Comments on: Expected Results: The Right Mix

By: neuhier

neuhier — Mon, 27 Jan 2014 21:14:09 +0000

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!

By: Noobeman

Noobeman — Fri, 24 Jan 2014 08:28:10 +0000

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

By: Noobeman

Noobeman — Thu, 23 Jan 2014 17:56:22 +0000

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.

By: neuhier

neuhier — Thu, 23 Jan 2014 10:51:19 +0000

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”.

By: Noobeman

Noobeman — Thu, 23 Jan 2014 10:15:35 +0000

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.

By: Noobeman

Noobeman — Thu, 23 Jan 2014 09:53:32 +0000

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.

By: neuhier

neuhier — Wed, 22 Jan 2014 17:26:59 +0000

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.