Expected Cost of Winning a Day 2 Token at the first MTGA Open

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]. 

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.