Magic Drafts as Markets
MARKET SYSTEMS
Anyone
who has taken a basic economics course can decribe a what a "Market System"
is. It's a system in which people (sometimes called market "agents") can
exchange goods and/or services for other goods and/or services.
For example, any store is a small market where people trade money for
goods, such as food, clothes, books, or cards. People with money are
refered to as the "buyers" and people with goods are refered to as "sellers".
In the one store system, there is one seller and many buyers.
Note that groups of stores (such as all stores within 20 minutes that sell
cards) also form markets. Such markets have multiple buyers and sellers.
These markets are very useful in most areas of economics, but we only need
to consider the one store market for the following analysis.
DRAFT MARKETS
Consider Booster or Rochester drafts as a Market System. In particular,
there is one seller (the judge who provides the cards) and eight buyers
(the drafters). The judge "sells" cards and the drafters "buy" cards
by expending draft picks. Normally in economics we consider the interactions
between buyers and sellers, but because there is only one seller, the interaction
is trivially a monopoly. Instead, lets consider the interaction of
buyers with other buyers. In other words, we're going to use economics to
explain how drafters interact with each other in a draft setting.
MERCANTILISM
Mercantilism
was an economic belief held by the British government in the
17th
and 18th centuries (1600s and 1700s). The idea was that all trade
with
colonies (eg. America, India) must go through the central government
(eg.
England). The purpose of colonies was to increase the wealth of the
central
government.
Note
that Mercantilism is very similar to socialism's economic policy of
central
planning. The ineffectiveness of Mercantilism and central planning
contributed
to the respective downfalls of the British and Soviet empires.
FORCING
COLORS
In
the draft market, a Mercantilist economic policy is embodied as the
strategy
of forcing colors. Forcing a color is intentionally drafting
a
lot of one color so that others will not draft that color and instead
draft
relatively worse cards. It's equivalent Mercantilism in that
in
both cases, one buyer (eg. England, or Jon Finkel) tries to force
another
buyer (eg. America, or Randy Buehler) to pay a higher price for
a
valuable commodity (eg. Food, or Saga Black).
FREE
MARKET
In
1776, Adam Smith wrote "The Wealth of Nations", a mammoth treatise
explaining
why Mercantilism was an ineffective economic policy. In "The
Wealth
of Nations", Adam Smith proposes a new market system, called a
"Free
Market", and explains why that system produces more economic
prosperity.
The
basic idea is that when the government leaves a market alone, sellers
naturally
maximize their profits and buyers naturally maximize their utility.
(Maximizing
utility is economic jargon for, "do the thing that makes me
happiest.")
Suppose
all buyers in a market have equal impact on the market, as do all
sellers.
Buyers and sellers can all make decisions about the market.
"I
am willing to buy X for any price less than $35." "I am willing to
sell
X for any price higher than $15." Buyers and sellers know what the
best
decision for them is. When the government tries to legislate decisions,
such
as, "All colonists in America will buy X for at least $40," they're
forcing
buyers and/or sellers to make decisions that aren't optimal. This
causes
loss of utility for the buyers AND the sellers. (Loss of utility is
economic
jargon for, "I'm not as happy as I could be.") See an economics
text
book for a more detailed treatment of why free markets work and what
limits
exist on them.
SURFING
THE DRAFT
In
the draft market, the free market economic policy is known as "surfing
the
draft." Surfing the draft refers to drafting whatever colors people
aren't
taking. It's like a free market system because you let the whole
market
(the other drafters) determine what the optimal choice for you is
(whatever
color exists in quantity).
To
understand why draft surfing works, we need to clear our minds of old
prejudices
of colors. We might say, "In Urza's Cycle, black and white are
good
in draft, but the red is terrible." Concluding we should always
draft
black or white, but never red, is a mistake.
View
the cards in a draft as providing a certain amount of utility
(usefulness)
that the drafters can buy by expending draft selections.
We
can assign point values to each color in the draft. In Urza's Cycle
drafts,
I personally assign points as follows:
White: 4
Blue: 3
Black: 4
Red: 2
Green: 3
Your
milage may vary. In any case, it's no coincidence that the point
totals
add up to exactly 16. In general, draft decks consist of two colors.
Mono-color
draft decks naturally have twice as much as one color. There
are
16 points divided between 8 drafters, so each deck should contain 2
points--
1 for each color.
Rather
than saying, "Urza's cycle black is good and red is bad," we should
say,
"Urza's cycle black can support 4 drafters but the red can only support
2
drafters."
FORCED
DRAFTS
If
a player tries to force a color, there is a good chance that color will
become
saturated. Suppose I tried to force black and took some white.
Lets
say that because of this, 5 people drafted black and 4 people took
white.
Then my deck is worth less than 2 points. The black cards are
worth
4 points spread between 5 drafters, so we each got .8 points from
black.
