Reading Your Opponent

[Kal]

Introduction​

I find this issue to be something many people have an egregious misunderstanding of. In particular, most players seem to think reading an opponent is equivalent to just guessing (or informed guessing) and committing 100% to that guess. I call this model the "Discrete" model for reacting to your opponent: "I think my opponent will do X, so I will do Y." I will discuss the "Probabilistic" model, which generalizes the Deterministic one. In particular, I will explain why the Probabilistic model is superior to the Deterministic one, provide theoretical examples of how to apply the Probabilistic model, and the provide a methodology for applying it to actual gameplay.

The Probabilistic Model​

The Probabilistic model works as follows: you simply assign a probability of an event occurring, and you assign a value to your possible reactions. It's not as complicated as it sounds. To show this, I will apply it to a simple gambling game.

Let's say I have a fair, two-sided coin. If I flip heads, you have to give me $10. If I flip tails, I have to give you $20. So then your decision making is simply whether you play the game. To calculate whether you should, you simply evaluate your odds multiplied by your expectation, keeping in mind that you assign a negative value to losses:

(.5)($20) + (.5)(-$10)

and the resultant expected winnings is $5. In mathematics, we would call this your Expected Value, and we would be a bit more precise about what all of this means. But, for practicality, it's easy to think of it this way: as you play more and more games, the amount you win will approach an average of $5 per game.

So, in fact, my "Probabilistic model" is just an application of first semester probability. Hopefully I'm not accused of plagiarizing Fermat or Pascal.

The Discrete vs. the Probabilistic Model​

As a general rule, guessing what your opponent will do is probabilistic. Unless your opponent is exceptionally bad, you will never, with absolute certainty, know what he will do. So you will necessarily apply probabilities to it. "Reading your opponent" is not a matter of guessing what action he will take in a particular situation. Instead, it's about recognizing patterns (e.g. that your opponent techs in place frequently, or that he rolls after every third fair). This isn't to suggest that you cannot guess what your opponent can do accurately. Rather, it's to suggest that people are simply not so predictable. In fact, what most people actually do is simply observe what their opponent does most often and assume that this is what they will do. This is necessarily a bad strategy for reading your opponent; even if what you guess they are going to do is their most likely course of action, the payout from your reaction may not outweigh the cost for being incorrect.

In other words, the Discrete model fails to factor in risk of failure, because it implicitly assumes with 100% certainty that your guess is correct. More importantly, any application of the Discrete model exists within the Probabilistic model. "My opponent will do X" is equivalent to "The probability that my opponent will do X is 1, or 100%." In this sense, the Probabilistic model generalizes the Discrete one, and so, unless the Probabilistic model is hopelessly impractical, it is clearly the superior model.

Theoretical Applications​

Luckily, it is not so impractical, and these theoretical applications should make that clear. For simplicity's sake, I will keep the tree of possible outcomes short, but this can be made as complex as necessary to help determine which solutions are optimal. We'll assign kills a value of 1 and deaths a value of -1.

Let's suppose that you are Sheik, and that you dthrow your opponent. Your opponent has a tendency to tech in place. In fact, he techs in place 70% of the time. Conversely, he techs left 15% of the time and he techs right 15% of the time.

Suppose further that you have three options: up smash in place, dash attack left, and dash attack right. Finally suppose that, if any of these attacks hits, you will get a kill, and if any of these attacks whiff, you will die. Then your expected payout for up smashing in place would be:

(.7)(1) + (.15)(-1) + (.15)(-1) = 0.4

Similarly, your expected value for dash attacking left would be:

(.7)(-1) + (.15)(1) + (.15)(-1) = -0.7

And the in the same vein, the expected value for dash attacking right would be -0.7. In other words, your best option (of these three; again, this is a very theoretical example) is to up smash in place, because its payoff is greatest.

However, this is not a particularly realistic example. We can come up with a more realistic, still theoretical example. Suppose you are Falco, and you are standing behind a Fox in his shield. You assess the situation (because you have infinite time in this theory-crafted example), and decide that Fox will bair 75% of the time, usmash 20% of the time, and spot dodge like a noob 5% of the time. You decide that, if your opponent bairs, a roll behind him would successfully gain you a kill, but a grab would get you killed; if your opponent usmashes, a grab would sucessfully get you a kill, but a roll would instead get you killed. Finally, you realize that, if your opponent spot dodges, a grab will get you nothing, but a roll will get you killed.

