Do People Really Think 2 Land Hands Should Be Mulliganed in Limited?

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It was brought up recently that some people think 2 land hands should be mulliganed. A simple mathematical exploration into this shows that for a generic 2 land hand, you have only a 14.3% chance to improve your lot, in terms of the number of lands and spells you end up with after your first draw. Conversely, 85.7% of the time you will worsen your lot in this regard. For this reason, it seems like it would have to be a remarkably poor 2 Lander to mulliganed at all. Further, if you think the majority of 2 Landers should be mulliganed, the same would have to apply to all 0, 1, 5, 6 and 7 landers as well, leaving only 3 and 4 landers as majority keepable. And these collectively account for just 55% of all 7 card hands drawn.

Does anyone have evidence suggesting 2 Land Limited hands should be mulliganed? Does anyone know of a professional player or article supporting this? 
Dude. I said keeping a two-land hand when you're curving out over 4 and have no playables in-hand is bad.

Strategies where you're casting nothing on turns 1-2 and "hoping" to hit your land-drop by T3 or T4 are bad.

If you had a one drop, one-drop, two-drop, three-drop, two lands and something else, that's a completely viable hand. You had a full fist of three+ drops and two lands. That's clearly a risk, hence the "chasing the straight" poker analogy which, again, you didn't understand.

You're red-herring your own analyses, focusing on the success/failure of mulligans as opposed to focusing on the success/failure of curving out. There are more than enough stats out there that say the player who plays the most spells win. Keeping a hand that doesn't let you play spells is poor playing. Mulliganing is a risk, but it's still a viable solution.

You're also just constantly seeking to blame a system for being imperfect when it's purposefully designed to be imperfect. Limited is not about being able to evaluate cards and putting the best ones you can cast into a deck and then winning because you have all good cards and know how to play them. That's part of it, but drafting towards deck synergy is hugely important, as is reading signals, knowing what signals to send, knowing when to hate draft, knowing your opponents' play-style and your LGS's or the formats meta, knowing when to mull... it's like you want to take this giant, beautiful, chaotic thing and turn into bobus's Magic Win Farm bc you can't believe you made a mistake not knowing when to mull or not mull.

Do you understand that or not?

I found Carmen Sandiego before you were born unless you're Zlehtnoba.

I bet if you channeled the energy you use discussing the shuffler and it's problems you could probably become a much better player. 
I think I might have said this but it was some advice a tournament player gave me about constructed, not limited.   

Probably a rule of thumb is something like "if you don't have 2 <=2CMC playables in hand with your 2/7 land hand, mulligan".   Your chances of drawing 1 land in 2 draws is pretty high, almost 70%.

But rules of thumb are made to be broken. 

Once you mull  to 6 or god forbid, 5, you are probably going to have to keep any remotely playable 2 lander. 
rstnme: "Everything looks good when your opponent passes 4 turns in a row."
Dude. I said keeping a two-land hand when you're curving out over 4 and have no playables in-hand is bad.

Strategies where you're casting nothing on turns 1-2 and "hoping" to hit your land-drop by T3 or T4 are bad.

If you had a one drop, one-drop, two-drop, three-drop, two lands and something else, that's a completely viable hand. You had a full fist of three+ drops and two lands. That's clearly a risk, hence the "chasing the straight" poker analogy which, again, you didn't understand.

You're red-herring your own analyses, focusing on the success/failure of mulligans as opposed to focusing on the success/failure of curving out. There are more than enough stats out there that say the player who plays the most spells win. Keeping a hand that doesn't let you play spells is poor playing. Mulliganing is a risk, but it's still a viable solution.

You're also just constantly seeking to blame a system for being imperfect when it's purposefully designed to be imperfect. Limited is not about being able to evaluate cards and putting the best ones you can cast into a deck and then winning because you have all good cards and know how to play them. That's part of it, but drafting towards deck synergy is hugely important, as is reading signals, knowing what signals to send, knowing when to hate draft, knowing your opponents' play-style and your LGS's or the formats meta, knowing when to mull... it's like you want to take this giant, beautiful, chaotic thing and turn into bobus's Magic Win Farm bc you can't believe you made a mistake not knowing when to mull or not mull.

Do you understand that or not?



I had a plains, swamp, Daring Skyjek, Basilica Screecher, Gift of Orzhov, Confessor and Basilica Gateguard in the example that I gave. Which is on par with a typical 2 land limited starting hand (a typical limited starting hand would have a 4 CMC card instead of a 5 CMC one) Saying that particular Limited 2 Land hand wasn't keepable was akin to saying that the average 2 land hand isn't keepable. I'd like to know if you are really saying that.
That hand is okay.  In general, if I have a two land hand with both of my colors and a non-intensive three drop, I will keep it, but probably wish it were something else.
Actually, I would mull that hand on the play, bc the perks of the screecher is its extort, and you didn't have the mana for extort, and the perk of skyjek is battalion, and you weren't guaranteed to get a 4-drop out by T5 at that point.

On the draw I'd have to think about it, but I also wouldn't build your deck so the whole idea of what I'd do versus what you did is moot. From what I see of your playables, though, you have a bloated curve in the 3-4-5, so I'd want at least 3 lands in-hand.

The thing that irks me most, however, is this implication that if you'd had your land drops, you would've won with those cards otherwise, yet your opponent clearly curved out against you and won. It's like you're blaming the shuffler on your mull strategy and deck-building. You keep focusing on this idea that lands are the only thing preventing you from being the perfect player, but there's enough that goes into why lands are important per deck (Curve, opening-hand playables, etc.) that you're completely ignoring.

I found Carmen Sandiego before you were born unless you're Zlehtnoba.

This depends entirely on the deck and the hand I've got. How does my deck's curve look? My hand's curve? How many colors am I playing and which colors do my lands produce? Am I holding any mana fixers? (Prophetic Prism for example.) How much of my hand can be cast with the mana I've got?

