Picture this: It's the final game of the final match of the tournament. The board state is such that either you or your opponent will be dead within the next turn cycle. You will win the game if nothing happens, but just barely. You have the opportunity to win the game this turn, but going for it creates a risk that you might lose immediately. How do you decide what to do?
I was recently in this situation. Perhaps because it was the final play of the entire tournament, or the uniqueness of some of the cards involved, this one has stood out to me. I spent several hours over the next day thinking about it and wondering if I actually got the play right. Thinking through conditional probabilities has lead to some confusing moments, but I think I've found an approach that results in clarity.
This post will talk about that situation, as well as some similar situations that arise as a thought experiment.
The Game State
With actual deck lists and board state photos, an exact answer should be obtainable.
Deck lists:
Noah Shanning - Counterburn
(SB for game three: -1 Wheel, -1 Chain, -1 Lat Nam, -1 Pyroclasm, +2 Crypt, +1 Maze, +1 Blood Moon) (This is his actual sideboarding which I will use for analysis. In game, I assumed he may have some Pyroblasts as well since it can race a Deep Spawn in some situations)
Ty Thomason - Reanimator
(SB for game three: -1 Mana Crypt, -1 Mox Emerald, -1 Mox Ruby, -2 Disenchant, -1 Ashen Ghoul, -1 Mind Twist, +4 Hymn +3 Contagion)
Board state:
8 life with one unknown card in hand
4 life with the 4 cards in hand
The Options
The two main decisions at this point in the game are whether or not I should attack with Deep Spawn, and whether or not I should try to remove the Gorilla Shaman if I do attack so that it represents lethal damage.
Not attacking will not let me win. I will be at one life on my next turn so even Demonic Tutor for Contagion won't work. If I draw Contagion, I could Demonic Tutor for Black Lotus (or vice versa), but would still be one mana short from paying the cost. Even Consultation after a top deck of Lotus or Contagion would require tapping City of Brass. Attacking also leaves the opponent at 1 life after his upkeep, which means the Serendib will kill him before he can attack on the following turn. So even if he draws a removal for Deep Spawn (REB or Chaos Orb), attacking will win the race. Therefore, I must attack.
There are two ways to attempt to remove the Gorilla Shaman. The first is to cast Demonic Consultation for the last Contagion in my deck. The other option is to cast Demonic Consultation for one of four Bazaar of Baghdad, play the Bazaar and activate, and draw Black Lotus and Chaos Orb. I'm not going to do the math, but I think the Consult for Contagion is a bit more likely...
Any time opponent has a burn spell in hand, I lose the game. I am already dead to Psionic Blast, and any other spell will finish me off after Serendib attacks on the opponent's following turn. I will also lose to burn spell when I tap City of Brass to attempt to Consultation. We can ignore those situations. Therefore, assume no burn spells in opponent's hand.
If I attempt to remove the Shaman and my opponent has a Counterspell (Counterspell, Mana Drain, or Force of Will in this case) I will lose on the swing back. If I do not attempt to remove the Shaman, I will lose only to a non-Psionic Blast burn spell off the top during my opponents following turn. Also, sometimes I lose to my own Demonic Consultation.
So which choice gives me the best chance to win?
Detailed Analysis
Any creature in hand would have been played by opponent. This would provide an option to block and survive while still having enough damage left to attack back for the win. It also removes my option of holding back Deep Spawn to block. Therefore, assume no creatures can be in hand.
Additionally other cards we can rule out from being in his hand: Maze of Ith and Mishra's Factory (he played a Volcanic Island last turn), Blood Moon, Chaos Orb, Lat-Nams Legacy, Merchant Scroll, Time Walk, Ancestral Recall, Braingeyser and Timetwister. I don't know if he would play Tormod's Crypt at this point, so we will assume he could still have that.
Possible cards in his hand:
4 Island
4 City of Brass
2 Volcanic Island
1 Library of Alexandria
2 Tormod's Crypt
1 Counterspell
1 Force of Will
1 Mana Drain
So 3/16 of the time he will have a Counterspell here. (~19%)
What are the outs he can top decks to win if we give him an additional turn to live?
4 Lightning Bolt
3 Incinerate
1 Chain Lightning
So 8/47 is lethal. (~17%)
5 Redraws with Ancestral Recall, Merchant Scroll, Timetwister, Lat-Nam's Legacy, and Braingeyser (Time Walk will not win as he will die to Serendib before his next draw)
Redraws represent an additional 2% or so.
3 Drawing the game with Psionic Blast (~6% plus ~0.5% on redraw)
Missing with Demonic Consultation - 14%
How to Interpret the Numbers
Here is where I may not have this exactly correct. How can you combine these probabilities to get the correct picture? (Reminder, all of this math is conditional on not being dead to burn spell in hand already.)
Is it right to say you lose 33% of the time by casting Consultation (19% to Counterspell and 14% to Consult itself)? No you have to combine the times they both fail and subtract from 100%, so this happens ~30% of the time.
Do you win 75% of the time you just attack without casting Consultation (100-17-2-6)? I think this approach works.
But where I'm not sure I'm confident is the comparison of these values: 70% to win by casting Consultation vs 75% to win by not casting it. This would say that not casting it is better by about 5%.
Another way to look at it:
Assume instead of Consultation you have Contagion in hand. Sometimes, you cast Contagion and win the game, but you also would have won that game by not casting it (opponent's hand is blank and they don't draw the burn to kill you). Therefore, you only should cast it if the odds they have burn spell on top is greater than the odds they have a Counterspell in hand. Our math places both of those probabilities right around 19%. So with Contagion in hand, you probably can go either way. However, the added 14% fail rate of Consultation means you should not cast it and instead hope to fade the top deck.
What if you have a read?
Sometimes you may have a read that the opponent has a Counterspell in hand. If you increase the chances they hold a counter, you can see the math will favor not casting a spell even more. This applies even if you have Contagion instead of Consultation.
Maybe you have the opposite read and know with high certainty the opponent is holding a land? You still would need to do the math on missing with Consultation vs them top decking a burn spell. This would favor casting Consultation by about 5%, but you can imagine situations where you should not cast it because it would add risk of losing compared to not.
What did I do?
I did not have time during the match to do such thorough analysis. My thought process was something like this: I lose 15% of the time to Consultation, I think it is likely his last card is a Counterspell given the way the past two turns had played out, so I should not play any spell and just attack. This is what I did and I won the game because of it. My opponent showed me the Mana Drain that was in his hand, along with the Chaos Orb he top decked that was a turn too late.
At the time, I wasn't sure I made the right play, but I feel a bit better about it after doing this analysis. And so I won the NEOS Season 12 December Monthly.
If you think there is something else to consider or a cleaner way to present this math, please let me know.
