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Enraging Puzzle (Saprolings, Sick of It)

Today I’m going to share with you an interesting puzzle that actually came up in a game I played a few weeks ago. But I wasn’t playing a normal game of Magic, so I better explain that first.

Pai Gow Magic

The origins of Pai Gow Magic are unknown to me, but Ben Rubin is the person who taught me how to play it. As with Pai Gow Poker, in Pai Gow Magic you are dealt a large hand of cards that you have to divide into smaller sets, which will battle your opponent’s sets. Specifically, in this version, each player opened a booster pack of 14 cards and had to make four face-down piles of 3 cards each (discarding the weakest 2 cards). Each of those four piles would be randomly pitted against one of the opponent’s piles in a tiny game of Magic.

The rules of the 3-card vs. 3-card tiny game of Magic are as follows: Opening hand size 3. No decking. 5 life (not 20). Infinite mana. Otherwise, normal Magic. Oh, and we were using the “Siggy’s blessing” instead of the city’s blessing. Named after Mike Sigrist, a player who is nice enough to give you his blessing if you have 3 permanents instead of the normal 10 (this counts for cards that say city’s blessing and makes it much more useful and fun in a 3-card format).

In Pai Gow Magic, you might have to decide where to put a Negate so that it protects an otherwise fragile 5-damage evasion kill. Or perhaps your pack has many creatures and you have to figure out which cards complement each other for the right mix of offense and defense. Stuff like that.

If neither player can advance the game state and deal 5 damage to the opponent, the game is a draw. No big deal either way—there are three other tiny games waiting to be played.

Example of a draw:

 

This game is a draw because even though both players will play creatures big enough to deal 5 damage to the opponent, neither can profitably attack. If the Cowl Prowler attacks, it gets double-blocked, which leaves the opponent with a winning position. If the 3/4 and 3/3 attack, with or without the 2/2, they don’t deal lethal and then what remains can never deal the final damage. So this game is a draw once both players realize that they can’t attack.

Example of a win:

 

Now you can see that the game no longer draws. Cowl Prowler can attack, again forcing a double-block (since a single block doesn’t leave a lethal attack back and forces chump blocks each additional turn), and once the double-block happens, Vanquish on either 3-power blocker lets the Cowl Prowler live, knock out the other blocker, and end the game the following turn.

The Puzzle:

I was the player with the Imperial Ceratops and The Ben Seck had the Overgrown Armasaur and the Saproling. The situation that led to this game state isn’t important to the puzzle, but if you’re curious, we traded off two other creatures, then I dealt 4 damage to the Armasaur and 2 damage to my Ceratops using Reckless Rage, and TBS saved it with a pump spell.

The puzzle is how the game ought to progress from here, and who wins (or is it a draw)?

A group of pro players spent about an hour on this and reached a consensus outcome. Then I began writing this article to show our work below, and our consensus answer changed!

We had a lot of fun with this. I recommend you get some cards or proxies out and try to work through the strategies each player might use. Try to solve it yourself and then click the spoiler below to see if your solution matches mine.

My Solution

The first thing you may realize is that I could never win. If TBS leaves his 4/4 back, I don’t have, and can’t gain, any way to attack through it. But in Pai Gow Magic the draw is often an available outcome even if you can’t win. So could I force a draw?

I didn’t think so at the time. If TBS attacks with his 4/4, my choices are to take it or block it. Taking it gets me nowhere since an attack back leaves me dead (TBS can just take 3) and blocking it gives me 2 life and TBS a Saproling. In my mind, I pictured this playing out 50 more times. I would go to 109 life or so, but TBS’ resulting 50 Saprolings could then finish me off easily in 3 attacks. So I conceded.

But then Huey asked, “Wait a minute, what happens if you get high enough in life not to die from an alpha strike, and then attack back with the 3/5?” None of us knew the answer right away.

But Huey and Shahar ended up siting down and working through it while we all watched.

Some shortcuts that help us solve it faster:

  1. If TBS ever doesn’t attack, the game is a draw. I will pass back, nothing will have changed, and so that decision to not attack is the same as conceding the draw.
  2. If TBS ever gets 5 Saprolings, he wins for sure. At that point, the Ceratops can’t ever attack without dying, and TBS gets to use his Armasaur attack to get more Saprolings until I’m overwhelmed even from a life total that is roughly 2x his number of tokens.
  3. If the combat sequences result in a loop that nobody can break out of profitably, the game is again a draw.
  4. If the best TBS can do is reach the initial state of the puzzle (with me at 7 or higher life) that forces a draw as the next steps will recursively also lead to the initial state or a drawn state, by virtue of the fact this was the best TBS could do the first time around.