If I'm playing Simic, I've got an island and a forest, and I'm holding Experiment One, Cloudfin, and a shambleshark, I'm not going to mull, even if my other two cards are 3-4 CMC, because I can probably count on drawing either another land, or another 2CMC card in the first three draws. If I've had to go Gruul with a splash of black, and I've got a forest and a swamp, a Syndicate Enforcer, and two 2CMC red creatures, I'm going to mull because I can't be sure I can cast anything at all for the first three or four turns. (I'll invariably end up with a hand that has one or zero lands after I mulligan, but that's just because I tend to be unlucky.) If the above hand included mana fixing, I'd keep it.
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Actually, I would mull that hand on the play, bc the perks of the screecher is its extort, and you didn't have the mana for extort, and the perk of skyjek is battalion, and you weren't guaranteed to get a 4-drop out by T5 at that point.

On the draw I'd have to think about it, but I also wouldn't build your deck so the whole idea of what I'd do versus what you did is moot. From what I see of your playables, though, you have a bloated curve in the 3-4-5, so I'd want at least 3 lands in-hand.

The thing that irks me most, however, is this implication that if you'd had your land drops, you would've won with those cards otherwise, yet your opponent clearly curved out against you and won. It's like you're blaming the shuffler on your mull strategy and deck-building. You keep focusing on this idea that lands are the only thing preventing you from being the perfect player, but there's enough that goes into why lands are important per deck (Curve, opening-hand playables, etc.) that you're completely ignoring.



The deck I was playing had a CMC curve of 4, 6, 6, 6, 1. Which means that the cumlative # of cards that could be played per land was 4, 10, 16, 22, 23. Roughly 70% of the deck could be played on 3 mana or less, and I missed getting that 3rd land 6 consecutive times. It took my opponent until turn 7 to beat me as it was, and this is the same opponent who I beat 40-0 the first game. This same opponent beat me the second round because he hit Sapphire Drake with Unexpected Results, and (this is important) because I never got to 4 lands in the first 7 turns, which meant I died holding both Grisly Spectacle and One Thousand Lashes. So yes, I think that not hitting my third land drop at all might have had an impact on that final game.

Further, it's not like I decided to draw a 2 land hand in the first place, but the math is clearly in favor of keeping 2 land hands in general and that 2 land hand in particular. As I've said before I have an online Limited rating that varies from 1800 to 1875, I win between 80-85% of games (games, not matches) where I keep my starting 7 and do not hit mana issues, and the vast majority of my losses occur in games where I hit mana issues. Given this, it's resonable to expect that I'll win the majority of 3 round online tournaments where I do not hit mana issues and it's resonable to focus on mana issues as the last significant obstacle. If you've got that all beat and think you have the answer to winning 3 round online tournaments consistantly then by all means lay it on me.
Your math's wrong. I already said this. I will keep saying it until you admit it, but I don't think you'll admit it because your "math" is the foundation of your game and these ridiculous threads.

You kept a hand with insufficient mana when your winningest strategy requires mana for creatures as well as extort.

You kept a castable creature that needs additional mana to be swell, mana that you didn't have.

You kept a castable creature that needs two more attackers or a vacant board to be something more than a chump blocker.

You kept other creatures you couldn't cast on-curve unless you drew into a desireable flood.

You kept forgetting that extort is powerful because of mana. Without mana, extort creatures are weak, vanilla beaters or 1/4 walls. A bevvy of 2-toughness creatures is not going to win in this format if you start behind on lands.

This is obvious. This is all obvious. This is not a mana issue, this is an issue with how you cope with losing. You lost because you kept the wrong hand. You chose to keep that hand. And from what the other opponent played, it looks like you would've lost anyway, but, no, you're incapable of admitting that.

Complaining that a system is broken because you couldn't play spells is wrong. You chose, for better or for worse, to keep that hand. That's part of the game.

The person who played the most spells won. The person who plays the most spells almost always wins. You chose to keep a hand that let you play two spells, and hopefully draw into playing three, and wouldn't let you actually extort for anything until turn five, assuming you hit 3 lands out of 5 draws, which already isn't likely.

In short, you chose to keep a hand that would likely let you cast less spells than your opponent.

So, yeah, consider it laid on you.

I'm all about discussions of what hands to keep and when, and I'm not saying this was an obvious hand to mull. It was one that would've been great if you hit your land draws, but you have no control over that aspect of the game, and therefor shouldn't play into relying on it. There's no way you looked at that hand and thought you were going to curve out into your five-drop or a three- and two-drop on T5. No way.

I found Carmen Sandiego before you were born unless you're Zlehtnoba.

 There's no way you looked at that hand and thought you were going to curve out into your five-drop or a three- and two-drop on T5. No way.



I like your  thoughts on this, but I think this is the wrong question.  The question is how good is this 2-land hand RELATIVE to the average 6-card hand.

I think there is at least a 40% chance that your mulligan hand is worse than this one. (1,2,5 or 6 lands).  Some of the 3 land hands are certainly, worse for example Swamp, Swamp, Swamp, Skyjek, confessor, basilica guards.

That being said - even if this hand is keepable (mathematically), there is a good chance you are going to lose (assuming competent opponent who curves better than thou).  Furthermore, if you knew (somehow) that you could ONLY beat your opponent with a perfect hand you must mulligan (even if there is a 10% chance you get a perfect 6 or 5 and a 90% you get the same or worse - if you have an autoloss, then it doesn't matter if you get a worse hand).

rstnme: "Everything looks good when your opponent passes 4 turns in a row."
It's not the wrong question at all. It's how you should approach every hand.

This is all backwards thinking, IMO. If you lose bc of mana screw, don't look at the shuffle, look at the reasons why you kept your opening hand.

I found Carmen Sandiego before you were born unless you're Zlehtnoba.

As I said before, the generally accepted strength of a starting hand in relation to the number of lands and spells contained in that hand is min(# lands, # spells) with # spells used as a tie breaker. So for 7 card hands the best number of lands to draw is 3, followed by 4, 2, 5, 1, 6, 0 and 7. For 6 card hands we have 3, 2, 4, 1, 5, 0, 6 and for 5 we have 2, 3, 1, 4, 0, 5.

