Variance, Non-transitivity and the "Highest Win Percentage"

I'm a student of mathematics, and I have to say that I'm not too convinced from how you describe probabilities. I also think there is some miscommunication about what one is trying to make your deck achieve.


First; probabilities:

Let's say I am playing deck A.

  • Let w(X) be my match-win percentage against deck X

  • Let f(X) be the expected proportion of the field playing deck X

Now the formula for calculating your deck's total expected win percentage is

w(A)*f(A) + w(B)*f(B) + w(C)*f(C) + w(D)*f(D)

On average w(A) - the mirror - is 0.5, but player strength factors in here. If I believe I'm more proficient than most players, w(A) > 0.5

By simply counting them up, we see that we have 7 unknowns. First the w(X)s, the individual win percentages, which we might have good idea about. Then there is the f(X)s, normally known as the meta. Let me reiterate that this is the only way - that makes any sense - of calculating my deck's win percentage. I don't know if OP agrees or not, but I didn't get the impressions that this was the case.

Note:

However, these numbers are quite difficult to know exactly, so we have to rely on other resources to decide on what deck to play. What I believe LSV was actually trying to say last week, is that if you play a consistent/safe deck then at least you won't lose to yourself. You'll always get to play magic, and that will normally favor the stronger technical player.


What I feel is lacking from the discussion is that no one is talking about what "best deck" means. Is it the deck with the highest win percentage or is it the deck with the highest expected prize return value? Due to tournament prizes being so top heavy, these are not always the same. You can never plan of getting lucky, but you can set yourself up so that if you do, it pays to do so. This is however a strategy which works best if your playing skills are below the average of the field, not if you're Efro or /u/LSV__.

I could go further into this, but I don't believe that statement is especially contested.


So in conclusion: if you're behind the field and only seek to get as high expected prizes as possible, high variance decks might be the way to go. On the other hand, if you're confident that your playing skills are solid and want to continue improving, consistent decks are better to you.

/r/lrcast Thread