"Mary", the Japanese word for "winning at Yomi"
Aug 30, 2016 18:33:00 GMT 1
Kraetyz and hamvvar like this
Post by Deleted on Aug 30, 2016 18:33:00 GMT 1
THE CONTENT OF THIS POST IS ACTUALLY BY REDLESS, NOT ME. WHILE I DO AND HAVE PLAYED BY THIS MANTRA, REDLESS IS THE ONE WHO CONSTRUCTED THIS POST. BOW DOWN BEFORE HIM.
I have been using Mary for a little while, and it was my friend Captain who originally introduced me to its building blocks. I'll explain what Mary is, how it works, and the assumptions it makes.
The Scene
Yomi’s combat phases can be categorized based on their “scene”. Scenes consist of all the information known to both players, such as hand size, life totals, known cards in hand, presence of aces in a given player’s hand, discards, etc. The scene does not consist of unknown cards in players’ hands. Once the scene is set, the players play ranges.
The Set of Plays
A range is defined as the set of options that a player plays in a given scene. It does not assign values that determine how often the players should play each option, like a “range” in game theory would. It is simply the set of options that the players play. Mary assumes that in the vast majority of scenes, each player must have options in their range with coverage against each opposing option some of the time. For example, a knocked down Zane with aces and jokers in discard with under twenty life must block some of the time vs a Troq with known Eagle Totem. He must also Throw and Attack some of the time vs Troq, to avoid losing to Troq’s other options.
Hidden Information Leads to Unpredictability
The problem that arises at this point is how to determine which combat option to play at a given time. Some would say that knowledge of the opponent’s tendencies or a purely RNG based mixed strategy is how to choose between options at this point in the game. However, both of these options fail to take into account a critical component of the game: the cards currently in the player’s hand, unknown to her opponent. These cards are conveniently present right in front of the player’s face, and they are also conveniently not-present in front of her opponent’s face. It is by virtue of this information discrepancy that Mary operates.
Play the Best Option
To put things simply, the player’s opponent will have some idea of what is in the player’s hand. However, the player’s hand will usually not look like the opponent pictures it. The hand will usually have some options stronger than what the opponent expects, and some options weaker than what the opponent expects. Mary players generally must play the option that is the best relative to what the opponent suspects, which nets an above-average payoff and is also relatively unpredictable.
Consequences of Mary
Because of the fairly unpredictable nature of Mary’s hand composition, opponents will be hard pressed to figure out or read what option Mary is going to play in a given combat with a specific scene. Because Mary tends to play the options that her hand favors the most, she gets generally good payoffs from winning combat, and she is able to play fast options with very decent coverage rather than options that are inferior relative to what Mary’s opponent expects.
How to Use Mary and Also Exploit People Who Don’t Understand Things
Sometimes your opponent is doing some really weird shit. You don’t really think it is anywhere close to optimal, but it boosts the variance up to such absurd levels that you end up losing to it a lot more than you should given how stupid it is. In that case, you want to adjust how much you value each option in such a way that you value options that beat their stupid thing get played a lot more. A good example of this is if you are Menelker and you have your opponent on a low hand, but your attacks are slightly better than your throws by pure Mary. It is ok to throw them in this situation because there is only a slight difference in the Maryness of your two options, and one of your two options is WAY better from a pure payoff analysis perspective. Of course you should still attack some of the time.
But Wait, Doesn’t Mary Lose to a More Optimal RNG Based Strategy
No. Because Mary bases her plays on what her hand favors, she will get better payoffs than the "Nash Equilibrium" or whatever on average if it is trying to play some “optimal” mixed strategy without taking into account hand composition. If opponent is playing an obviously exploitable range, see above.
But Wait, Isn’t Mary Pretty Damn Random
Welcome to Yomi!
But Wait, Doesn’t Mary Lose to People Who Are Very Good At Hand Reading
Firstly, the fact that Mary’s valuation is stronger than that of these players is usually enough to keep them at bay. Secondly, topdecks are the shit. They are not possible to read so if you need to you can just play based on whichever option your topdeck favors, with some traditional Mary mixed in. Thirdly, Mary can adjust what she expects her opponent will read her hand as if the opponent is super good at hand reading. This technique is not one I have ever needed to break out, which is a good indicator that the first two techniques are effective.
But Wait, Isn’t Mary Really Simple To Play
In many hands and scenes, yes. In others, no. Also, not that each character has slightly different patterns in how their Marys work, so once you have learned to use Mary to a reasonable degree with one character, you cannot transfer the whole skill intact to other characters. Keep in mind that not all of a character’s difficulty comes from what it decides to play in combat (at least for most characters), so you can continue to improve at the out of combat aspects of a character, like combos, hand management, and other things, even after you have mastered a character’s Mary (which you will not do in a trivial amount of time).