Straight up a 2 land, 5 spell hand is only beaten by 3 land, 3 spell hand on the mulligan. All of the other 6 card hands are worse, in addition to all of the 5 card hands. So that 31.3% chance to draw a 3 land, 3 spell hand on the mulligan is the only chance to improve the situation. In addition, a 2 land hand that draws a land on it's first draw becomes a 3 land, 5 spell hand, which is better than either a 3 land, 4 spell hand or a 4 land, 3 spell hand you might get from mulliganing into a 3 lander. And for a 2 land, 5 spell hand this happens 45.4% of the time.

So if you take that mulligan on a 2 land hand, you are improving your hand only 14.3% of the time, and hurting it the remaining 85.7% Hence why you do not mulligan 2 land hands. Certainly a 2 lander like the one I had can become unplayable, provided it misses drawing a land for the several turns, but there is no way to say this deterministically at the start of the match. Hence keeping the 2 lander will be the correct choice.

It's never a choice between keeping a 2 land hand, 5 spell hand and a 3 land, 3 spell hand. It's does my current 7 card hand beat the average 6 card hand drawn from the same deck. The answer in this case was "of course it does" My initial hand was:
Plains, Swamp, Skyjek, Screecher, BGG, Gift of Orzhov and Confessor

I just drew 10 6 land hands and got the following:

Swamp, Screecher, BGG, BGG, Balustrade, Smite - Unplayable
Plains, Thrull, BGG, Plains, Confessor, Swamp - Equal
Confessor, Thrull, Daring, Guildgate, Swamp, BGG -  Much Worse
Thrull, Daring Skyjec, Swamp, Balustrade, Smite, Swamp  - Unplayable
Kingpin, Guildgate, Charm, Plains, Guildgate, Swamp - Much Worse
Swamp, Riot Gear, Plains, Charm, Plains, Swamp - Unplayable
Swamp, Swamp, Balustrade, Swamp, Confessor, Charm  - Much Worse
BGG, Enforcer, Swamp, BGG, Plains, Swamp - Better
Screecher, Smite, Swamp, Ghast, Swamp, BGG - Much Worse
Plains, BGG, BGG, Guildgate, Plains, Swamp - Equal

So, collecting all of the six card hands, there were 3 Unplayables, 4 that were much worse, 2 that were equal, and only one that was better. And all of that is provided the 2 lander does not draw a land as it's first draw, if it makes that draw the original hand is better than all of them. Considering that hands made up of the full 7 cards beat hands of 6 cards or less 3:1, that's not very surprising. You need to get into the 0,1,6 or 7 land range to have a realistic expectation to improve your lot by mulliganing.

Another piece of information is that even on the play, keeping a 2 land hand you are expected to make the third land drop on turn 3 over 70% of the time, and the cumlative probability of making your 3rd land draw goes up with every turn. 85% -> 92% -> 96% by turn 6.
It's not the wrong question at all. It's how you should approach every hand.

This is all backwards thinking, IMO. If you lose bc of mana screw, don't look at the shuffle, look at the reasons why you kept your opening hand.



The reason I kept my opening hand is that it was the correct choice given the information I had at the point I made the decision. Had I been able to look and see the next land was over 6 cards in I would have decided differently, but I do not have that power.
It's not the wrong question at all. It's how you should approach every hand.

This is all backwards thinking, IMO. If you lose bc of mana screw, don't look at the shuffle, look at the reasons why you kept your opening hand.



You seem like a reasonable dude so I will continue this conversation.   If you lose due to mana screw - there is a strong (1 in 5? 1 in 4?) possibility that NOTHING IS WRONG you were just destined by shuffle to loose by mana screw (or flood, or whatever).   I taught my wife to play and in her third game she was bitching about mana screw.  At which point I pointed out that she was now officially a Magic player.

But of course you know that (being a reasonable sort of dude).   And I do think that you are correct that learning to mull correctly is *extremely important* for even above-average play.  So I am striving to understand it in gory detail.

I will rephrase:  this basic "mulligan" question:  "will you curve out into your 5 drop and/or a 2+3 drop with hand X" IS a critical question.  But it's only PART of the question.
The only way it can be the *entire* question (whether or not to mull) is IF and ONLY IF if the answer is "NO" then you lose 100% of the time.
If you can theoretically win with hand X even if you KNOW you are unlikely "to curve out into turn 5", then you are not done asking question.

So, we have the first question:  Can we play something on turns 2/3/4/5 (I assume we skip 1, but obviously YDMV)?
IF Yes then (keep_hand) - and play.
But actually that's 100% impossible.   We only have 7 cards.  So the BEST ("perfect shuffle?") we can do is one of:

LLL2345
LLL2342 or 2343 2234 are good
LLLL234  233 or 232 even is pretty good

But in order for THESE hands to curve to 5 we need to draw 1-2 lands OR no CMC 4+ cards (assuming we have kind of a weeine deck)
These are just like poker hands.  We can enumurate them and calculate their distribution/probability for any deck.  Now, this math may be USELESS but it's absolutely 100% correct.

Note that I am ignoring colors, although have >1 color will guarenteed make your starting hands worse on average (unless you draw all shock lands)

But back to mulliganning 2 land hands.
What is the best possible 2 land hand?
something like (if you have 1-drops I would add 1 -maybe even 2 if they were good)
LL23233 
Assuming you are on color - this hand has to be playable, maybe if they were mostly auras and artifacts you would pitch it.

conversely something like:
LL54431 is not playable (like mountain mountain and 5 white spells - this can, of course happen with 3-4 land hands as well). 

So - establishing that SOME 2 land hands are playable (while the rest you should mull) the FUNDAMENTAL question is:
Will I more likely with with THIS 7 card 2 land hand than with a RANDOM 6 card hand.  And we know that 20% of 6 card hands (at least) are junk.
But you have to (and in fact, do this unconscioiusly) estimate your chance of winning with a current hand.  Not the chance of "curving" (which is merely a quantitative way of suggesting you are more likely to win), the chance of WINNING.  