4 points of white between 4 drafters gives me 1 point, so my deck
is
worth 1.8 points. If I had tried to draft mono black, then the table
would
have 6 black drafters (2 of which were me), and my deck would be worth
4
* 2 / 6 points, or 1.333 points. Of course, others players would be
likely
to drop black, so perhaps there would only be 5 drafters: 4 * 2 / 5
is
1.6 points.
SURFED
DRAFTS
When
surfing a draft, each player chooses colors that other players are
not
drafting. Since no player chooses a color that has become saturated,
there
will always be 4 white drafters, 3 blue drafters, 4 black drafters,
2
red drafters, and 3 green drafters. In this situation, each player gets
1
point from each color, so everyone's deck is worth 2 points. This is
a
perfectly balanced draft.
REAL
DRAFTS
Real
world drafts are a mixture of forcing and surfing. Some player
inevitably
thinks that the best thing to do is force the draft, and the
players
who surf take advantage of the situation. Here's how that works.
Lets
suppose that all other players at the table have selected their
colors
but you, and that they are overdrafting blue.
White:
2 (Max 4)
Blue:
4 (Max 3)
Black:
4 (Max 4)
Red:
1 (Max 2)
Green:
3 (Max 3)
Note
that the numbers add up to 14 because only 7 players have made color
selections.
The two unclaimed colors are white and red. Incidently, no
matter
how you break out the numbers, there will always be an underdrafted
color
if there is an overdrafted color. (For a proof of this, just apply
the
pidgeon hole principle.)
You
must either draft white twice or white once and red once. If you
draft
double white (100% white), your deck will be worth 2 * (4 / 4),
or
2 points. If you draft white and red (50% of each), your deck will be
worth
4/3 + 2/2, or 2.333 points.
I
think the optimal solution is to draft 67% white, 33% red. Your deck
will
be worth 2 * (2/3 * (4 / (3 + 2/3)) + 1/3 * (2 / (1 + 1/3))) points.
Simplified,
that is: 2 * (2/3 * 12/11 + 1/3 * 3/2), or 2 * (8/11 + 1/2).
This
is 27/11, which is 2.4545 points. The optimal solution can be
derived
using maximization techniques from calculus.
In
any case, the best thing to do is draft heavy white and splash some red.
By
contrast, the average blue/black deck will be worth 1.75 points, because
3
blue points got spread out between 4 blue drafters.
ADVERTISING
COLORS
"If
surfing the draft is such a good idea," you ask, "then why do some
profession
players advertise what colors they like?" It certainly seems
like
they're trying to force colors.
Well,
they are and they aren't. Think of it as letting other players
know
ahead of time which colors you would like to claim. This encourages
the
drafters to select colors you have not selected. Advertising colors
helps
everyone do a better job of surfing the draft.
Remember
how Jon Finkel would only draft Red, Blue, and White during Rath
Cycle?
It doesn't matter which three colors Finkel chose as long as everyone
knew
what those colors were. Darwin Kastle did as well as Finkel, but Kastle
advertised
that he played Black and Green. The colors themselves are
worthless
compared to the information that the other drafters in the market
receive.
Giving other players information about what colors you draft helps
them
help you.
BROKEN
ASSUMPTIONS: BOOSTER DRAFT
Advertisement
helps solve the problem of missing information, which plagues
booster
drafts. Many pros prefer rochester draft to booster draft because
in
rochester, it's obvious who is drafting what color. This enables drafters
to
avoid oversaturating colors. In booster draft, maybe some packs just
had
a lot of black in them, despite the fact that three people upstream
from
you are taking black. You could accidently oversaturate black because
you
didn't have all the information.
So
if you try surfing a booster draft and things just don't work out, it's
probably
because of this. The Draft Market assumes that each player knows
how
much of the colors the other players are drafting, and this isn't true
in
booster draft.
BROKEN
ASSUMPTIONS: ROCHESTER DRAFT
Rochester
draft breaks a different assumption. The Draft Market also
assumes
that each player starts with identical resources. This is not
true
in rochester draft, because some players have to take their first
picks
earlier than other players.
Normally
rochester drafts don't get oversaturated colors. Sometimes,
however,
the drafts are more suceptable to color forcing. If I have the
very
first pick in the draft and draft corrupt, I'll want to play black.
But
after that, I only get 8th/9th pick, and then 7th/10th pick. It's
quite
likely that I won't get any decent black cards for a while, if the
players
to my left force black.
Of
course, even in this situation the players who force colors don't get
decks
worth that much more than 2 points. The players who really win
from
this situation are the players in seats 6-8, who haven't expended
their
early picks on a card it turns out they can't play.
In
either draft format, someone can screw you if they want to, but it's
better
off for both of you to help each other and not draft the same colors.
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