This week's hypothetical was a bit long; check back here for the details.

So...

Our deck en total:

DECKID=1187218

Our life total - 9
Our hand - Arid Mesa
Our graveyard - Searing Blaze, Searing Blaze, Goblin Guide, Magma Jet
Our board - Mountain, Mountain, Teetering Peaks, Mountain, Mountain

Opponent's life total - 2
Opponent's hand - 0 cards
Opponent's graveyard - Wild Nacatl, Wild Nacatl, Lightning Bolt, Tribal Flames
Opponent's board - Hallowed Fountain, Overgrown Tomb, Mountain, Temple Garden, two 3/4 Tarmogoyfs

Given where we left off there are a range of possible plays, even though we only have one card, and it is a land.

We can summarize those plays thusly:

1. Play Arid Mesa and sacrifice it immediately [to get basic Mountain].
2. Play Arid Mesa with the intention of sacrificing it prior to our draw step the next turn.
3. Play Arid Mesa but without the intention of sacrificing it prior to our draw step the next turn.
4. Hold Arid Mesa.

You see MTGO streamers -- even very good players sometimes -- make plays like #1 all the time "to save time" ... Sometimes that is fine, but like the point I made to use Island over Hallowed Fountain last week, this is not the kind of play you want to get in the habit of. In this case we can knock #1 off as being strictly worse than #2.

For one thing, we have two Searing Blazes still in our deck, and if we break the Arid Mesa on our own turn, we deny ourselves the opportunity for a landfall kill next turn if we draw Searing Blaze.

For another thing, we are at nine life, and only because our opponent screwed up on the order of his Tribal Flames last turn!

Our collective graveyards at this point are:

Us: Searing Blaze, Searing Blaze, Goblin Guide, Magma Jet
Him: Wild Nacatl, Wild Nacatl, Lightning Bolt, Tribal Flames

Or...

Us: Instant, instant, creature, instant<
Him: Creature, creature, instant, sorcery

The Tarmogoyfs, ergo, are 3/4 creatures that can attack for six.

If we use the Arid Mesa we go down to eight life and make the Tarmogoyfs 4/5s, which will kill us unless the opponent blatantly screws up [again]. This is not something I particularly want to gamble on. So we can cross #1 off the list; #2 is the strictly superior version of #1.

There are two major tensions that divide #2 and #3 versus #3 and #4.

#2 vs. #3

Basically we have no bluff in either scenario (all our cards are now on the table). It is a question of whether we want to try to thin a land out of our deck prior to our next draw. Regardless of our intent going in, we always have the option of changing our minds, remember. For instance if he finds a fetch land of his own and breaks it to give his Tarmogoyfs eight power, we won't break our Arid Mesa no matter what, as we will die.

Assuming the opponent blanks (i.e. he draws another non-lethal, enters-the-battlefield-tapped land) #2 vs. #3 is a question of math.

#3 vs. #4

The differentiation between these two lines is not one of math. We aren't changing the top card of our library. What we are doing is seeing if we can influence our opponent's play. Our opponent has already shown us some relatively weak mental game; players who complain a lot tend to move their focus off of what matters at hand and instead imagine themselves in some alternate reality where they are entitled to everything going their way. Our opponent didn't miss the opportunity to complain about not drawing extra lands -- but did manage to miss two points of damage by attacking in the wrong order. This is a kind of player we can potentially game.

We already have enough lands in play to do anything we want in terms of a topdeck.

The question is whether there is any bluff to play #4. That is, what can we possibly represent that will influence our opponent's behavior?

Now seems like a good time to review the contents of our deck (cards in bold denote cards we have seen).

Goblin Guide
Goblin Guide
Goblin Guide
Goblin Guide
Hellspark Elemental
Hellspark Elemental
Hellspark Elemental
Hellspark Elemental
Keldon Marauders
Keldon Marauders
Keldon Marauders
Keldon Marauders
Lava Spike
Lava Spike
Lava Spike
Lava Spike
Lightning Bolt
Lightning Bolt
Lightning Bolt
Lightning Bolt
Magma Jet
Magma Jet
Magma Jet
Magma Jet
Rift Bolt
Rift Bolt
Rift Bolt
Rift Bolt
Searing Blaze
Searing Blaze
Searing Blaze
Searing Blaze
Skullcrack
Skullcrack
Skullcrack
Skullcrack
Spark Elemental
Spark Elemental
Spark Elemental
Spark Elemental
Arid Mesa
Arid Mesa
Arid Mesa
Arid Mesa
Mountain
Mountain
Mountain
Mountain
Mountain
Mountain
Mountain
Mountain
Scalding Tarn
Scalding Tarn
Scalding Tarn
Scalding Tarn
Teetering Peaks
Teetering Peaks
Teetering Peaks
Teetering Peaks

We have over 20 burn spells left in our deck, essentially any of which would be lethal in this spot.