Taking the worst possible 2 land hand:
Swamp-Swamp-4-4-5-5-6(all req. white mana).   You can estimate your chances of winning as very close to 0% with this hand (remember the other guy gets manascrewed at the same rate as you do)  So you should pitch it.   I would say a typical LL54431 is no where near 0% chance of winning if there are no color issues (mono- deck or one of each starting).   However, it's also probably <50% chance of winning.   It's actually in pretty decent shape if you draw L, L - which (although not probable does occur roughly 17% of the time).  It can also probably pull some games out if it gets L-2drop-L or even L-L-3drop.  

It probably wins ~30% of the time (assuming equal decks and players, YMMV, yada yada).  That's just a guess.   So, if you think you WP% with a random 6 card hand (remember that 20-30% it will be worse than LL54431) is >30% pitch, otherwise suck it up and play.

So, tell me where my thinking is backwards again?
 
rstnme: "Everything looks good when your opponent passes 4 turns in a row."
Backwards thinking: when you thought my comment about bobus's thinking was about yours Wink

Stick around the boards, and you'll see that bobus posts 1-5 threads a month about when he loses to mulligans/mana screw. Basically, he wants to get rid of the variance of drawing cards/needing mana because he believes that's the reason why he loses, and not his (in?)ability to figure out when to mull or just respecting the fact you can't win every game.

It gets old hearing someone rant about how they'd never lose if MTG was mathematically sound, when the mathematics behind that argument aren't sound and the absence of variance in the game would inifinitely diminish its enjoyability.

Curve is a very specific thing, and the foundation of building a synergistic limited deck. I'm sure you know it's called a curve bc it looks like one, I don't think it's a misnomer in that regard. For more and better info, you can check out the podcast Limited Resources. They did an episode on curve a couple of weeks ago. Bobus's 4-6-6-6-1, for example, is not a good curve.

I would go so far as to say the player that curves out almost always beats the player who doesn't.

I found Carmen Sandiego before you were born unless you're Zlehtnoba.

I agree with bobus that I would not mulligan that hand.  It have both colors and early plays, and a possible game-ender if gift comes out and sticks on the skyjek.  I wouldn't be too happy with it because mana is critical in Orzhov to power extort, but would not expect to have a better than 50% chance of hitting a better hand off a mulligan here.

Most of the time I keep two land hands if they have both colors unless I can't actually cast anything else in the hand, or I got one two drop then all of the top of my curve. 
SB, this will make more sense to you when you stop disrespecting everyone that you play against and assume that you will win every single time unless you don't get mana.  Whenever your present made up statistics, you never talk about the cards that your opponent has or doens't have.  You really need to get over yourself.  Once you do, you'll improve.  Good luck.
SB, this will make more sense to you when you stop disrespecting everyone that you play against and assume that you will win every single time unless you don't get mana.  Whenever your present made up statistics, you never talk about the cards that your opponent has or doens't have.  You really need to get over yourself.  Once you do, you'll improve.  Good luck.



Why are you saying 'made up statistics'? For a long time I kept records. Every time I played a game I wrote down whether I won or lost, mulliganed (and how many cards I ended up keeping), whether I hit my first 3 mana drops and whether I ended up drawing more lands than spells. Then I tallied up the totals to see how well I did under the various conditions.

No mana issues, no mulligans was in front by far, with between 78% and 83% game win rate across all sets. But once you get into games where I was forced to mulligan it drops to just over 50%. The games where I have mana issues are all below 30%. Looking back at the results its not difficult to see that whether I mulliganed and/or hit mana issues is the best indication of whether I won or lost a game. And I don't think this is specific to me, I think this is true for all players.

What I don't understand is why you have such a problem hearing this.

Do you really think talking about individual cards would help?

Alright, another one of the mana issue loses was against a Boros deck. It was an interesting matchup with many turning points, but ultimately I stablized with 2 extorters, a Balustrade Spy and a Dutiful Thrull. My opponent played a Debtor's Pulpit, taking the Spy out of the equation, and was attacking me with a Skyknight Legionnaire. I'd play another extorter, get in a 2 point extortion with my two extorters, he'd kill an extorter with a Mugging or Massive Raid. Finally it reached a point where I needed to draw, literally, any spell in addition to the Smite that was already in my hand, and I knew I could even cast Smite on my own attacking creature to extort off of it if it came to that. At one point I was ahead something like 16-3 due to all the extortions. But instead I drew 3 straight lands, which means I mana flooded, and my opponent had time to draw into his Aurelia. Certainly the Aurelia was key, accounting for 8 additional points of damage the turn it came into play, and ensuring I didn't get one extra turn to draw the 'any spell' I needed to close it out.

So, certainly individual cards were important, the Debtor's Pulpit to delay the game long enough to close it out with Aurelia, in addition to all of the stuff I had to do to not lose in the early game. But ultimately it fit into the pattern that most games fit into:

No mana issues -> Win, 4 times out of 5
Mana issues -> Loss, 2 times out of 3
ah, ok RST.  Yeah I am closing in on my 1 month forum anniversary and already have seen 4 sb threads.   I get that.  But I am trying to help him?  Maybe because I think he's a solid drafter?    I have to say, I don't mind his whine threads -- although I have seen 4 not 400 because I think they DO address serious questions, like "when to mulligan" and why is this deck curved bad.

I am also (obviously) very intersted in MTG as a mathematical problem.  Poker is very mathematical too, although (like most magic players I have met) most great players have a great intuition and experience about the math rather than theoretical rigor.  Intuition is better because no on this side of Rain Man can do 7-9 card hypergeometic distributions in their head in a 30 sec. mulligan period.

I can't abide podcasts but I guess they are better than youtube tutorials.  I read about 100 times faster than I hear. 

I don't think curve is a misnomer at all -- it just that it something like a 4-6-6-6-1 curve is A curve for A deck.  But a "bad curve" doesn't make sense without context.   So I am trying to get people to define the context explicitly.    Or more precisely - 4-6-6-6-1 is bad, but HOW bad.  5% worse? 10? 20% (in winrate I am talking here).   Obviouusly it nees more 2s and 3s but would you cut an enforcer to put in a gutter skulk?   What about a Spectacle?  Would you cut a Spectacle to put in a Court Street Denizen?    

from his 20-0 extort, his 6 4 drops were
2x Enforcer, Spectacle, Crypt Ghast, Lashes, Balustrade Spy.

