On this fourth article of my Probability in MTG series, I
discuss what it takes to be able to “go infinite” in MTG: Arena BO1 drafts.
What are MTG: Arena BO1 drafts?
Arena drafts are events that cost 5000 gold or 750 gems. You
get to play best-of-one (BO1) matches until your either accumulate 7 wins or 3
losses and gain prizes depending on your number of wins.
What is “going infinite?”
In the current MTG:Arena BO1 draft event, winning 6 times or
more ensures that you gain enough prizes to join another event. Winning fewer
times than that allows you to recoup some of your entrance fee, depending on how
many games you won. Going infinite means being able to win enough games on
average such that on average, you gain more gems than you lose. This is described
as having positive expected value (EV). I wrote a previous article on EV here
but the examples used are more related to MTGO than Arena (the concept of
EV is the same in either platform).
The Math: Negative Binomial Distribution
I discussed probability distributions and how they relate to
MTG in another previous article. Here I will just cut to the chase and say that
in the MTG:Arena BO1 draft event, the probability distribution of interest is
the negative binomial. This distribution fits the random variable that counts
that number of successes before the rth loss. In our situation, we want to be
able to determine the probability of winning X number of times before our 3rd
loss. This probability is affected only by our probability of winning; a number
which we have to assume. With this distribution defined, we can then use it to
compute our expected value for playing the game. The following table provides a
summary of expected values across different win rates.
Win Rate
|
30%
|
40%
|
50%
|
60%
|
75%
|
80%
|
EV (in Gems)
|
-597
|
-518
|
-403
|
-251
|
5
|
80
|
As you can see from the table, a win rate of about 75% is needed
in order to “go infinite.” That is, if you believe that you win at least 75% of
your games in draft, then by playing a large number of games, you should end up
gaining more gems than you lose. A caveat of this computation is that expected
value is an average. That is, there is considerable variance involved in that
estimate so that even if you do have a 75% win percentage, you will still need to
bankroll your drafts at the beginning in order for you to be able to weather out
early losses.
So what does all of this mean?
First, going infinite on BO1 drafts is no easy feat.
However, it is also far from impossible. If you are just starting out in MTG, playing
more drafts should improve your understanding of the format and push your win
rate up. A nice element of draft is that your win rate is not affected by your
wallet. That is, you do not need to have a tier 1 constructed deck to win consistently.
Second, even if you’re not yet quite at 75%, doing drafts is still a good idea.
An EV of -251 gems means that if you start on 9,200 gems ($49.99), you’d be
able to do about 36 drafts on average before your stash of gems gets depleted. That
means you’d have opened about 108 boosters, not counting the ones you win from
prizes. This is valued at 18,000 gems which is double of the number of packs
that 9200 gems would have been able to buy. Even if your win rate is just 30%,
you’d still end up with the same value on average as the number of packs that
9200 gems would have been able to buy. One factor that I did not take into
account here is that of wildcards, which you would get more of by just opening
packs than by drafting. However, the difference in raw value should be able to
make up for this as long as your win rate is not too low.
Finally, drafting looks
like a solid way to build one’s collection in preparation for standard. Daily
rewards enable one to accumulate enough gold to do a draft a week. In my opinion,
similar to how MTGO has a golden rule to never to open packs, it is in the best
interest for Arena players to never use gold/gems for buying packs. Perhaps
with the exception of really needing those wildcards to make a specific deck
quickly.
Experience disclosure
I have only done just 4 GRN drafts on Arena so far, myself
(I still mainly play MTGO). My records were 7-1, 3-3, 2-3, 7-2. So This means
that from an initial input of 1550 gems, I am at 950 gems (losing 600 gems
after 4 drafts so far) with enough gems to buy into another draft without needing
to purchase more gems yet. That’s with a sample win rate of about 68%.
May the shuffler be with you.
Comments
Post a Comment