As Magic players, there are times when we feel we are invincible in the game. This happens typically when we are able to choose the
best deck in the format and learn it well enough to be able to crush tournament
after tournament with it. Yet at the same time, we also experience losing
streaks, where nothing we do seems to keep us from going 0-3 drop at each FNM
week after harrowing week. These unfortunate periods, especially when they
occur after we have just had some excellent runs with our deck, can be very frustrating,
with the first few losses leading us to tweak our deck to “fix” what seems to
be wrong, only to lose again. On MTGO, the ability to join 5-round league
tournaments at one’s fancy accelerates the rate of occurrence of both winning
and losing streaks, and the facelessness of an online gaming platform can and
does add to the stress of losing after a very hard-fought game for that 4-1 or
even 3-2 competitive league finish. However, it is important to be able to
maintain a level head and look at the bigger picture, and this article seeks to
help with the latter, particularly by discussing the concept of expected value
and relating it to what one’s personal expectations ought to be when grinding
tournaments.
Expected value or EV is a concept in probability that
provides a measure for the average outcome of an activity. As a basic example,
suppose you are playing a game that costs $5 to join, where you win $10 if a
die roll comes out even and lose otherwise. Thus, each time you play, you
either lose $5 or you win $5, and there is a 50% chance of the game going
either way assuming that the die is fair. The expected value is computed as the
sum of the product of each outcome and the probability of getting that outcome.
In this case, this sum would be: EV = $5 (0.50) + (-$5)(0.50) = 0. What does
this mean? It means that if you play the game a very large number of times and
take the average of your total winnings/losses, that number will be close to
zero. But what about your total winnings? A single simulation in MS Excel of
100 games showed the total winnings to be -$40 in one trial and then $50 in the
next. Both of those numbers are far from $0 which is the expected value. This
means that if you did actually do this, you can end up very lucky and win a lot
of money or very unlucky and lose a lot of money.
An interesting thing happens suppose we change the
probabilities. Suppose it is certain that you have a 60% match win rate versus
the field and that you enter a tournament where you pay $5 to play and will get
$10 for each match you win (net win of $5). The expected value now is $5(0.60)
+ (-$5)(0.40) = $1. Running a simulation with 100 matches shows that the sum is
$70 in one simulation, $150 in the next, $40 in the next and so on. It is still
possible to get negative sums of course but unlike in the first situation where
the probability of winning is 50%, it is far less likely. This means that in
theory, if it is true that you have a 60% win rate versus the field, you will eventually
come out ahead as you grind in more matches in the tournament described above.
Essentially, this happens every time your EV is computed as positive, but it is
not guaranteed that you will experience this gain in a small number of matches.
For example, in the same setting, suppose we simulate only 5 matches, the total
winning can be as high as $25 in some trials (winning all 5 matches) and as low
as -$25 in others. Only when you play a sufficiently large number of matches in
“fair” tournaments will you realize the gain. And even then, you are still
bound to experience losing streaks where you lose one league after the other.
This can happen no matter how good a pilot you are or how well-positioned your
deck is in the meta; it does not necessarily mean that there is something wrong
with your deck. Thus, making knee-jerk reactions like drastically changing your
deck configuration or switching to another deck entirely based on the outcomes
of a couple of tournaments can actually hurt more than help your chances in the
next tournament.
Finally, personal expectations must be tempered by the
reality that losing a match, just like winning a match, is an inevitable
outcome that one will experience as one plays more games. Remaining calm and
looking at the bigger picture, which in the case of grinding games on MTGO is whether
or not one is winning more tix than one loses, is essential to making the
experience feel pleasant and rewarding. As long as your EV is positive, you’re
good. Just keep playing and enjoying the game.
So, were there any decks that you feel/felt invincible using at some point of your Magic playing career? Let me know in the comments!
May the shuffler be with you!
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