Not an Orzhov master but you have to keep 3 of those, don't you?   He was already running Riot Gear , 1x Skulk and Gateway Shade (not that that's a bad card... but it's hardly a 3.0 in Orzhov... even with 3 gates).   He's also running 2 smites and 2 dutiful thrull which seems about right.

So, did he have 3 CMC 2-3 cards better than Enforcer and Spy???  Maybe.  But maybe all you are saying is that with this kind of curve you expect to get manascrewed a few times in 3-4 rounds.  Which is certainly true.

I would go so far as to say the player that curves out almost always beats the player who doesn't.




Clearly, that was the jist of an earlier comment to SB.  Hi SB!     Thinkin' about you, ace!
 

 
rstnme: "Everything looks good when your opponent passes 4 turns in a row."
Of your wins, how many of those happened when your opponent mulliganed, or missed a land drop, or drew more lands than spells?

If you don't keep track of that information, your "statistics" are meaningless.

None of this is novel, and it certainly does not warrant a new thread every couple of days.
I'm going to leave this thread open for the time being, since SB asked a specific question related to improving his play. But it will be on a short leash.

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"While a picture is worth a thousand words, each lolcat actually produces a negative wordcount." -Ith "I think "Highly Informed Sarcasm" should be our Magic Online General motto." -Ith "Sorry, but this thread seems just like spam. TT is for off-topic discussion, not no-topic discussion." -WizO_Kwai_Chang "Stop that! If you're not careful, rational thinking may catch on!" -Sax "... the only word i see that fits is incompitant." -Mr44 (sic) "You know a thread is gonna be locked when it gets to the hexadecimal stage." -Gathion "It's a good gig" - Gleemax "I tell people often, if you guys want to rant, you've certainly got the right to (provided you obey CoC/ToS stuff), and I don't even really blame you. But if you see something you think needs changing a well thought-out, constructive post does more to make that happen." - Worth Wollpert
Of your wins, how many of those happened when your opponent mulliganed, or missed a land drop, or drew more lands than spells?

If you don't keep track of that information, your "statistics" are meaningless.

None of this is novel, and it certainly does not warrant a new thread every couple of days.



I didn't keep track of those things because they can't be tracked with certainty the way my own stats can. I have no idea whether the last card my opponent is holding is a bluff land or a spell he lacked a target for. No way to know for certain if he missed a land drop or just forgot.

The statistics I collected for myself are meaningful regardless. They answer the question of how often I win under various conditions. I'm not trying to create a matrix to see my win rate based on the strength of my opponent or how they did under the various conditions themselves. Just how I did against my average opponent hitting all of the conditions an average amount of times. So, in the average case I won around 80% of the time hitting no mana issues and no mulligan, but only 30% of the time hitting any mana issues at all. 80%->30% is significant by itself, regardless of any other factors.

As for other spells that could have been in the deck but didn't make the cut, I had a Beckon Apparition that got drawn in against decks with substantial creatures with 1 toughness (like the Daring Skyjek), 1 Corpse Blockade that never came in because I had 4 Basilica Gateguards. The gift of Orzhov actually started in the sideboard (it was a really strong deck, and I didn't want to risk a 2 for 1) but I subbed it in against my Simic opponent who played 0 removal across all 3 games. There was also a Shielded Passage and Shattering Blow that were never subbed in. Scratch that, I think I did bring in the Passage against the Boros deck, just failed to draw it. Certainly I would have liked a lower curve, getting out the Confessor and Enforcers for Syndic of Tithes and Thrull Parasite would have been ideal, but I also took 100% of the Syndics and Thrull Parasites that were passed to me. Which was none.

The great thing about playing Orzhov is that you curve out pretty much regardless of what you play, since the extra mana goes into extortion kickers. That is, if you draw the mana at all. I would have been tempted to maindeck 18 lands in the deck, except that any opponent with a decent amount of removal (like my Boros opponent) would have made short work of that and I already had one mana flood loss as it was.
Lets see here.

17 lands
23 spells

of those spells, lets say 30% cost 4 or more.

If I keep a two land hand, what are the chances I make 4 lands by turn 4?

Draw 1


  • 2 Land: 55.5%

  • 3 Land: 45.5%


Draw 2


  • 2 Land: 55.5*53.1 = 29.5%

  • 3 Land: 55.5*46.9+45.5*56.2 =51.6%

  • 4 Land: 45.5*43.8 = 19.9%


Draw 3: 


  • 2 Land: 28.5*52.6 = 15.0%

  • 3 Land: 28.5*48.4+51.6*54.8 = 42.0%

  • 4 Land: 51.6*45.2+19.9*58.1 = 34.9%

  • 5+ Land: 8.1%


Draw 4:


  • 2 Land: 15.0*50.0 = 7.5%

  • 3 Land: 15.5*50.0 + 42.0*43.3 = 25.9%

  • 4 Land: 42.0*46.7 + 34.9*19.8 = 26.5%

  • 5+ Land: 40.1%


So on the play, I reach 4 lands by Turn 4 less than half the time, while on the draw I do it a little under 70% of the time. What does this mean for me having dead spells in hand? If I have less than 4 lands, that means I have anywhere from 7-9 spells (depending on play/draw, 2-3 lands). LEts say I have 7 spells, how many of them are going to be dead? 

Spells Costing 4 or more:


  • 0: 8.2%

  • 1: 24.7%

  • 2: 31.8%

  • 3: 22.7%

  • 4: 9.7%

  • 5+: 3.9%



That leaves me with at least 2 dead spells at least two thirds of the time. That leaves me with not only less powerful options than my opponent, but less options, period. I don't like putting myself in that situation, I would have to have a strong reason to risk it (and note, I keep more 2-land hands on the draw, because your chances are improved to not flounder).