While this decision tree is noticeably more complicated, the following table might make it clearer:

|bair|usmash|spot dodge
roll|+1|-1|-1
grab|-1|+1|0

And so we simply apply the probabilities, as in the above example. For rolling, your payout is:

(.75)(1) + (.20)(-1) + (.05)(-1) = 0.5.

On the other hand, for grabbing, your payout is

(.75)(-1) + (.20)(1) + (.05)(0) = -0.55.

In other words, in this (again, simplified) example, rolling is clearly your best option.

In-Game Applications​

While it's more or less impossible to really quantify all of this information, this decision-making model is still quite practical. In general, you simply want to maximize your gains and minimize your risks. One example of a clear application of this is whenever you have a guaranteed option instead of one which requires you to make a guess. For example, while Marth does have combos against Fox and Falco which utilize throws other than uthrow, your payout from uthrow is virtually guaranteed (determined more by whether you mess up than what your opponent does). Comparatively, with throws like fthrow and dthrow, you are instead dependent on correctly guessing what your opponent does. Since the payouts would be equal (we're expecting a kill in the end, since Marth's combos on the space animals very often lead to death), it's clear that Marth would prefer to uthrow.

However, many players would find this application too obvious. Of course you would go for a guaranteed thing over something which requires guess work! Let's consider a less obvious application (I will use Marth again because I am not terribly familiar with the rest of the cast): suppose you grab Sheik at 0% damage. The obvious response is to uthrow. From this, you can utilt. If the utilt hits, you are guaranteed a combo of at least 60% damage. However, she can nair out of this and hit you before your utilt comes out, in which case you will surely get grabbed and suffer a similar combo. On the other hand, if you shield after the uthrow and she does not nair, the fight will reset and Sheik will only receive the damage from the uthrow. If she does nair, then you will get a regrab and from here you can uthrow, and the utilt to follow is guaranteed to hit.

So, we could possibly assign estimates of the damage received and given as payouts for this, but that goes against the idea of quickly and practically assessing these sorts of situations. Instead, simply consider that, should you go for the utilt, you will suffer a combo every time your opponent decides to nair out of shield. Instead, if you simply shield, and your opponent does nair, you will successfully combo them by regrabbing. But, if your opponent does not nair, the gameplay simply resets, and you lose nothing. Thus, the risk is clearly minimized by the latter option, with the reward being roughly equal.

Now, should you notice a pattern in your opponent's gameplay then you can adjust your strategy. If, for example, your opponent does not seem to ever nair out of the uthrow, then you can simply always go for the utilt. Conversely, if your opponent seems to always nair out of the uthrow, then you simply always shield.

Conclusion​

When applying the probabilistic model, a player needs to avoid being what is called "results oriented." It's pretty much exactly what it sounds like. If the option you are choosing to take pays off in the long run, then you should not become upset with yourself if it does not pay off a particular time. That's not how probability, and particularly reading players, works. And, in the same vein, you can't assume that just because something worked once that it was the right thing to do. In other words, the logic "it worked didn't it" and "that didn't work" should not influence decision making within this model.

I hope people find this guide helpful. It should hopefully shed some light on what is the best way to make use of your ability to read your opponent and recognize patterns. Rather than simply taking the course of action that will solve what your opponent will most likely do (which, as mentioned before, is a hopelessly terrible methodology for reacting to your opponent), it should allow for players to maximize their rate of success.

 

[nateychan]

Good read, I learned a bit from this. I'm into psychology so getting inside people's heads is always nice :D

 

[SamusPoop]

Really it's coming down to knowing your options, their options, and the percent of the time they go for what as you adjust to their adjustments faster if at all possible, however I would think you could CC sheik's nair to follow up(percent based of course). I would rather break down all 16 dis and options like jumping, counters, shines, and nairs first and have a default of which ever is most common for most players mixed in with which gives the highest reward for the first try against them.

Also noting how they di/react to other cases can give clues to how they may react for a different throw.

Really just get ahead of the metagame before the match.

 

[the_CAM_factor]

woah, i approve of this post. thanks for putting the time into writing something like this up

 

[reqy]

i never nair out of upthrow lol

 

[KirbyKaze]

Most important thing about reading your opponent is to not isolate their gameplay to single moves but rather look for behavioural patterns.

