Game state complexity and valuation modes
Nov 6, 2016 15:16:45 GMT
+Mozzy, masscherano, and 4 more like this
Post by RationalPi#1895 on Nov 6, 2016 15:16:45 GMT
Playing 
is all about looking at a game state and picking the move that maximizes your chance of victory, but there are multiple ways of arriving at that move, and I'd like to lay those out. Odds are that you've used all of these modes of thought at some point or another, either consciously or unconsciously, but specifically recognizing them can help you pick the right one for the job.
Deterministic Mode
The deterministic mode is when you use logic to find the specific line of play that guarantees a winner. This is at once the most powerful and the most specialized mode of thought, as it is only usable when the game state can be "solved." Most games end with this mode, as "spotting lethal" is usually a matter of taking a deterministic approach to recognize the cards that must be played to win the game right now. But the deterministic mode can sometimes move beyond this situation. For example, Freeze Mage and Aggro decks can often use a deterministic approach to find multi-turn lethals, and control decks can use a deterministic mode to find the line of play that leads to assured victory in fatigue. If you know the opponent's deck list (or strongly suspect their deck list), you can use a deterministic approach to valuate their remaining threats and line up your available answers to leave the opponent with no way to win. Miracle rogues with only a small number of cards left in their deck can use a deterministic mode to play out the rest of their deck, if they properly track their draws throughout the game.
The deterministic mode can also be used to eliminate plays that would result in an opponent winning.
More than any other mode, failing to enter the deterministic mode at the earliest possible time will result in a loss of winrate. Even if you always "spot lethal" in the moment, you could be missing out on 1, 2, or even 3 turn lethals by failing to jump into the deterministic mode.
Probabilistic Mode
Just below the deterministic mode in power is the probabilistic mode. In this mode of analysis you explicitly recognize all of the possible outcomes of each line of play and select the path that maximizes the chances to win. Again, this mode of thought requires you to have a full understanding of the situation, but the main difference between this mode and deterministic mode is that there is simply no choice that has a 100% chance for victory.
The probabilistic mode is best exemplified by "counting outs." When playing an aggro deck, for example, you might find yourself in a situation where the only way to win is to draw a direct damage card off of the top of the deck. As a control deck, the only way to not immediately lose might be to use random removal like Brawl and hope for the best outcome. The opponent's hand or cards might also figure into the probabilistic mode. For example, the best line of play might depend on whether the opponent draws a taunt minion or a heal, so determining the odds of a lucky top deck may be worthwhile.
There are shortcuts to the probabilistic mode. For example, you might focus only on the random outcomes that end the game immediately by trying to maximize immediate victory and/or minimize immediate loss, without explicitly determining the odds for the remaining cases where the game continues. An example of this would be a late-game state where the player can either go face with a minion or make a trade. Going to face maximizes the odds of immediate victory by top-decking a direct damage spell, while taking the trade minimizes the odds of immediate loss by the opponent having reach. In this case, the remaining game states have a big impact on which choice is the best, and it may be worthwhile to apply a more abstract mode of valuation to pick which line of play is correct.
Statistical Mode
Not to be confused with the probabilistic mode, the statistical mode relies on data gathered over many games to determine the correct play. For example, one may have data that shows that playing an Argent Squire on turn one has a higher percentage chance of victory than playing a Leper Gnome. There is no specific logic behind this move (though perhaps arguments can be made), but repeated gameplay and access to a large pool of data makes these statistics known.
The statistical mode is powerful, but very rare. Gathering a large amount of reliable data is difficult and time consuming, and often not worth the effort considering how fast the meta moves in and how situational play choices are. I choose to include it only for completeness, and because statistical modes can be good for "out-of-game" decision making like deck, card, and mulligan choices. The statistical mode can also be useful for early game decisions that come up often like "Is it better as a warrior to armor up on turn 2 or develop a Firey War Axe against an empty board?"
Abstract Modes
At the end of the day, we are only human and the Deterministic and Probabilistic modes can only be used in relatively simple situations in the end game where victory is within sight. Throughout the early and midgame, though, more abstract methods of play valuation can help a player find the best move to win.
There are dozens of abstract modes a player can use, many of which have excellent articles written about them: tempo, mana efficiency, card advantage, clock and reverse clock, equivalent mana, threats and answers, beatdown, variance minimization/maximization (greed), etc. Each of these paradigms helps decision making by giving a metric on which you can determine the best move. Some paradigms are more applicable in certain matchups than others. For example, aggro decks will more often invoke the clock/reverse clock while control deck mirrors are played around the threat/answer paradigm and midrange decks live and die on tempo. So much can be said about each of the paradigms, and there are plenty more out there, but here's a quick overview of the most important:
Tempo: A good play is one that maximizes the amount of stats you have on board and minimizes the stats the opponent has on board. Building a large and resilient board is the key to victory.
