Expected Results: The Right Mix

Posted on January 22, 2014 by neuhier

You are currently browsing comments. If you would like to return to the full story, you can read the full entry here: “Expected Results: The Right Mix”.

 

  1. Well, neither 2 nor 3 swamps is reasonable for the number of cards that would be dead if you drew no swamps, so perhaps starting from there makes sense?
    Also, the general rule is that creatures are on-curve and spells are not, so separating those two would also make sense if you really want to accomplish much more than the MTGO default land suggester.

  2. 3 swamps seems doable, if not ideal. < 50% chance of drawing a card w/black that you can't play. The shipwreck singer makes it all a lot more awkward since having a dead 2-drop in hand is pretty bad, but on the other hand at least the singer can still be a good play in the mid-to-late game depending on board state. I would have gone with 9 Forests, 3 Swamps, 5 islands probably, though maybe 8 forests, 6 islands is better. I don't see how you run less than 3 swamps though.

  3. Hey Noobeman, Hi Chris, thanks for the feedback.

    I totally agree that 2 swamps seem to be way to few.

    Actually the reason that my approach is recommending such a small number of swamps is that each card has the same relevance (so this is about what you are saying noobeman): The accumulated lower probability of playing any green or blue cards (20) on curve has just more impact when playing 4+ swamps than the increased probability of playing one of the three black cards.

    Of course one could (and should!) argue if this approach is correct. But I think it is a reasonable starting point. Especially as any software will have a hard time to determine which cards are more or less important to play on curve. But I am working on a solution to change the time you want to play single cards of your deck manually (like Marshall likes to do it in his videos). Then we will be able to get even more sophisticated solutions.

    In the meantime this has one great pro vs. MTGOs recommendations: We know what is happening inside. ;-)

  4. Hi again, thought some more about the subject. I don’t think you should be multiplying those probabilities. They don’t and in many cases can’t happen at the same time. Perhaps start by just summing them up and try to adjust the formula from there?
    The last deck is a very interesting example by the way. It is quite obvious that it’s impossible to build a proper mana base for it, so it’s a case of doing the best possible. I probably would just go for 8 forest 6 island 4 swamp, but I can see cutting a forest for a swamp just fine. Playing with 3 sources for 4 cards is madness, I would rather play with 19 or 20 lands instead, which is actually more likely to be correct.

  5. Also, you have 3 cheap-cost double white things in first example. That should give more white than blue, certainly not 7 plains 10 islands, since the probability to cast those on curve goes down sharply with each plains removed. Imo, that indicates something is wrong with the premise itself – perhaps the formula.

  6. Hey Noobeman: I really appreciate your feedback! Thanks!

    1. Why multiplication instead of taking the sum of the probabilities?

    At the start I made the whole thing the way you suggested it. The result was, that taking the sum leads to non plausible results for splashes. Splashed cards will always have a lower probability to be played on curve. But on the other side they tend to be more powerful. So we cannot accept a too low probability for them.
    Now if you take the sum of the probs one card may have a very low prob as long as all the other cards have high probs and the resulting score will still be fairly high. But if you take the product a single very low prob will lead to a very poor overall score. E.g.:

    (0.9 + 0.9 + 0.9 + 0.1)/4 = 0.7 while (0.9*0.9*0.9*0.1)^(1/4) = 0.52

    Thats why I prefer the product: It forces a better prob. for every single card in the deck as it is more sensible vs. outliers.

    2. You are talking about 4 black cards. I think you got that one wrong, as there are only 3 black cards in that example.

    3. I’ll definitely check the code for the first example again. As you mention it I have to agree that the recommended results seem to be too “blue”. :-)

  7. 1) It is true that, at first glance, the multiplication formula should give the proper result. I will be honest and say that I suggested taking a sum without giving it much thought, the logic being: wrong result means wrong approach to getting said result. Now that I think about it, the formula should give the proper answer – but it clearly doesn’t, as example 1 shows.
    2) My mistake, in that case 4 sources is sort of acceptable.

    Splashes and the required manabase are an interesting topic in general. People often talk about “1 more source than you have spells”. A recent episode of Simon Says on this site discussed this problem as well. The conclusion seemed to be that even with 1 card splash you are far better off with 3 sources than 2, and with larger splashes it quickly gets ugly, a 3 card splash requiring something crazy like 6 sources to be reasonably certain of getting the mana in time.
    There is also the issue that after a certain number of lands (around 6-8) you can assume you will draw one land of this type in every game. And this gets into a weird relationship with the first conclusion. =)

    This is why I am curious to see the results your approach will bring. Even if it brings nothing tangible, it is certainly fun to try.
    The number one problem right now is of course that even on a simple example (the first one), the results do not match the expectations.

  8. It is possible that higher average CMC of blue cards means that their probability is easier to max with lands, leading to skewed results.

  9. Hey, sorry for my late reply. I’m quite busy at the moment but I will check the web app asap and post when I found the reason for the strange results in case 1!

    I will for sure go deeper on this and try to enhance the app with more sophisticated functions. We’ll see how useful it can become! :-)