The key insight Huey had was that if I block the Armasaur once and go to 9, TBS does not have a lethal single-turn attack. His total power will be 6 (Armasaur and 2 Saprolings). TBS’s Armasaur is now tapped, so my Ceratops can attack.

 

I attack with my Ceratops. TBS can take it and go to 2, or block it.

Let’s say he doesn’t block. TBS falls to 2 life, and on his turn he can attack back for 5 with the Armasaur and 1 Saproling, leaving back a Saproling to keep him alive. I fall to 4 life. On my turn, I attack, forcing TBS to chump block, and sending me back up to 6 life. When TBS untaps, he has to attack with something or the game is a draw, so he attacks with the Armasaur and sends me to 2 life. On my turn, I can no longer attack (2 life won’t be enough to get to me 5+ and survive the crack back). So I say go. TBS untaps with a Saproling and the Armasaur. He attacks with both since I must block the Armasaur, which then will generate a chump blocker. When I do so, I fall to 1, but gain 2 back, ending at 3 life. TBS gets a chump blocker and is clearly ahead as my next turn resembles my previous one in that I cannot attack and survive a crack back. This next alpha strike from TBS is even worse for me. I lose.

Let’s say he blocks it. In that scenario, his board moves to 1 Armasaur and 1 Saproling, and I move up to 11 life. His turn now begins. We know from shortcut 1 that if he doesn’t attack the game is a draw. So he can attack with both creatures, just the Armosaur, or just the Saproling. Just the Saproling sends me to 10, but then when I untap we are in the initial game state but with me +3 life.

If TBS attacks with both creatures I fall to 6 life and then he falls to 2 when I attack back. Now TBS still has to attack with something or the game is a draw. If he sends the 4/4, I go to 2 and then I can no longer attack (because he could chump with the Saproling and crack back with the 4/4 for lethal). So I say go. TBS must attack again with something to avoid the draw. He might as well send both creatures since I am forced to block the 4/4. The Saproling knocks me to 1 but the trigger brings me back to 3. TBS makes another Saproling. On my turn, if I attack TBS chumps, I go to 5, and then die to the crack back. I can’t attack still, so then TBS again attacks with everything and again I must block the 4/4. So this is a recursive pattern where TBS is making tokens and I can’t attack. I lose.

Okay, so I lose if I decide to crack back at 11 life against 2 Saprolings and the Armasaur. What if I crack back when I’m at 13 against 3 Saprolings and the Armasaur?

Now TBS can either block and stay at 5 or take it and go to 2.

If TBS blocks, he loses a Saproling (down to 2) and I gain 2 life (up to 13). He has to attack with something. Let’s say that he sends it all. I will take 6 falling to 7, then attack him back (he goes to 2). If I don’t attack then I’m letting the game become solved—TBS attacks with the 4/4 and I end up at lower than 11 life with an otherwise identical starting position. So I attack TBS down to 2. On TBS’ following turn, he can attack with all but 1 Saproling, dealing 5 damage and sending me down to 2 life. When I untap, I can’t attack because a chump block by TBS only sends me to 4, and the crack back is lethal. If I stay home, TBS can attack with everything and finish me off. I lose again.

Let’s try one more time and maybe the pattern will be clear.

 

In this scenario, I’ve blocked 3 times already and gotten to 13 life. Now I send in my Ceratops. TBS might now want to test the pattern we’ve seen, so he blocks with 1 Saproling and untaps with 3 and the Armasaur. An attack with all 4 creatures sends me to 6. On my turn I can’t attack, so this devolves to the starting position except I have fewer life against more Saprolings. I lose.

We already know what happens whenever TBS gets 5 Saprolings: I can never attack and TBS will build an army of even more Saprolings until they swarm me.

So how did a group of us get it so wrong for so long? For some reason, we just didn’t realize that every time I fell to 4 life or lower, TBS could attack with everything and I’d be forced to block the Armasaur. Seems obvious now, but we all missed it. Maybe you solved it right away like I did once I got out the pen and paper. Maybe it took you a while like it did for me before I got out the pen and paper. Let me know in the comments what your path to the solution was.

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