# MtG Arena Open Expected Value

This was calculated based ont he Baldur’s Gate Open. I’m pretty sure the other Opens work a bit differently, but this probably gives you an idea.

The assumption here is win percentage of 50, which is reasonable assumption, because each match must have a winner and a loser, so overall average win percentage will be exactly that. Obviously, if you have a higher expextation of your own wins, your EV will be higher. This also assumes everyone plays as long as they are allowed to.

At this moment, I’m a bit too tired to explain all of this, but hopefully it’s self-explanatory enough. Maybe I’ll remember to return an open this up a little bit. The key here is that on the left you have wins, on the top you have losses. Each number in the sheet is the probability that you end up in that position and some positions mean an end to your tournament.

After five wins, you can also find the prize times the probability to receive it if you are always matched against a 50/50 opponent. This does not take the qualification for the next tournament level into account and all dollar values are changed into gems based on the cheapest option in the store (200k gems for around \$100).

 0 1 2 3 Winnings 0 0,50 0,25 0,125 win% 0,5 1 0,5 0,5 0,375 0,1875 2 0,25 0,375 0,375 0,1875 3 0,125 0,25 0,3125 0,15625 4 0,0625 0,15625 0,234375 0,117188 5 0,03125 0,09375 0,164063 0,082031 1000 82,03125 6 0,015625 0,054688 0,109375 0,054688 2500 136,7188 7 0,007813 0,027344 0,054688 5000 449,2188 0 0,5 500 22,46094 1 0,5 0,25 2500 56,15234 2 0,25 0,125 5000 56,15234 3 0,125 0,0625 20000 112,3047 4 0,0625 0,03125 100000 280,7617 5 0,03125 0,015625 200000 280,7617 6 0,015625 250000 350,9521 1827,515

So, your total EV is 1827,515 or roughly 36.7% of your initial investment. So, not very high. Obviously, if the qualifier prizing is better, this can go up quite a bit… but they don’t. Obviously, playing has it’s own value, but if you want to do this professionally, this is not the way.

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