Example of Mary
Alright let's do an exciting example of Mary in action. Gwen is playing against Menelker. It is turn one and Menelker has just played his facedown combat card. What should Gwen do? Here is her hand:
2, 3, 4, 6, 7, J, joker
At first blush, 7 throw looks exciting! Gwen can combo from it into 4J6, 234, or 6J. Not only that, but Menelker likes to block in the early game, especially against a robust character like Gwen, who has strong attacks. 7 throw would not be terrible in this situation, for sure.
However, consider that Gwen often has an opening hand with Aces that she can combo her throws into. Aces are really card efficient and a great early game throw follow up for Gwen. The hand that Gwen has drawn this game has no Aces! Menelker doesn't know that, however. Menelker is probably AFRAID of Gwen's Ace-backed throws, even though they don't exist! We don't need to play throw on this hand AT ALL to show the opponent that we might throw them first turn.
Next we look at Attacks. It is pretty clear that 2 is the best starter on this hand. J may do more damage but 2 is faster and it has normal draw. Also, it leads into a nice straight that will fetch us an Ace. What will we do after a straight on this hand? Likely J6 is our best follow up, since it does lots of damage. That is definitely a strong turn 1 option. But what about Block?
If we were looking to block on this hand, we would likely use our 3 or 4 block to block with. That would be strong. We need cards to kill Menelker and we don't want him catching us out with a fast option. As it turns out, however, most Gwen hands are much much worse than this one. On those hands, Gwen often wants to block. She can block those times; she has a great attack right now that she can use to catch out Menelker's throw punish or bonecracker.
So Gwen attacks, using her two. Maybe it wins combat, maybe it doesn't. But in the long term, it was a very strong option to play on this opening hand. Look at your hand, think about what you expect to have, and play based on the difference.
When to Not Use Mary
Whenever you feel like not using Mary, don’t use it. I generally use it as much as possible, defaulting to a semi-optimal range in certain lategames (specifically ones with super mixups). I also sometimes use behavior heuristics that I have accrued instead of Mary, though I don’t really enjoy this or do this in competitive settings.
If I were you, I would choose not to use Mary in certain very specific situations. If you are playing against a Grave who has just seen your whole hand, maybe don’t use Mary. Then again, maybe do. Generally Persephone, Lum, Jaina, Gloria, Quince and other annoying characters with recurring options and specific mixups like Mary a lot less once they have recurred some stuff and have a mixup down. If they use Mary in their mixups and the opponent catches on, it’s a very sad day.
Even if you decide that you are going to primarily use a strategy besides Mary, consider using Mary for the first several turns of each game (this is when it is strongest).
I have been using Mary for a little while, and it was my friend Captain who originally introduced me to its building blocks. I'll explain what Mary is, how it works, and the assumptions it makes.
The Scene
Yomi’s combat phases can be categorized based on their “scene”. Scenes consist of all the information known to both players, such as hand size, life totals, known cards in hand, presence of aces in a given player’s hand, discards, etc. The scene does not consist of unknown cards in players’ hands. Once the scene is set, the players play ranges.
The Set of Plays
A range is defined as the set of options that a player plays in a given scene. It does not assign values that determine how often the players should play each option, like a “range” in game theory would. It is simply the set of options that the players play. Mary assumes that in the vast majority of scenes, each player must have options in their range with coverage against each opposing option some of the time. For example, a knocked down Zane with aces and jokers in discard with under twenty life must block some of the time vs a Troq with known Eagle Totem. He must also Throw and Attack some of the time vs Troq, to avoid losing to Troq’s other options.
Hidden Information Leads to Unpredictability
The problem that arises at this point is how to determine which combat option to play at a given time. Some would say that knowledge of the opponent’s tendencies or a purely RNG based mixed strategy is how to choose between options at this point in the game. However, both of these options fail to take into account a critical component of the game: the cards currently in the player’s hand, unknown to her opponent. These cards are conveniently present right in front of the player’s face, and they are also conveniently not-present in front of her opponent’s face. It is by virtue of this information discrepancy that Mary operates.
Play the Best Option
To put things simply, the player’s opponent will have some idea of what is in the player’s hand. However, the player’s hand will usually not look like the opponent pictures it. The hand will usually have some options stronger than what the opponent expects, and some options weaker than what the opponent expects. Mary players generally must play the option that is the best relative to what the opponent suspects, which nets an above-average payoff and is also relatively unpredictable.
Consequences of Mary
Because of the fairly unpredictable nature of Mary’s hand composition, opponents will be hard pressed to figure out or read what option Mary is going to play in a given combat with a specific scene. Because Mary tends to play the options that her hand favors the most, she gets generally good payoffs from winning combat, and she is able to play fast options with very decent coverage rather than options that are inferior relative to what Mary’s opponent expects.