If you can understand when they're trying to trick you and how they're trying to do it, you're way more equipped to process and figure out what their plan is than if you think, "Oh, he's gonna bair here."

Or at least that's how I find it.

 

[Kal]

Most important thing about reading your opponent is to not isolate their gameplay to single moves but rather look for behavioural patterns.

If you can understand when they're trying to trick you and how they're trying to do it, you're way more equipped to process and figure out what their plan is than if you think, "Oh, he's gonna bair here."

Or at least that's how I find it.

Yeah, this is what I'm trying to emphasize. In real life, even if you're trying to assert that there is something they are very likely to do, that is still attaching a probability, which implies some sort of pattern. And, as a general rule, subtle patterns, such as "my opponent tends to tech in place" are much more likely to exist than some sort of obvious one, like "my opponent is likely to bair here."

 

[KirbyKaze]

I skimmed your post but it looked more like you were just playing the numbers game.

I'll read it more carefully later I guess.

 

[tarheeljks]

I skimmed your post but it looked more like you were just playing the numbers game.

I'll read it more carefully later I guess.

i think it's fair to say it focuses less on reading opponents and more on juggling the relative risks and rewards of available options in order to make optimal decsions. so a title change might be appropriate, but valid/good points nonetheless

 

[Massive]

Why do you have to post in red? It's like when a girl gives you a note written in highlighter. Painful to the eyes.

The info itself is reasonably sound, although I'd wager taking the safer option is not always best.
Smash as a game is an NP-Complete problem set, we can figure out the best thing to do in a situation, but we cannot plot the path to that situation reliably or quickly.

The "numbers game" style play is very close to optimal, but sometimes you have to gamble in order to win (especially when you're evenly matched or don't know what to do). This is a pretty good introduction to predictive logic though.

 

[Kal]

i think it's fair to say it focuses less on reading opponents and more on juggling the relative risks and rewards of available options in order to make optimal decsions. so a title change might be appropriate, but valid/good points nonetheless

Yeah, I couldn't think of a good name for the guide. It's about how to adequately make use of your reads, and not how to actually read your opponent.

Why do you have to post in red? It's like when a girl gives you a note written in highlighter. Painful to the eyes.

Sorry about the red text. Going for the red Marth main theme. Regardless, you can disable reading colored text in your options. I'll change the text color soon, though. I would like to point out that it's dark-red.

The info itself is reasonably sound, although I'd wager taking the safer option is not always best.
Smash as a game is an NP-Complete problem set, we can figure out the best thing to do in a situation, but we cannot plot the path to that situation reliably or quickly.

I did not suggest that the safer option is always best. My only example was that you have two options which pay equally well, but one of those two options is clearly safer.

Just because the game is NP-Complete does not mean we cannot apply probability theory. In fact, I would say quite the opposite; probability theory is not necessary when there exists an algorithm which tells you the optimal solution.

The "numbers game" style play is very close to optimal, but sometimes you have to gamble in order to win (especially when you're evenly matched or don't know what to do). This is a pretty good introduction to predictive logic though.

You always gamble. Every choice you make is a gamble in some way, and that was the point I was making: that you should be making good long-term choices. You need to maximize your gain in the long run. Of course, this assumes you can actually attach probabilities and numerical rewards to everything, and you can't. So you take a sort of risk-reward style of measuring things to compensate. In general, if something is incredibly risky, with minimal reward, you would avoid doing it. Conversely, if something has virtually no risk, with very good reward, you would do it.

I will edit the first post with something on being results-oriented so that people better understand what the long-term means and what it means to be "successful" when applying this theory. To make it clear, in the first example I gave (with the coin flip), you would not have made the wrong choice by playing the game simply because you had lost $10. Because, in the long run, you are making the correct decision.

 

[Signia]

Excellent read for those who do not yet understand the concept of risk/reward and how it's optimized in theory. In all practices, one should learn the rigid and basic theories that govern the practice, and then slowly branch into exceptions until the theory appears to break down. Develop the proper form, then become formless once you understand everything.

This method of developing a strategy with all other things equal is the best, no doubt. But unfortunately, in Smash this is impossible. In order for game theory tables to be useful beyond the qualitative knowledge you're trying to model in the first place, you need a few things that can't be obtained in this game.

