Game Development Reference
In-Depth Information
Who Wants to Be a Thousandaire?
According to the rules of the game, if players get to the $32,000 level in
Millionaire
,
they are also guaranteed that if they lose over the next few questions they will still
receive that $32,000. There are a few of those safety net values in the game that
guarantee that, once you achieve those levels, you won't go home empty handed.
Imagine that you are a player who is at a prize level of $125,000. Obviously, you
have passed the $32,000 safety net—you are guaranteed that you will take home
that much. The next prize level is $250,000—
if you get the question right.
If you risk
going forward by attempting the next question, you
could
win another $125,000 for
a total of $250,000. On the other hand, you could also risk losing $93,000—drop-
ping you back to the $32,000. So, if your odds were 50/50 on winning $125,000 or
losing $93,000, which would you choose? Also, remember that your third option is
to
not wager
any more and simply walk away with the $125,000.
Solving this mathematically from a strictly value standpoint (which is the only
thing numbers can convey without context) is fairly simple. Working with the as-
sumption that we have a 50/50 chance of selecting the right answer (which, in fact,
one of the “lifelines� will guarantee you) makes things even easier. We have a 50%
chance of winning $125,000 and a 50% chance of losing $93,000. We'll shave the
zeros off for simplicity.
This equation says that our estimated winnings (
E
(
W
)) are statistically likely to
be a gain of $16,000. Of course, that is based entirely on the odds being extended
over time. According to the rules of the game, there is no way that after this single
decision we could actually walk out with $16,000 more than the $125,000 we have
at the moment. The formula only shows us that the advantage is slightly in our
favor… and would be statistically more accurate if we were to make this bet numer-
ous times over the long term. Because we are only making this wager one time,
however, the bottom line is that we will either have $32,000 or $250,000. But what
about
not
wagering? We still
do
have the option of not continuing on and simply
taking our $125,000 off the table.
Given those three values—$250,000, $125,000, and $32,000, many of us have
an opinion about the
utility
of the three prizes relative to their face values. Most of
us would be quite pleased to walk away at this point. You often hear players or their
families saying, “That's good enough—I don't want to risk it anymore.� Taking
home $125,000 is “enough� to make us happy about our little adventure. On the
other hand, for others, simply knowing that the
minimum
that they could leave with
was 32 Big Ones is fine with them—they would be willing to risk losing that $93,000
to try for
another
$125,000. But why the difference? Aren't the numbers clear?
