You know what's fun? When your LGS charges €15,- for a draft and has a whopping 4 packs total of prize support, rare redraft included.
Screw that noise time for some MODO:
My Collection:
With my stuff plus an entry into the Momir basic Daily I have around 48 tix. Lets play some magic for free by figuring out the best way to go infinite. 48 tix isn't enough for a real deck in any format so we'll stick to Momir Basic and sealed for now.
Let's lay down some assumptions:
- Packs are 3 tixs on the secondary market, buy and sell.
- Packs are worth 0.1 tixs once opened.
- I have a 57% game win rate across the board or a 60% match win rate .
Based on this I can calculate chances for specific finishes in either swiss or single elimination, these are shown below.
3 Round Single Elim:
- 0-1: 40%
- 1-1: 24%
- 2-1: 14.4%
- 3-1: 21.6%
3 Round Swiss
- 0-3: 6.4%
- 1-2: 28.8%
- 2-1: 43.2%
- 3-0: 21.6%
4 Round Swiss
- 0-4: 2.56%
- 1-3: 15.36%
- 2-2: 34.56%
- 3-1: 34.56%
- 4-0: 12.96%
With that out of the way I can calculate an expected amount of tix out of any tournament (if the assumptions hold). The estimated values I have calculated are given as a ratio of expected tickets out over tickets in. This means numbers above 1 are profit and numbers below 1 are losses.
Limited:
8-4 Draft: 0.6556
- 11 Ticket Entry
- At 3-0 we win 8*3 = 24 tickets at a probability of 21.6%
- At 2-1 we win 4*3 = 12 tickets at a probability of 14.4%
- For the rest we win nothing at a whopping 64%
- Final Value 24*0.216+12*0.144+0.3 (guaranteed from packs) yields an expected output of 7.212 tix per draft
4-3-2-2 Draft: 0.5116
- 11 Ticket Entry
- At 3-0 we win 4*3 = 12 tix
- At 2-1 we win 3*3 = 9 tix
- At 1-1 we win 2*3 = 6 tix
- For the rest we win nothing at a lower 40%
- Final Value 12*21.6% + 9*14.4%+6*24% + 0.3 (guaranteed from packs) yields an expected output of 5.628 tix
Swiss: 0.5133
- 11 Ticket Entry
- At 3-0 we win 3*3 = 9 tix
- At 2-1 we win 2*3 = 6 tix
- At 1-1 we win 1*3 = 3 tix
- For the rest we win nothing but the probability has changed:
- 9*21% + 6*43.2% + 3*28.8% + 0.3 = 5.646 tix
- Slightly better than a 4-3-2-2
4 pack sealed: 0.548
- 14 Ticket Entry
- At 3-0 we win 4*3 = 12 tix
- At 2-1 we win 3*3 = 9 tix
- At 1-1 we win 1*3 = 3 tix
- For the rest we win nothing and the probabilities are the same as the swiss:
- 12*21% + 9*43.2% + 3*28.8% + 0.4 = 7.672 tix
- Higher yield with a higher entry
Phantom Sealed: 0.7965
- 4 Ticket Entry
- At 3-0 we win 3*3 = 9 tix
- At 2-1 we win 3*1 = 3 tix
- For the rest we win nothing and the probabilities are swiss:
- 9*21% + 3*43.2%= 3.186 tix
- Very Close to breaking Even
Sealed Dailies: 0.7104
- 20 Ticket Entry
- At 4-0 we win 11*3 = 33 tix
- At 3-1 we win 6*3 = 18 tix
- At 2-2 we win 3*3 = 9 tix
- For the rest we win nothing and the probabilities are now 4 round swiss:
- 33*12.96% + 18*34.56% + 9*34.56% + 0.6 = 14.208 tix
- Not quite as close to 1 as phantom but still kinda close
Constructed looks like:
2-Mans: 0.9
- 2 Ticket Entry with a 60% chance of 3 tickets out means I have 3*60%/2 for my EV
8-Mans: 0.97
- 6 Ticket Entry
- At 3-0 we win 5*3 = 15 tickets at a probability of 21.6%
- At 2-1 we win 3*3 = 9 tickets at a probability of 14.4%
- At 1-1 we win 2*3 = 6 tickets at a probability of 24%
- Final Value 15*21.6% + 9*14.4% + 6*21.6% = 5.832 tix
Dailies: 1.75
- 6 Ticket Entry
- At 4-0 we win 11*3 = 33 tix
- At 3-1 we win 6*3 = 18 tix
- For the rest we win nothing but the probability has changed:
- 33*12.96% + 18*34.56% = 10.4976
- Actual Positive EV
In case your are to lazy to read the math (I don't blame you), the expected value of limited tourneys run from 0.51 (Swiss and 4-3-2-2 Draft) all the way up to 0.80 (Phantom Sealed). What you should take away from this is that if we have only an above average win rate we need to stay the hell away from limited because in the long term you will lose money. However phantom sealed is so cheap and has an EV close enough to 1 we should use this to practice for major events and to satisfy any limited cravings we might have.
Constructed is a lot more static as the tournament payouts do not vary format to format and only vary by tournament structure so there are only 3 EV's:
2 - Mans: 0.9
8 - Mans: 0.97
Dailies: 1.75
These results speak for themselves, in order to expect to go infinite you need to play a lot of dailies. These EVs are based on a game win rate of 57%, which is something you could expect out of a Momir basic game if you play extremely tight. In other formats you could expect a 60%+ game win rate with the right deck and skill which translates to a 65%+ match win rate, which scales are EV up even further.
This means my current plan is to play Momir Basic dailies until I can build up enough of a bank roll to buy into pauper or block constructed with enough of a cushion to fall back on if things get rough.
I went 1-2 in the daily. I made some pretty bad play mistakes though so I'm not upset that I didn't cash. I wasn't focusing because I was writing this. I will do better next time.
I am currently writing a calculator that will be able to calculate these EV's based on a number of parameters which I hope to finish by the end of the month.
This week's value -6 tix down to 42.