to actually be applied 
in real life. 
Another reason that's worth mentioning is 
that third kind of decision that I 
mentioned at the beginning of the 
lecture, namely decisions with ignorance. 
Sometimes you don't even know the 
probabilities and if you don't know the 
probabilities, you can't enter the 
probabilities in the formula for expected 
utility or expected financial value or 
expected overall value. 
If you don't know the probabilities, how 
you going to calculate? 
You can't. 
Now there lots of tricky rules that 
people have proposed, for decisions under 
uncertainty, or decisions with ignorance, 
as I call them, 
but none of those are really conclusive, 
and there's big dispute about which one 
is the right rule. 
So a lot of this discussion is going to 
be inconclusive. 
You might have wished that I would come 
in here and tell you, here's how you 
figure out exactly what to do in every 
area of your life. 
Well, I'm sorry, but I just can't do it, 
and nobody else can either. 
Nonetheless, if you think in terms of the 
various factors that we've been 
discussing, Financial value, other kinds 
of values, probabilities of the different 
outcomes. 
Maybe at least you'll be able to avoid 
some of the worst mistakes that people 
make in decisions.