How to Use Mary and Also Exploit People Who Don’t Understand Things
Sometimes your opponent is doing some really weird shit. You don’t really think it is anywhere close to optimal, but it boosts the variance up to such absurd levels that you end up losing to it a lot more than you should given how stupid it is. In that case, you want to adjust how much you value each option in such a way that you value options that beat their stupid thing get played a lot more. A good example of this is if you are Menelker and you have your opponent on a low hand, but your attacks are slightly better than your throws by pure Mary. It is ok to throw them in this situation because there is only a slight difference in the Maryness of your two options, and one of your two options is WAY better from a pure payoff analysis perspective. Of course you should still attack some of the time.
But Wait, Doesn’t Mary Lose to a More Optimal RNG Based Strategy
No. Because Mary bases her plays on what her hand favors, she will get better payoffs than the "Nash Equilibrium" or whatever on average if it is trying to play some “optimal” mixed strategy without taking into account hand composition. If opponent is playing an obviously exploitable range, see above.
But Wait, Isn’t Mary Pretty Damn Random
Welcome to Yomi!
But Wait, Doesn’t Mary Lose to People Who Are Very Good At Hand Reading
Firstly, the fact that Mary’s valuation is stronger than that of these players is usually enough to keep them at bay. Secondly, topdecks are the shit. They are not possible to read so if you need to you can just play based on whichever option your topdeck favors, with some traditional Mary mixed in. Thirdly, Mary can adjust what she expects her opponent will read her hand as if the opponent is super good at hand reading. This technique is not one I have ever needed to break out, which is a good indicator that the first two techniques are effective.
But Wait, Isn’t Mary Really Simple To Play
In many hands and scenes, yes. In others, no. Also, not that each character has slightly different patterns in how their Marys work, so once you have learned to use Mary to a reasonable degree with one character, you cannot transfer the whole skill intact to other characters. Keep in mind that not all of a character’s difficulty comes from what it decides to play in combat (at least for most characters), so you can continue to improve at the out of combat aspects of a character, like combos, hand management, and other things, even after you have mastered a character’s Mary (which you will not do in a trivial amount of time).
Example of Mary
Alright let's do an exciting example of Mary in action. Gwen is playing against Menelker. It is turn one and Menelker has just played his facedown combat card. What should Gwen do? Here is her hand:
2, 3, 4, 6, 7, J, joker
At first blush, 7 throw looks exciting! Gwen can combo from it into 4J6, 234, or 6J. Not only that, but Menelker likes to block in the early game, especially against a robust character like Gwen, who has strong attacks. 7 throw would not be terrible in this situation, for sure.
However, consider that Gwen often has an opening hand with Aces that she can combo her throws into. Aces are really card efficient and a great early game throw follow up for Gwen. The hand that Gwen has drawn this game has no Aces! Menelker doesn't know that, however. Menelker is probably AFRAID of Gwen's Ace-backed throws, even though they don't exist! We don't need to play throw on this hand AT ALL to show the opponent that we might throw them first turn.
Next we look at Attacks. It is pretty clear that 2 is the best starter on this hand. J may do more damage but 2 is faster and it has normal draw. Also, it leads into a nice straight that will fetch us an Ace. What will we do after a straight on this hand? Likely J6 is our best follow up, since it does lots of damage. That is definitely a strong turn 1 option. But what about Block?
If we were looking to block on this hand, we would likely use our 3 or 4 block to block with. That would be strong. We need cards to kill Menelker and we don't want him catching us out with a fast option. As it turns out, however, most Gwen hands are much much worse than this one. On those hands, Gwen often wants to block. She can block those times; she has a great attack right now that she can use to catch out Menelker's throw punish or bonecracker.
So Gwen attacks, using her two. Maybe it wins combat, maybe it doesn't. But in the long term, it was a very strong option to play on this opening hand. Look at your hand, think about what you expect to have, and play based on the difference.
When to Not Use Mary
Whenever you feel like not using Mary, don’t use it. I generally use it as much as possible, defaulting to a semi-optimal range in certain lategames (specifically ones with super mixups). I also sometimes use behavior heuristics that I have accrued instead of Mary, though I don’t really enjoy this or do this in competitive settings.
If I were you, I would choose not to use Mary in certain very specific situations. If you are playing against a Grave who has just seen your whole hand, maybe don’t use Mary. Then again, maybe do. Generally Persephone, Lum, Jaina, Gloria, Quince and other annoying characters with recurring options and specific mixups like Mary a lot less once they have recurred some stuff and have a mixup down. If they use Mary in their mixups and the opponent catches on, it’s a very sad day.
Even if you decide that you are going to primarily use a strategy besides Mary, consider using Mary for the first several turns of each game (this is when it is strongest).