Introduction:
In
this post I am going to discuss a trick for not letting the mulligan tilt you.
Granted it won’t always work, we’re all susceptible to cognitive and emotional
biases. However, I find the underlying logic of the Game Show Door Problem
helps me avoid negative thoughts when I see a hand post-mulligan. I don’t write
this article to make you feel better about a crappy hand you get to ship away,
but hope to help you feel at ease with the new hand you are dealt. Now, on to
our scenario!
You
have made it to the final of a game show (congratulations!), and the grand
prize is a brand new car. What’s that? You don’t need/want a new car? Well substitute
any prize you would like (maybe it’s a pro-tour invite?). The catch is the car is
behind one of three doors, and behind the other two doors are goats as booby
prizes. “Wait!” You say, “what I really wanted was a goat!” In this case the goat
is something you absolutely, positively, not in a million years, would ever
want. For me, that’s a goat, but that will remain a story for a never time. Okay,
now that we are on the same page, and we know 2 doors have items we don’t want,
and 1 door has our precious, we can begin.
Now,
you must choose a door! So for simplicity’s sake, you choose door number 1. The
crowd hushes, and the room gets eerily silent because the crowd knows the
catch. Before the announcer reveals what’s behind your door, she shows you that
behind door number two is a goat. Now the announcer gives you a choice between
sticking with door number 1 or changing to door number 3. The underlying
problem is not what your decision is, but why you make it. I love proposing
this question, and learned it from a professor as an illustrating just how bad
we can be at looking for reasons behind our decisions. In a class with 13
advanced graduate students, who for many this was their last class the decision
was split in half. In other classes this professor has received about the same
50/50 split, and it mirrors the responses I get when I ask people. So should you stick with your guns, or switch
doors?
The
Big Reveal:
You
should switch your pick once the goat is revealed. Generally when people stick
with their door, they believe they have a 50/50 chance of being right, and so switching
doesn’t improve their odds. Most people who choose to switch cite the same
logic, and believe they too had a 50/50 chance. In both cases, the why is
incorrect, and in actuality you have a 66% chance to be right if you choose to
switch.
In
this scenario, people tend to think the chances of their door being right
changed once a goat was revealed. People believe they went from having their
choice be correct only 1/3 of the time to ½ the time. The flawed reasoning
behind this is they ignore the fact that no matter what door you choose, there
will always be a goat behind one of the other two doors. Therefore, when we
reveal a goat, there is still only a 33% chance of the initial choice being
correct, and a 66% chance of a goat being behind your door. Revealing the goat
did nothing to change the odds. However, now door number three is has a 66.67%
chance of having your precious, and so you should switch.
This
underlying logic of probability not changing based on new, but irrelevant information
is a problem I believe M:tG players struggle with when it comes to seeing their
hand after mulligans. I know I’ve sat there decimated looking at my hand after
a mulligan to six, or five, or four. All I can think about is just how bad this
hand is, when really I could focus on something more productive. Human beings
are emotional creatures, we feel before we think, and even feel and react
before we think (which has positives and negatives, but in the realm of M:tG,
it is usually a negative). My trick is to take a breath, and think about this
logic problem.
Before
you took the mulligan you believed your chances of winning the game were lower
if you kept than if you shipped. The fact you now see a hand with 1 fewer
cards, no matter how bad that hand is does not change the probability of
winning with a mulligan. And instead of thinking about how to win the game with
this hand, or a hand with 1 fewer cards, we get caught ruminating on how bad
our hand is. I’m not the original decision to mulligan is always correct, and I
know I am constantly trying to get better at determining the win probability
with my current hand versus an average mulligan hand. However, if you decide to
mulligan, you can’t focus on how the last hand compared to this specific hand,
because that wasn’t the choice you made. You chose to mulligan because the
chances of winning were lower with the hand you shipped versus a random hand
with one less card.
I
hope this article provides a different way to deal with hands after you
mulligan, and as always look me up on twitter, email me, or comment on the
blog, because I dig the feedback. Until next time, may the variance be with
you.
----D.
@djkmtg
No comments:
Post a Comment