Mana Efficiency: A good play uses more mana and allows for the use of more mana over time. Maximizing mana usage through ramp effects is good, drawing more cards to use more mana is good, and lining up plays to prevent "floating" mana is good.
Card Advantage: The player with more cards in hand and in play is at an advantage. Card draw is good, as is answering multiple of an opponent's cards with one of your own (2-for-1). This is also known as "value."
Clock/Reverse Clock: Doing damage to an opponent and setting up boards that threaten to end the game quickly establishes a "clock" on the game until you win and a "reverse clock" that counts down to when you lose. Moves that shorten the clock and extend the reverse clock are good.
Equivalent Mana: An alternative way to evaluate tempo that values boards based on how much mana the minions would be worth at their current stat values.
Threats and Answers: Games consist of players trading off on placing down threats and providing answers. Victory is attained by forcing the opponent to either run out of threats or run out of answers for your own threats. Long term planning is needed to ensure that you save answers for cards they line up best against.
Beatdown: One player should be aggressively seeking to end the game and the other should be trying to extend the game. Victory is attained by correctly assessing which player you are.
Variance Minimization/Maximization (Greed): At any point in time you are either "ahead" or "behind." A player that is ahead should seek to minimize variance through safe plays, while a player that is behind should seek to maximize variance through greedy plays. This paradigm usually relies on the other paradigms to determine what it means to be "ahead" and "behind." IE, you can have a greedy tempo play or a greedy card advantage play, depending on the situation.
Personally, I'm always on the lookout for new paradigms to explore and master. So, feel free to share your favorites.
Intuitive Mode
The final mode is what I call the "Intuitive Mode," where plays are chosen based on feel. This may seem like the weakest mode, but it can be very powerful in the hands of a good player. In essence, the intuitive mode is fueled by the player's past experience, practice, and the abstract modes that they have internalized. As such, developing a strong intuitive mode requires study, reflection, and deliberate practice and avoiding the pitfalls of results-oriented thinking and other cognitive biases.
Which Mode is "Best?"
While all of the modes are situational, I think there is a hierarchy. It's a good habit to get into to run through each of the methods in order to find the best play. Here's my checklist:
That said, flipping the last two options is good if you are working on developing a specific abstract paradigm, or if you feel you are a weak player with a given deck and lack reliable intuition.
So, what are your opinions? Are there any modes that I've left out? Are there any abstract mode paradigms that you think I should have mentioned? What techniques do you use for developing each of these modes?
is all about looking at a game state and picking the move that maximizes your chance of victory, but there are multiple ways of arriving at that move, and I'd like to lay those out. Odds are that you've used all of these modes of thought at some point or another, either consciously or unconsciously, but specifically recognizing them can help you pick the right one for the job.Deterministic Mode
The deterministic mode is when you use logic to find the specific line of play that guarantees a winner. This is at once the most powerful and the most specialized mode of thought, as it is only usable when the game state can be "solved." Most games end with this mode, as "spotting lethal" is usually a matter of taking a deterministic approach to recognize the cards that must be played to win the game right now. But the deterministic mode can sometimes move beyond this situation. For example, Freeze Mage and Aggro decks can often use a deterministic approach to find multi-turn lethals, and control decks can use a deterministic mode to find the line of play that leads to assured victory in fatigue. If you know the opponent's deck list (or strongly suspect their deck list), you can use a deterministic approach to valuate their remaining threats and line up your available answers to leave the opponent with no way to win. Miracle rogues with only a small number of cards left in their deck can use a deterministic mode to play out the rest of their deck, if they properly track their draws throughout the game.
The deterministic mode can also be used to eliminate plays that would result in an opponent winning.
More than any other mode, failing to enter the deterministic mode at the earliest possible time will result in a loss of winrate. Even if you always "spot lethal" in the moment, you could be missing out on 1, 2, or even 3 turn lethals by failing to jump into the deterministic mode.
Probabilistic Mode
Just below the deterministic mode in power is the probabilistic mode. In this mode of analysis you explicitly recognize all of the possible outcomes of each line of play and select the path that maximizes the chances to win. Again, this mode of thought requires you to have a full understanding of the situation, but the main difference between this mode and deterministic mode is that there is simply no choice that has a 100% chance for victory.
The probabilistic mode is best exemplified by "counting outs." When playing an aggro deck, for example, you might find yourself in a situation where the only way to win is to draw a direct damage card off of the top of the deck. As a control deck, the only way to not immediately lose might be to use random removal like Brawl and hope for the best outcome. The opponent's hand or cards might also figure into the probabilistic mode. For example, the best line of play might depend on whether the opponent draws a taunt minion or a heal, so determining the odds of a lucky top deck may be worthwhile.
