With these formulas, we can obtain the following table. The third is the probability of going 6-2, multiplied by the probability of winning the next game. The second is the probability of going 6-1, multiplied by the probability of winning the next game. The first is the probability of going 7-0. This represents the sum of three probabilities. The probability of stopping at 7 wins is given by: After all, every run with fewer than 7 wins must end in a loss. This represents the binomial probability of getting N wins and 2 losses in N+2 games, multiplied by the probability of losing the final game. Then the probability of ending the event at N wins, for N smaller than 7, is given by: In the first type of event, typically used for best-of-1 matches, you keep playing until you reach 3 losses or 7 wins, whichever comes first. Probability of Reaching a Certain Record in “Stop at 3 Losses” Events But I wanted to go a bit deeper on some topics and share my own take on the subject in article form. On Reddit, for example, I found an EV calculator spreadsheet by CombatAnimal and an event reward analysis by AnnanFay. I’m not the first person to analyze the value of MTG Arena events. Once I had those values, I also could determine whether it would be possible to “go infinite” in certain events, which is another way of saying that the expected prizes of some event are sufficient to pay for its entry fee. The expected value (EV) is calculated by multiplying the prizes for each of the possible outcomes by the likelihood each outcome will occur, and then summing all of those values. More specifically, I set out to determine the expected value, which describes a long-term average, of the various events’ prizes. Today, I will analyze how the various types of events on MTG Arena stack up in terms of value. MTG Arena also offers nice opportunities for mathematical analysis, so you can expect several Arena Math articles from me in 2019. I have a bunch of grievances with the program that haven’t been adequately solved in over a year (such as the logic of the auto-tapper and the inability to set default stops-no, I never want to cast anything in my own beginning of combat step) but it also does a lot of things right, and I’ve been having fun playing games on MTG Arena, hitting daily quests, and growing my collection. Once Ravnica Allegiance drops, I intend to play a lot of MTG Arena, if only to prepare for these paper tournaments. I follow the expected value, and the same type of thinking also applies to MTG Arena. So whereas I was originally planning to skip all the 2019 editions, I have now committed to attending them all. Since this will hopefully cover my flights, it has become more appealing to compete in them. The esports announcement alluded to a lot of changes, including doubling the prize money for the tournament series formerly known as the Pro Tour.
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