Heck, even if you aren't running that many 4 drops, you want too be able to play 2 spells per untap step, whether it be two creatures, or a creature and removal, or creature and a counter. It gets even worse in Orzoph, when the effective CMC of every card goes up with the number of extorters you have. Which leads me to the 4 by 4 rule of mulliganing, and although I wont rehash the math now, mulliganing a 2-land hand does increase your chances of getting 4 lands by turn 4.
"I think me going Bang bang bang I win is pretty intuitive" Mafia Record: Wouldn't you like to know? 2011 Mafia Awards - Mastermind of the Year
mymoment
\
57817638 wrote:
58060728 wrote:
88318561 wrote:
58060728 wrote:
Moriok Rigger does absolutely nothing to boost other riggers. You are incorrect.
Moriok Rigger is not a Rigger in print. Only in Errata WHAT NOW! (yes, I did put that phrase in for that exact reason)
Congratulations, they have activated your trap card!
Thought exercise, bear with me. What if they eliminated mana hose by separating your deck into two- spells and land. You have two stacks in your library. At the start of the game, you draw three cards from the land stack, and four from the spells. Then, every third turn, you draw from the land pile instead of (or in addition to) the spell pile. Nobody gets mana hosed ever again. Does this help the existing game?

In my opinion, no- it hurts it severely. It will destroy a lot of deck variety. Everyone may start building decks with a higher mana curve. Offbeat decks like mono-black tribal rats will suffer. (I've got one, I run it with 20 land and will not mull if I have even a single swamp, because I know it can successfully go with only two mana for half the game.) People will cut their lands down to 12 or fewer- or make a 3CMC deck that will have a vastly higher concentration of spells and win because of it. Ramp decks will start getting really weird.

In short, random mana is part of the game as we know it today, and I feel it's better for it. Take it away, and you'd have something that wasn't quite Magic anymore.
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Take The Magic Dual Colour Test - Beta today!
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Addendum to SB: if you keep losing on mana issues, you really need to look at what you're drafting and your deck construction. Your curve should probably be majority 1-2 CMC spells, if you can swing it. Also, Gatecrash limited wants 2 color decks, and hurts more than RtR did from going three color. Sometimes it's inevitable- make sure your splashes only require one mana of that color if possible.

And sometimes, yes, you just get flat out hosed in the draft. You'll usually be able to feel when that's happening. If that's the case, just grab a money card or hate draft and try to make some investment back. I did that last FNM, and walked away with two shocklands - one from the consolation for losing pack- that more than covered the cost of the event. (To everyone else- come on, everyone does it. Would you pass a Jace in RTR if you didn't already have a full playset?)

Booster draft is probably the toughest format. I regularly end up pretty low ranked- it's one thing to know theory, but acting on it and using it is tougher. I was mana hosed a in about a third of my games last Friday, but I'm not complaining, it goes with the territory.
You are Red/Blue!
You are Red/Blue!
Take The Magic Dual Colour Test - Beta today!
Created with Rum and Monkey's Personality Test Generator.
You are both rational and emotional. You value creation and discovery, and feel strongly about what I create. At best, you're innovative and intuitive. At worst, you're scattered and unpredictable.
Demento, I think you have an unusual definition for dead card. When I say that a card is dead it means I didn't get a chance to play it over the course of the game, or alternatively it's a card that I missed playing early and when I was finally able to play it (for example due to it being a low CMC card in a color absent from my starting hand) it was useless, where it would not have been had I been able to play it at the earliest possible point. 4 drops are generally good from the point you can play them until the end of the game. Mulliganing a two land hand may make it more likely you will hit your first four land drops (6*17/40=2.55>2), but it also means you are considerably more likely to hit an unplayable hand as well. If you can hit your first 3 land drops in your first 3 turns, and your fourth land drop by turn 5 you should generally be in good shape landwise against most opponents. It certainly isn't worth dumping a 2 land hand for minimally enhanced possibility of hitting the first 4 lands, since the vast majority of time you are hurting your chances of winning the game overall. Hitting 0, 1 or 2 lands for those 6 cards puts you in a position that was strictly worse than the one you were in and that'll happen 48.9% of the time. Hitting 5 or 6 lands, while not strictly worse is objectively worse, as is 4 lands, but by a smaller margin. So the only potentially better hand is 3 lands, 3 spells, which happens only 31.3% of the time. And that only becomes better if the 2 lander misses drawing a land for its first turn, something it will do 45.4% of the time.

I don't think it should come as a shock to anyone that vast majority of 6 card hands are worse than 7 card ones. If you look at the aggregate statistics for people playing their starting 7 vs the people playing less than 7 you'll see the people with 7 winning 3:1 over the people who mulliganed.
Thought exercise, bear with me. What if they eliminated mana hose by separating your deck into two- spells and land. You have two stacks in your library. At the start of the game, you draw three cards from the land stack, and four from the spells. Then, every third turn, you draw from the land pile instead of (or in addition to) the spell pile. Nobody gets mana hosed ever again. Does this help the existing game?

In my opinion, no- it hurts it severely. It will destroy a lot of deck variety. Everyone may start building decks with a higher mana curve. Offbeat decks like mono-black tribal rats will suffer. (I've got one, I run it with 20 land and will not mull if I have even a single swamp, because I know it can successfully go with only two mana for half the game.) People will cut their lands down to 12 or fewer- or make a 3CMC deck that will have a vastly higher concentration of spells and win because of it. Ramp decks will start getting really weird.

In short, random mana is part of the game as we know it today, and I feel it's better for it. Take it away, and you'd have something that wasn't quite Magic anymore.