We clearly can't win with what we have right now; however we might be able to win with what we have on top (and we certainly have drawn / looked at a lot of damn lands in a row).

We need to be able to live to that next draw step (which is yet another reason why Option #1 is such a bad play); however it is possible we can get multiple draws!

From our side, our deck has cards in essentially three classes:

A - Assassins (Rift Bolt, Lava Spike, etc.)
B - Behavioral Kills (Spark Elemental, Hellspark Elemental, Goblin Guide, etc. that might kill based on the opponent's Behavior)
C - Crappy Cards (Mountain, Arid Mesa, Scalding Tarn, Teetering Peaks)

The cards on the table tell us the opponent can attack for six, which does not kill us outright given the current game state. There are a fair number of cards that the opponent can pull that will kill us on the spot (Lightning Helix, Lightning Bolt, Tribal Flames, and possibly Might of Alara). We know there are about 50 cards left in the opponent's deck and we have seen two cards of this class. He is probably playing something like 12-14 of them total; this means if the opponent draws a card of this class we are about 26% to lose on the spot, assuming the opponent takes the kill. We can do nothing about cards in this class.

Assessment: We can do nothing if he draws one of these.


If and only if the opponent is playing a card like Path to Exile maindeck, there is a weird situation where we can draw a (B)ehavioral Kill and the Path to Exile wins the game; there is nothing we can actually do about that other than draw an (A)ssassin, plus there is no guarantee a Tribal Flames deck even plays any copies of Path to Exile (let alone four) main deck. It might be wrong but I wouldn't even consider this in my math.

Assessment: We can do nothing if he draws one of these.


That said, there is a class of cards that the opponent can draw that will not kill us, no matter what. Figure he plays somewhere around 22 lands. We have seen four. So 18/50 of the time (call it 36% of the time) we definitely live the turn. In fact there are certain cards in this class (say Misty Rainforest) that can put the opponent at one, so that we can kill him with a Keldon Marauders off the top or a non-landfall'd Searing Blaze.

Assessment: We can play in such a way that affects our chances of winning if he draws one of these.


Finally there is a class of cards that he is most likely to draw from. Some amount of his remaining 'goyfs, Geists, and assorted one-drop creatures.

Assessment: Again, we can play in such a way that affects our chances of winning if he draws one of these.


We are going to make it to our next draw step 3/4 of the time unless we do his work for him. The question is how often we can win the rest of the time. There are two schools of thought on this, and they are what divide Option #3 and Option #4.

In Option #3 we have no bluff. Our Arid Mesa is on the battlefield and the opponent can put us to three if he wants to.

In Option #4 we have a bluff of...something. Note that we are actually holding a C. There is no point in trying to represent an A, as if the opponent takes a moment to think about this he would realize that if we had an A, he would be dead. Ergo we can only be holding a C or a B. If we want to bluff Option #4, we have to be representing a B.

So if we go with Option #4, we really have to think about whether the opponent will believe we have a B, or the C that we actually do.

If we are holding a B (and the opponent doesn't draw an (A)ssassin of his own), it is a question of how many Tarmogoyfs he leaves home. If he believes we are holding a B and he doesn't draw a blocker, he is likely to leave at least one Tarmogoyf home. Note we have no objective way of gauging what the opponent will do, other than the fact that he has not played in a particularly focused manner to this point.

- If we draw an (A)ssassin, we win.
- If we draw another (C)rappy Card, we probably need to draw an (A)ssassin next, provided we live to a seventh draw.
- If we draw a [B]ehavioral Kill, what we actually want is for the opponent to behave in a way that we will win.

For me, I would play my Arid Mesa and probably make a show about how unlucky I was after my Magma Jet; under no circumstances would I break the Arid Mesa prior to my draw step.

Got that Option #2 choosers?

Here's the math:

Per the above, we have 50 cards in our deck, including 21 (A)ssassins, 15 (B)ehavioral Kills, and 14 (C)rappy Cards.

