I’m pretty sure that concerns of what deck we might be playing against (without any information about our opponent’s deck) are null. At this point we have to consider the hand on it’s own merits. If the deck isn’t good against the metagame as a whole, then we probably shouldn’t even be sleeving it up.

And the math is important. It tells us how often this hand will do what we need it to do. Sure, ideally we would measure the probability of making this hand against the probability of making a better hand with a mulligan, but the calculations for that would likely be complicated enough as to be impractical.

First, I want to be clear that I don’t think your conclusions are wrong. Good hand to keep. The problem I have is how you arrive at that conclusion. More importantly, what your article is emphasising as important. I don’t think the effort to do the math to 1% is worthwile, and at the same time the article ignores or plays lipservice to the things that are important. That’s what I feel is misleading.

I’d propose the simple rule:

You should mulligan if:
In the game you are expecting, a random smaller hand is likely to be better than your current hand.

Let’s look at the things you aren’t paying real service to:
- you don’t discuss what you expect your opponent to be playing at all. You don’t say in this metagame I expect… or knowing my opponent I expect him to be playing…
- you hint that this hand is better than random hands if it draws out properly, but I’m not reading this as being a clear “this is probably a great hand if I draw out”.

Maybe I’m just not aware of the greater context of this article. But it seems to me that you barely noticed two really important parts of the background and the mulligan decision.Instead this article focuses on math.

A fair bit of math actually. You work out the percentages of drawing the right mana help to within a percentage point. And I have to ask if that level of precision is meaningful. Here’s a question you don’t answer: at what percentage do you throw back the hand. If you have a 78% percent chance of drawing out is that keepable? Maybe 77%? What about 76%?

I don’t think you can answer that question because I don’t think there is a good answer. The stats just don’t matter to the precision you are discussing. The bulk of the article (the mathy parts) should reasonably be replaced by your conclusion “(Keeping) is a good bet, so I kept.”

Unless you present an argument that is based on being that precise by saying something like “I keep if the odds of drawing the mana I need are 57% or better” then the exercise of narrowing down to a specific number is pretty much meaningless. Its a distraction, it is not the important part of the argument. You are going down a rabit hole to a depth that really doesn’t matter.

And that’s the fault I have with this article. You skip lightly over some really important things (expected matchup, what a random smaller hand is likely to look like) and are very focused on a level of precision that doesn’t matter.

Which I think is misleading.

The difference between the exact 79-80% number and my rough estimate that you’ll draw out somewhere between 7/8 (1-1/2*1/2*1/2) and 2/3rds (1-1/2*1/2*2/3) of the time isn’t meaningful. Its a good bet, keep the hand.

As I said in my reply to the blog presenting this mulligan issue, the hand shown is a great hand for the deck. You’ve heard/read people whine about how Jund Ramp sometimes just fizzles by drawing lands and fixers with no goodies. They ARE correct. If you have played this deck often, you know it can flood with fixers and not find gas. Well, THIS hand doesn’t walk that path too often. Gift of the Gargantuan in that hand is terrific.

You can only measure to the extent that you can take action. Well, I suppose you can measure beyond that point, but such measurements become meaningless. The only question is whether or not to keep the hand. If you go back and look at the comments from other readers, you will probably come to understand that anyone considering this build of this strategy wants a lot of hands that look almost exactly like this. With one more mana source, this is the cream dream hand for many Jund players.

Are you going to outright lose if you miss mana source #3 on turn three? Of course not. There are too many factors in an unknown matchup. The opponent could stop on one and discard fourteen times. By the same token, hitting your own third land on turn three is no guarantee of success. If you are playing against a combo deck, you’re probably dead in the water.

We make decisions based on completely arbitrary points all the time. 1/3 of my readers thought the hand wasn’t good at all, whereas I would happily keep it against any of the “reasonable” and known decks in the format (and I did). I was trying to explain how to make an informed decision… based on data we had or could reasonably approximate.

And again, the only decision we can make is mulligan or no for this hand. There is no reason to complicate the hypothetical beyond the parameters of the question at hand (in my opinion).

If I had a sub-50% chance of drawing the lands I wanted, I would have asked a different question (like how are my chances going to be if I mulligan). But in this case we didn’t have to ask that question. Also, if I knew my matchup I could do things like cross off cards I expect to be useless (Broodmate Dragon is poor against Fog, for instance). But again, we can’t act with knowledge we don’t have.

Thanks for your post!

–m

The stats of drawing a land/land equivlant are pretty meaningless by themselves. You don’t even mention what happens if you fail to draw your third land until the fourth turn. Going purely by the writeup, one would think that the thinking about keeping/tossing should be based purely on whether or not you get that third land. This post says “drawing a third land is the important thing, winning or losing is a footnote to making sure I got the math right.”

That probably isn’t your message. The decision to keep should be based on the likelyhood of WINNING not on the likelihood of getting a third land in time. You don’t even mention winning or losing. Just wow I was probably going to get that third land; here is the exact details about how likely that is. Would you have kept if you’d had a 76% chance of drawing the land but thrown it back if the odds were only 74%?

Were you definitely going to lose without the third land on turn 3? What happens if you get it on turn 4? Were you definitely going to win if you got it on turn 3?

I’m pretty sure you were thinking clearly at the time, but this blog post presents the math about some relative trivia and not the decision you were actually making. It. You are yak shaving (worth looking up if you haven’t seen that expression, it happens a lot in magic and magic articles).

The article should be “I figured I’d win if I drew that third land in time. Roughly half my deck was land/equivlants, so my odds were pretty good.” The exact numbers are pretty trivial.

You had a pretty good shot of getting the third land, and you thought you’d win if you drew it.

Isn’t that all you need to say?

@StaplerGuy
Sounds like something I would do.