One, you need a collection of hard counters. The set of options must be discrete and each ordered pair representing both player's options must have predictable results. It's hard to even talk about the game in terms of specific options because there are tiny variations to them that can change the way a situation plays out. There are too many possibilities to map out in most situations. The amount of common situations, let alone simple enough ones, that can be cited is very small and preparing in any way for them, let alone this method, is an exercise in futility (or obsession).

Two, you need a value system. We have percentage, but it doesn't tell the whole story. In fact, it tells very little. In this game, you win by sending players off the stage. You literally have nothing to work with unless you assume players are super consistent (nobody is except MAYBE the best of the best of the best) and get kills when a guaranteed opportunity is presented. Without semblance of quantifiable payoffs, you're left with the same qualitative intuition you started with.

Three, you need to know the frequencies of your opponent's options. Approximations would work just fine and if you have never played your opponent you may assume each viable option will come at close to equal frequencies and you'll be pretty close to optimal... but in the case of Smash players, THIS IS NOT THE CASE lol. When I ask people how they play and what they think about, it's often shocking. Many claim they do not make predictions and simply react accordingly to each situation. Players don't really mix it up or change what they did last time if it worked since the last situation won't come again and what they did will probably work again since player ignorance to the best counter is expected in a such a complex game. I'm no high level player, but it seems this game is not about reading your opponent, but rather much MORE about playing the matchup and your character optimally and baiting committal actions from your opponent (i.e. waiting for your opponent to do something suboptimal). Basically, it's more about your own execution and evaluation of situations than it is about the interaction (picking apart your opponent, discerning their strategy and abilities, you know, the multiplayer part of the game).

Of course, none of those three things are not nearly as much of a problem in every other fighting game. In Smash, it's impossible to reach a controlled, rigid, and refined form. Never have I played anyone with such deliberation in their choices. The perfect formlessness I described earlier is out of reach too. There are no rules to break, no real metagame to crack. You can only play "gayer" (read: play the matchup better) or improve your execution. But none of this applies if you are GODLIKE (and I mean world-class level).

 

[Kal]

Excellent read for those who do not yet understand the concept of risk/reward and how it's optimized in theory. In all practices, one should learn the rigid and basic theories that govern the practice, and then slowly branch into exceptions until the theory appears to break down. Develop the proper form, then become formless once you understand everything.

This method of developing a strategy with all other things equal is the best, no doubt. But unfortunately, in Smash this is impossible. In order for game theory tables to be useful beyond the qualitative knowledge you're trying to model in the first place, you need a few things that can't be obtained in this game.

One, you need a collection of hard counters. The set of options must be discrete and each ordered pair representing both player's options must have predictable results. It's hard to even talk about the game in terms of specific options because there are tiny variations to them that can change the way a situation plays out. There are too many possibilities to map out in most situations. The amount of common situations, let alone simple enough ones, that can be cited is very small and preparing in any way for them, let alone this method, is an exercise in futility (or obsession).

A collection of hard counters is certainly ascertainable. Sure, it may not be complete in any sense, and the options may be vague, but there are plenty of useful scenarios to apply this theory. For example, suppose, as Fox, you notice your opponent smash DIs your uthrow uair about half the time. When you successfully hit with the uair, you see very positive results (again, while we would like hard numbers, they simply don't exist here). When you don't, you typically only get hit once. You know that, should you uthrow bair, you have no risk of being attacked, but also that the payoff noticeably less. Then, it would be logical to conclude that you should continue to uthrow uair rather than uthrow bair, despite the latter option being safer. But, this is contingent upon how often your opponent DIs the uair; if he DIs most of them (say 75%) then you might (and here's the subjective part) conclude that uthrow bair is better.

Two, you need a value system. We have percentage, but it doesn't tell the whole story. In fact, it tells very little. In this game, you win by sending players off the stage. You literally have nothing to work with unless you assume players are super consistent (nobody is except MAYBE the best of the best of the best) and get kills when a guaranteed opportunity is presented. Without semblance of quantifiable payoffs, you're left with the same qualitative intuition you started with.