Simple Math:

42% A
30% B
28% C

In theory (and assuming the Arid Mesa doesn't kill us), we would theoretically reduce our number of cards to 50-1 (49 cards), changing the math to:

~43% A (21/49)
31% B (15/49)
27% C (13/49)

However!

We just pushed two Mountains to the bottom of our deck! So in fact, the original simple math is simply wrong. We in actually have a sub-deck of 48 cards from which we can actually draw, and a different sub-deck of 2 Mountains underneath our main sub-deck! Therefore our actual topdeck math this turn is:

~44% A (21/48)
~31% B (15/48)
25% C (12/48)

We actually increase (!!!) our likelihood of drawing a (C)rappy Card if we break the Arid Mesa, while simultaneously reducing our chances of drawing a card in class B or (ideally) A.

The important math here is that...

Option #1 is strictly worse than Option #2, and...
Option #2 is, surprisingly maybe, statistically (if not strictly) worse than Option #3!

Obviously there are cases where Option #2 wins and Option #3 loses (we have yet another consecutive land on top), but we have no evidence that is the case here. If we run the same situation 1,000 times, we will win more by not breaking land than we would leaving our Arid Mesa be.

I think Option #3 versus Option #4 is a question of preference. This is why I prefer Option #3..

My experience is that players with weaker mental games tend to play impulsively, but less aggressively, often worrying over boogeymen that don't even exist. In this case no boogeyman exists but one might exist. As he can't kill us with the cards on the table, we don't actually want to increase his boogeyman sensitivity as an as-yet-unseen boogeyman is going to be our plan to win in this spot 10/ZZZ of the time.

We are 2x as likely to draw a 3/1 haste trampler than a Keldon Marauders. Topdecking Keldon Maruaders is a kill only if the opponent has already attacked with a single Tarmogoyf and fails to draw a burn spell the next turn. We need to not only draw a particular (B) but it only works if the opponent has already made a specific play. Ergo I would not tend to play for Keldon Marauders.

What I want in this spot is the opposite: To get him to attack with both Tarmogoyfs, even if it is against his nature, and probably the wrong play. To be clear, we have no objective control over this, but if we act all helpless and annoyed, it might increase the likelihood of that double attack happening. This increases the number of wins we get from our (B)ehavioral Kills pile dramatically (with Goblin Guide a kill as well, assuming no blocker / no answer).

Mike's Play: Option #3.


Randy Buehler
Team CMU founder, long-time Head of Magic R&D, and Hall of Fame Member

Our Celebrity Guest Randy Buehler did the same math, but opted for Option #4.

"Well I'm clearly not going to be cracking that Arid Mesa because the theoretical 'thinning' effect of removing a Mountain from our deck is more than off-set by the two Mountains I pushed to the bottom with Magma Jet. The only issue is whether to hold it in hand so my opponent can distract himself by trying to figure out what I'm holding or play it so it doesn't get knocked out of my hand by some sort of discard effect (which would both pump up the 'Goyfs and also remove Searing Blaze as an out). He seems like the kind of guy who is capable of making a(nother) mistake so I don't want to make his life easy, plus playing the Mesa now means Searing Blaze only kills him if I can afford to pay a life next turn. More importantly, what the heck discard spell would come out of his deck? Liliana is the hypothetical nuts for him (it could be stranded in his hand waiting for a second black mana), but nobody runs her in Zoo and this guy seems like the kind of guy who is playing a stock list off the 'Net, not brewing. So I ship the turn, and plan to topdeck a spell.

"It's just too bad I don't run Lightning Helix in my deck."

Randy's Play: Option #4.

This week's winners:

● $25 to Melissa Ranhofer for agreeing with Mike.
● $25 to Peter Holzberger for agreeing with Randy.

Make sure you send a message to our Facebook page - MTGatTCGplayer - to claim your prizes!

Thanks so much for playing!

LOVE
MIKE

Randy Buehler is a seven-time Grand Prix Top 8 competitor, Pro Tour Champion, the 1997-1998 Rookie of the Year, and a member of the 2007 Magic Pro Tour Hall of Fame. On the other side of the game, he is a former Developer, Director of Magic R&D, and VP of Digital Games for Wizards of the Coast. You can follow Randy on Twitter at @rbuehler and check out his commentary from the booth at GP Melbourne starting tomorrow at DailyMTG.com.