There are shortcuts to the probabilistic mode. For example, you might focus only on the random outcomes that end the game immediately by trying to maximize immediate victory and/or minimize immediate loss, without explicitly determining the odds for the remaining cases where the game continues. An example of this would be a late-game state where the player can either go face with a minion or make a trade. Going to face maximizes the odds of immediate victory by top-decking a direct damage spell, while taking the trade minimizes the odds of immediate loss by the opponent having reach. In this case, the remaining game states have a big impact on which choice is the best, and it may be worthwhile to apply a more abstract mode of valuation to pick which line of play is correct.
Statistical Mode
Not to be confused with the probabilistic mode, the statistical mode relies on data gathered over many games to determine the correct play. For example, one may have data that shows that playing an Argent Squire on turn one has a higher percentage chance of victory than playing a Leper Gnome. There is no specific logic behind this move (though perhaps arguments can be made), but repeated gameplay and access to a large pool of data makes these statistics known.
The statistical mode is powerful, but very rare. Gathering a large amount of reliable data is difficult and time consuming, and often not worth the effort considering how fast the meta moves in
and how situational play choices are. I choose to include it only for completeness, and because statistical modes can be good for "out-of-game" decision making like deck, card, and mulligan choices. The statistical mode can also be useful for early game decisions that come up often like "Is it better as a warrior to armor up on turn 2 or develop a Firey War Axe against an empty board?"Abstract Modes
At the end of the day, we are only human and the Deterministic and Probabilistic modes can only be used in relatively simple situations in the end game where victory is within sight. Throughout the early and midgame, though, more abstract methods of play valuation can help a player find the best move to win.
There are dozens of abstract modes a player can use, many of which have excellent articles written about them: tempo, mana efficiency, card advantage, clock and reverse clock, equivalent mana, threats and answers, beatdown, variance minimization/maximization (greed), etc. Each of these paradigms helps decision making by giving a metric on which you can determine the best move. Some paradigms are more applicable in certain matchups than others. For example, aggro decks will more often invoke the clock/reverse clock while control deck mirrors are played around the threat/answer paradigm and midrange decks live and die on tempo. So much can be said about each of the paradigms, and there are plenty more out there, but here's a quick overview of the most important:
Tempo: A good play is one that maximizes the amount of stats you have on board and minimizes the stats the opponent has on board. Building a large and resilient board is the key to victory.
Mana Efficiency: A good play uses more mana and allows for the use of more mana over time. Maximizing mana usage through ramp effects is good, drawing more cards to use more mana is good, and lining up plays to prevent "floating" mana is good.
Card Advantage: The player with more cards in hand and in play is at an advantage. Card draw is good, as is answering multiple of an opponent's cards with one of your own (2-for-1). This is also known as "value."
Clock/Reverse Clock: Doing damage to an opponent and setting up boards that threaten to end the game quickly establishes a "clock" on the game until you win and a "reverse clock" that counts down to when you lose. Moves that shorten the clock and extend the reverse clock are good.
Equivalent Mana: An alternative way to evaluate tempo that values boards based on how much mana the minions would be worth at their current stat values.
Threats and Answers: Games consist of players trading off on placing down threats and providing answers. Victory is attained by forcing the opponent to either run out of threats or run out of answers for your own threats. Long term planning is needed to ensure that you save answers for cards they line up best against.
Beatdown: One player should be aggressively seeking to end the game and the other should be trying to extend the game. Victory is attained by correctly assessing which player you are.
Variance Minimization/Maximization (Greed): At any point in time you are either "ahead" or "behind." A player that is ahead should seek to minimize variance through safe plays, while a player that is behind should seek to maximize variance through greedy plays. This paradigm usually relies on the other paradigms to determine what it means to be "ahead" and "behind." IE, you can have a greedy tempo play or a greedy card advantage play, depending on the situation.
Personally, I'm always on the lookout for new paradigms to explore and master. So, feel free to share your favorites.
Intuitive Mode
The final mode is what I call the "Intuitive Mode," where plays are chosen based on feel. This may seem like the weakest mode, but it can be very powerful in the hands of a good player. In essence, the intuitive mode is fueled by the player's past experience, practice, and the abstract modes that they have internalized. As such, developing a strong intuitive mode requires study, reflection, and deliberate practice and avoiding the pitfalls of results-oriented thinking and other cognitive biases.
Which Mode is "Best?"
While all of the modes are situational, I think there is a hierarchy. It's a good habit to get into to run through each of the methods in order to find the best play. Here's my checklist:
- Are there Deterministic plays that ensure victory? (Stronger version of "Do I have lethal?")
- Are there a small enough number of possibilities that I can calculate exact Probabilities?
- Have I been in this exact situation enough to have reliable Statistics?
- Does any play feel Intuitively best?
- Of the plays that feel similar, can any Abstract Mode help pick the best?
That said, flipping the last two options is good if you are working on developing a specific abstract paradigm, or if you feel you are a weak player with a given deck and lack reliable intuition.
So, what are your opinions? Are there any modes that I've left out? Are there any abstract mode paradigms that you think I should have mentioned? What techniques do you use for developing each of these modes?
