Frank Karsten recently released analysis showing the
expected value of participating in the first MTGA Open as a function of one’s
win rate. Based on this graphic, players need at least a 52% win rate to break
even in the event. This computation is made under the assumption that each
player enters the event only once. Given the mechanics of Day 1 allowing entries
for as long as you can pay for them, it is likely that many players will try
more than once. Thus, this article explores what it means for people of a given
win rate to enter the event as many times as they can in order to acquire a Day
2 token.
Expected Cost as a function of win rate
The following graph shows expected cost as a function of one’s
win rate. This represents the amount (in $) that a player with a given win rate
needs to spend on average in order to get a Day 2 token.
As can be seen from the graph, a player with a 70% win rate
has an expected cost of about $34, which is roughly two runs. Another way of
looking at this is that on average, a player with a 70% win rate will need about two entries into the event in order to get a Day 2 token. A
player who only has a 60% win rate has an expected cost of about $75, which is
more than double that of the 70% win rate player. At 52%, the expected cost is about $161 or about 32200 gems or 161000 gold. That is, a 52% win rate player will
need, on average, about 8 tries before they can secure a Day 2 token.
Considering the prize structure for Day 2, 5 wins gives the equivalent of $100
(20k gems), 6 wins gives $1,000 and 7 wins $2,000. Thus, a 52% win rate player
will, on average, need to reach at least 6 wins on Day 2 in order to recoup
their losses from Day 1. This has a probability of 7.6% (given that the player already
has a token). In contrast, a 70% win rate player will, on average, only needs to
make 2 wins in Day 2 to recoup their costs.
It is also important to look at the overall distribution of costs at different win rates in order to account for variance. This is shown in the following figure which shows the distributions for 52%, 60%, and 70% win rates.
At a 52% win rate, 95% of costs fall within the interval [$10, $470]. For a 60% win rate, this interval is [$10,$206] and for 70% this is [$10,$92].
It is also important to look at the overall distribution of costs at different win rates in order to account for variance. This is shown in the following figure which shows the distributions for 52%, 60%, and 70% win rates.
At a 52% win rate, 95% of costs fall within the interval [$10, $470]. For a 60% win rate, this interval is [$10,$206] and for 70% this is [$10,$92].
Implications
Thus, the takeaway from this is that a player who is confident
that he/she has a 52% win rate versus the field should be aware that on average,
players similar to him/her will need 8 tries or 160k gold to win a Day 2 token.
This is not to say that it is impossible to do it in one try, of course this is
possible, but not easy. Correspondingly, this also informs players who have a
52% win rate and a lot of gold about how much gold on average they will need in
order to have a good chance to get a Day 2 token. At $160, this is equivalent
to the cost of an on-site Magic Fest plus some extra for food and other expenses
for the day, which is really quite reasonable. It is important to stress that spending
this money/gold/gems does not guarantee a token, only that it is the average amount
needed to secure one at a 52% win rate. Looking at the interval, the upper limit of the middle 95% of costs actually reach $470. I do not think anybody wants to pay that much for a token.
Overall, the MTGA Open does appear to be a great
opportunity. In my opinion, the biggest benefit that this event provides is
that it is currently the only way for people to convert the gold and gems that
they earned playing the game into actual cash. This event gives those in-game
resources actually monetary value which is certainly a step in the right
direction.
May the shuffler be with you.
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