You're not left with the same qualitative intuition you started with. No, you can't objectively prove that any option is better than any other. When you apply to theory to something as complex as Smash, you're necessarily going to have some subjectivity. A theory to encompass all of Smash would being insanely complex. But the existence of subjectivity in this model does not mean that the intuition used is as bad as the intuition used without the model. In other words, even if you can make a strong argument for this model being impractical to use, it can still be better than having no model at all.

Three, you need to know the frequencies of your opponent's options. Approximations would work just fine and if you have never played your opponent you may assume each viable option will come at close to equal frequencies and you'll be pretty close to optimal... but in the case of Smash players, THIS IS NOT THE CASE lol. When I ask people how they play and what they think about, it's often shocking. Many claim they do not make predictions and simply react accordingly to each situation. Players don't really mix it up or change what they did last time if it worked since the last situation won't come again and what they did will probably work again since player ignorance to the best counter is expected in a such a complex game. I'm no high level player, but it seems this game is not about reading your opponent, but rather much MORE about playing the matchup and your character optimally and baiting committal actions from your opponent (i.e. waiting for your opponent to do something suboptimal). Basically, it's more about your own execution and evaluation of situations than it is about the interaction (picking apart your opponent, discerning their strategy and abilities, you know, the multiplayer part of the game).

This ties in with the first part; you don't need to have any exact numbers to apply the theory. And I feel you're simply taking this out of context as though I've implied this theory summarizes all of Smash. I don't think this at all. It's a simplified method which can be applied to some situations, particularly situations where you have some sort of guess as to the frequency your opponent tends to do something. This could be as simple as "most often, my opponent techs in place" or as complex as "my opponent screws up 1/3 of his l-cancels, I counted."

Of course, none of those three things are not nearly as much of a problem in every other fighting game. In Smash, it's impossible to reach a controlled, rigid, and refined form. Never have I played anyone with such deliberation in their choices. The perfect formlessness I described earlier is out of reach too. There are no rules to break, no real metagame to crack. You can only play "gayer" (read: play the matchup better) or improve your execution. But none of this applies if you are GODLIKE (and I mean world-class level).

I feel you may have missed the point of my guide. It's not to suggest that this guide will turn anyone into a great player; it's simply a practical method for evaluating some situations.

 

[EWC]

So uhh you aren't actually saying anything useful at all????

I mean first off it's kinda silly to talk about maximizing expected value of exchanges in melee, because a match usually doesn't last long enough for the average case to overcome noise.

But even ignoring that subtlety, your entire premise doesn't really make any sense. You go in with the assumption that you have an accurate probabilistic model of your opponents decisions. Which is silly. If you really want to apply probability theory to this kind of thing, the place to focus is: How do I construct an accurate model of the probability distribution underlying my opponents to decisions? And the answer to that question is called Bayes Theorem.

 

[Kal]

Did you ignore all of the examples in my first post? And is it necessary to act like such a ****ing ***? I didn't mention any sort of assumption that you have an accurate probabilistic model for your opponent's decisions. You need a probability distribution in order to make this theory rigorous, but I clearly gave examples of how it can be used without needing an actual probability distribution of your opponent's decisions. The theory itself applies even given modest estimates of what your opponent will do; you can apply this to observations of tech frequency as vague as "my opponent techs in place more than he techs to the left or to right."

And I really don't see how Baye's Theorem answers the question provided.

 

[KirbyKaze]

I used to feel that you could just play the numbers game and work the odds and play with good probabilities.

Then I played M2K and I realized that while such an approach can work, there are people in existence with enough depth to their gameplay to do things you can't anticipate and who are much better than you at the "numbers game". Consequently, I gave up on the approach entirely and began to shift towards a more "feeling" based smash game based on what I think they're trying to do because of their behavior and what their actions tell me about how they're feeling.

I wish I could say it's permanently changed me for the better, but not really. It's provided mixed results. Some people, I'm worse against. Some people, I'm better against. Time will tell if trying to do it this way is the correct idea.

 

[Kal]

If someone beats you because of a superior numbers game, wouldn't that simply validate that the method works? And there being methods outside of your knowledge doesn't really invalidate any of this. It just means you haven't taken enough into account.

Regardless, I don't like the way people are using this "numbers game" term to suggest some trivialized methodology of how to play. Some situations are simple enough to apply this directly (I could probably come up with situations by the edge where this model applies very well), whereas others would require a much broader, subjective application.