I do think this would be a better game than the one we have currently, although I do not feel it is the best possible solution. I'm not certain that the fix needs to be a guarenteed land every x turns, just a way to prevent the draws that are extremely non-representative of the decks as a whole. A partial fix might be giving out a free muligan for 0,1,6 and 7 land starting hands, a mechanic for cycling basic lands. Something along those lines. The solution I would like to see implemented would prevent the extreme 5-10% of cases from happening. Something that wouldn't guarentee you always got your 3rd land on turn 3, but made it either extremely unlikely or impossible that you'd still be stuck on 2 lands on turn 5.
Demento, I think you have an unusual definition for dead card. When I say that a card is dead it means I didn't get a chance to play it over the course of the game, or alternatively it's a card that I missed playing early and when I was finally able to play it (for example due to it being a low CMC card in a color absent from my starting hand) it was useless, where it would not have been had I been able to play it at the earliest possible point. 4 drops are generally good from the point you can play them until the end of the game. Mulliganing a two land hand may make it more likely you will hit your first four land drops (6*17/40=2.55>2), but it also means you are considerably more likely to hit an unplayable hand as well. If you can hit your first 3 land drops in your first 3 turns, and your fourth land drop by turn 5 you should generally be in good shape landwise against most opponents. It certainly isn't worth dumping a 2 land hand for minimally enhanced possibility of hitting the first 4 lands, since the vast majority of time you are hurting your chances of winning the game overall. Hitting 0, 1 or 2 lands for those 6 cards puts you in a position that was strictly worse than the one you were in and that'll happen 48.9% of the time. Hitting 5 or 6 lands, while not strictly worse is objectively worse, as is 4 lands, but by a smaller margin. So the only potentially better hand is 3 lands, 3 spells, which happens only 31.3% of the time. And that only becomes better if the 2 lander misses drawing a land for its first turn, something it will do 45.4% of the time.

I don't think it should come as a shock to anyone that vast majority of 6 card hands are worse than 7 card ones. If you look at the aggregate statistics for people playing their starting 7 vs the people playing less than 7 you'll see the people with 7 winning 3:1 over the people who mulliganed.


Cool, where did you find those statistics?

I would like to compare the statistics of 2-land hands vs. players who mulliganed. 
"I think me going Bang bang bang I win is pretty intuitive" Mafia Record: Wouldn't you like to know? 2011 Mafia Awards - Mastermind of the Year
mymoment
\
57817638 wrote:
58060728 wrote:
88318561 wrote:
58060728 wrote:
Moriok Rigger does absolutely nothing to boost other riggers. You are incorrect.
Moriok Rigger is not a Rigger in print. Only in Errata WHAT NOW! (yes, I did put that phrase in for that exact reason)
Congratulations, they have activated your trap card!
Addendum to SB: if you keep losing on mana issues, you really need to look at what you're drafting and your deck construction. Your curve should probably be majority 1-2 CMC spells, if you can swing it. Also, Gatecrash limited wants 2 color decks, and hurts more than RtR did from going three color. Sometimes it's inevitable- make sure your splashes only require one mana of that color if possible.

And sometimes, yes, you just get flat out hosed in the draft. You'll usually be able to feel when that's happening. If that's the case, just grab a money card or hate draft and try to make some investment back. I did that last FNM, and walked away with two shocklands - one from the consolation for losing pack- that more than covered the cost of the event. (To everyone else- come on, everyone does it. Would you pass a Jace in RTR if you didn't already have a full playset?)

Booster draft is probably the toughest format. I regularly end up pretty low ranked- it's one thing to know theory, but acting on it and using it is tougher. I was mana hosed a in about a third of my games last Friday, but I'm not complaining, it goes with the territory.



I've been doing strict 2 color decks since the first 4 drafts or so. Every so often I'll draft a card along the power level of Ground Assault or Skarrg Guildmage and I think to myself that I'll try to splash it into Boros, then get to the end of the draft and realize I already have 23 good Boros playables and no Gruul guildgates. I don't think getting 12 or more 1-2 CMC spells is realistic or even desirable outside of Boros/Orzhov, but I generally succeed at getting decks where the majority of cards are 3 CMC or less. I would say I lose roughly every fourth game to mana issues, and I would say my opponents do as well. So 1-3 games per tournament decided in my favor on mana issues and 1-3 against. The reason that is still problematic and doesn't cancel out is that it makes it much more difficult to go 3-0. Hit two mana issue games in the same round and 3-0 is generally not possible. Even if me and my opponent hit a mana issue each in the same round (which also happens often) it makes it less likely that I'll win that match than if we just played out the full 2-3 games without either of us hitting mana issues at all.

Cool, where did you find those statistics?

I would like to compare the statistics of 2-land hands vs. players who mulliganed. 



For the 3:1 winning ratio, it isn't quite that, the exact ratio is 73:27, but 3:1 is a good approximation. To determine that ratio I just looked at the tournament reports from the Magic Limited GP top 8s from... let's see, I think it was 2009 (2008?) till the present. I could have looked back further but the results weren't changing from year to year. The people mulliganing were getting massacred when their opponents kept their starting 7, and it didn't appear to matter much if it was a single mulligan or two.
I think the only time i mulligan 2 land hands is if i have one color of lands and all the cards are different colored.  So for instance, 2 Forests and 5 non-green cards.  2 lands in an opening hand is good.  
Thought exercise, bear with me. What if they eliminated mana hose by separating your deck into two- spells and land. You have two stacks in your library. At the start of the game, you draw three cards from the land stack, and four from the spells. Then, every third turn, you draw from the land pile instead of (or in addition to) the spell pile. Nobody gets mana hosed ever again. Does this help the existing game?.



No idea, but I think you might be right.  I am just posting because this is how we used to play "WizWar" (boardgamegeek.com/boardgame/589/wiz-war) this way... it didn't have mana and you shared the two decks but it did have similar issues.
rstnme: "Everything looks good when your opponent passes 4 turns in a row."
I would say I lose roughly every fourth game to mana issues, and I would say my opponents do as well.



I think this is pretty much what everyone should expect.  Maybe 20%.

As for the 4x4 rule.... I *will* rehash the math because I don't believe you.

Assuming 17/23 split:

We are comparing a 6 card "new hand" + 3 or 4 draws vs. a LLABCDE hand that gets LL- after 3 or 4 draws.

The formula for this is: en.wikipedia.org/wiki/Hypergeometric_dis...   Or you can use HYPGEOM.DIST() in excel (with cumulative=FALSE)

For the 2 land 7 card hand (on the play)  its' HYPGEOM.DIST(2,3,15,33, FALSE) - need 2 "hits" in 3 draws.  There are 15 lands left in the deck and 33 cards (we already drew 7).     This value is 34.6%.  On the draw (replace 3 with 4)  it's 38.3%.  With a 20% chance of getting 5 lands which is meh.

For the 6 card mull hand it's HYPGEOM.DIST(4,9,17,40,FALSE) on the play and replace 9 with 10 on the draw.  
These values are 29.3% and 28.3%, respectively.   So, no, you are MUCH less likely to get 4 lands by turn 4 if you mulligan.
However, the chances of getting 4 _or_ 5 lands is pretty comparable (about 50% for the mulligan, 60% for the no mulligan on the draw and 42% for the no mulligan on the play).

But I'm probably no better than the average magic player at statistics.
 
rstnme: "Everything looks good when your opponent passes 4 turns in a row."
Sometimes you make the right decision and you still lose. I would have kept that hand too (on the draw, anyway). Not all games are winnable. Focus on winning the ones that are. (Unexpected Results into Sapphire Drake? Must be nice...)
I would say I lose roughly every fourth game to mana issues, and I would say my opponents do as well.



I think this is pretty much what everyone should expect.  Maybe 20%.

As for the 4x4 rule.... I *will* rehash the math because I don't believe you.

Assuming 17/23 split:

We are comparing a 6 card "new hand" + 3 or 4 draws vs. a LLABCDE hand that gets LL- after 3 or 4 draws.

The formula for this is: en.wikipedia.org/wiki/Hypergeometric_dis...   Or you can use HYPGEOM.DIST() in excel (with cumulative=FALSE)

For the 2 land 7 card hand (on the play)  its' HYPGEOM.DIST(2,3,15,33, FALSE) - need 2 "hits" in 3 draws.  There are 15 lands left in the deck and 33 cards (we already drew 7).     This value is 34.6%.  On the draw (replace 3 with 4)  it's 38.3%.  With a 20% chance of getting 5 lands which is meh.

For the 6 card mull hand it's HYPGEOM.DIST(4,9,17,40,FALSE) on the play and replace 9 with 10 on the draw.  
These values are 29.3% and 28.3%, respectively.   So, no, you are MUCH less likely to get 4 lands by turn 4 if you mulligan.
However, the chances of getting 4 _or_ 5 lands is pretty comparable (about 50% for the mulligan, 60% for the no mulligan on the draw and 42% for the no mulligan on the play).

But I'm probably no better than the average magic player at statistics.
 


I meant 4 or more, the rule I actually use is 4x4x4, in which the minimum criteria is 4 lands and 4 spells by turn 4. Thank you for working through the math yourself though, it has been a long time since I actually did this math (I was in a statistics class at the time, and bored), and I forgot the exact techniques I used. I should probably redo the math someday, if only to refresh my statistcs.
"I think me going Bang bang bang I win is pretty intuitive" Mafia Record: Wouldn't you like to know? 2011 Mafia Awards - Mastermind of the Year
mymoment
\
57817638 wrote:
58060728 wrote:
88318561 wrote:
58060728 wrote:
Moriok Rigger does absolutely nothing to boost other riggers. You are incorrect.
Moriok Rigger is not a Rigger in print. Only in Errata WHAT NOW! (yes, I did put that phrase in for that exact reason)
Congratulations, they have activated your trap card!
I meant 4 or more, the rule I actually use is 4x4x4, in which the minimum criteria is 4 lands and 4 spells by turn 4. Thank you for working through the math yourself though, it has been a long time since I actually did this math (I was in a statistics class at the time, and bored), and I forgot the exact techniques I used. I should probably redo the math someday, if only to refresh my statistcs.



This is probably pretty close then. Close enough that it matters significantly which 5 spells you have in your 2 land 7 card hand.

rstnme: "Everything looks good when your opponent passes 4 turns in a row."
I often mulligan three land hands if there is nothing I can play or they are all the same color and I have a strange mix of spells. This seems to work out for me pretty well. I never keep one land hands, that's an ironclad rule for me, and I often ship 2 land hands. I don't seem to have much problem with mana flood or mana screw so I must be doing something right! 
If you are making mullgian decisions based solely on the number of land in your hand, you are probably not a very good Magic player.

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"While a picture is worth a thousand words, each lolcat actually produces a negative wordcount." -Ith "I think "Highly Informed Sarcasm" should be our Magic Online General motto." -Ith "Sorry, but this thread seems just like spam. TT is for off-topic discussion, not no-topic discussion." -WizO_Kwai_Chang "Stop that! If you're not careful, rational thinking may catch on!" -Sax "... the only word i see that fits is incompitant." -Mr44 (sic) "You know a thread is gonna be locked when it gets to the hexadecimal stage." -Gathion "It's a good gig" - Gleemax "I tell people often, if you guys want to rant, you've certainly got the right to (provided you obey CoC/ToS stuff), and I don't even really blame you. But if you see something you think needs changing a well thought-out, constructive post does more to make that happen." - Worth Wollpert
If you are making mullgian decisions based solely on the number of land in your hand, you are probably not a very good Magic player.



This.

I found Carmen Sandiego before you were born unless you're Zlehtnoba.

I often mulligan three land hands if there is nothing I can play or they are all the same color and I have a strange mix of spells. This seems to work out for me pretty well. I never keep one land hands, that's an ironclad rule for me, and I often ship 2 land hands. I don't seem to have much problem with mana flood or mana screw so I must be doing something right! 



If avoiding mana screw / mana flood was the only consideration in the mulliganing decision I would mulligan a lot more often than I currently do. The primary consideration is "does taking a mulligan here improve my overall chances to win the game over keeping my current hand". Often that means taking a calculated risk on hands that you wouldn't choose to draw, because the alternative, mulliganing to 6 cards (or less) is much worse. The best possible 6 card hands are considerably worse than the average 7 card ones. If your opponent kept their initial 7 it often means that only a 7 card hand is capable of beating it and you are better off risking a hand that needs to make specific draws, than taking a 6 card hand that is doomed to failure from the start.

I am curious to see, for people who employ a mulliganing strategy where they routinely mulligan 2 land hands, how often they win games starting with 6 cards or less overall.

Or at a more basic level, I'm curious to see if anyone has a better than even record after mulliganing in games where their opponent kept their starting hand.
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