 

[Signia]

Regardless, I don't like the way people are using this "numbers game" term to suggest some trivialized methodology of how to play. Some situations are simple enough to apply this directly (I could probably come up with situations by the edge where this model applies very well), whereas others would require a much broader, subjective application.

I can agree with this. It's just that usage of game theory seems to work in such a limited number of situations in Melee as opposed to other fighting games. This method is used to make your mixups optimal, and Melee is far less mixup-centric than any other FG I've played. Maybe 3D fighting games are more up your alley, those are all about mixups.

 

[Kal]

Sure, its application to Melee might be less practical than in some other game. This doesn't mean we shouldn't use the theory when we can. And, more importantly, the theory gives you a methodology for decision making, even if that decision making is subjective. It allows you to at least look at two decisions and ask "which decision is better?" Without any theory at all, this is impossible.

 

[EWC]

I didn't ignore your examples at all though; If anything they highlight most clearly where you are in error. They just consist of you assigning probabilities to various decisions that an opponent might make in various situations, and then calculating expected utility of different responses. All of this is completely useless without some reasonable method of getting those numbers in the first place.

Bayes Theorem tells you how to update your model in response to new information. For example, if you have assigned a .7 probability that your opponent will tech in place, and they keep not teching place, the your assigned distribution should clearly be updated. Bayes Theorem says exactly how you should do this.

 

[Kal]

I didn't ignore your examples at all though; If anything they highlight most clearly where you are in error. They just consist of you assigning probabilities to various decisions that an opponent might make in various situations, and then calculating expected utility of different responses. All of this is completely useless without some reasonable method of getting those numbers in the first place.

You're citing my examples which explain the theory rigorously. You're ignoring the entire part labeled "In-Game Applications." Moreover, you're assuming that the theory is necessarily useless without hard numbers, when at the very least it's simply not completely accurate. Again, my "In-Game Applications" section suggests that there are definite uses to this model without having hard numbers.

Bayes Theorem tells you how to update your model in response to new information. For example, if you have assigned a .7 probability that your opponent will tech in place, and they keep not teching place, the your assigned distribution should clearly be updated. Bayes Theorem says exactly how you should do this.

Baye's Theorem established a relationship between conditional probabilities. Specifically, it gives:

P(B|A) = P(A|B)P(A)/P(B)

provided P(B) is non-zero. Now, probability has never been my strong suit, but I don't see how this theorem can be applied in the way you're mentioning. What is the conditional probability? How the opponent techs a second time would be (presumably, though not necessarily) independent of how he teched the first time. But, more than this, how do you "update" your distribution by using this theorem?

However, as I said, probability is not my strong suit (in fact it's probably my weakest), so it may simply be my lack of understanding that's causing me to not see how Baye's Theorem applies here.

 

[EWC]

I'm not sure I understand what it is that you are calling "the theory" if it is anything other than the explicit use of numerical utility estimates. What you describe in the "In Game Applications" is exactly how people tend to think about mixups already (ie in vague intuitive terms).

Uhh I don't really want to type up a whole explanation of Bayesian decision theory but you can start by reading something like this, which does a pretty good job I think. If you still have questions after I would gladly answer them.

I'm sorry if I came off as being overly abrasive; That was not my intent. I really like what you're trying to do in principle, but I think your approach is a little too unrefined at this point.

 

[Myztek]

This topic can be summed up as:

Notice your opponent's habits so that you can narrow down the options you have to watch for. The less options you have to consider, the more likely you are to be successful in picking the correct one.

 

[Lovage]

most good reads come from experience

when you've been in the same situation 500 times, it becomes a lot easier to recognize all of your opponent's options. once you can visualize all of their options in your head and prepare your fingers to react quick enough, you can then easily remember the patterns of what they've done before, as well as what they're likely to do based on the situation (why people will roll into the stage from the edge on their last stock more than their first stock)

the more i play this game the more i realize "reading your opponent" isn't as much about the miniscule details (omg is he gonna dash dance at me or SH nair at me,) but more about getting a solid feel on the playstyle of your opponent and countering it.

this is why people feel swells of improvement after national tournaments, you get exposed to so many different playstyles that you're forced to adapt to them and exploit them to win.

 

[Deleted member]

EDIT: NEVer MIND

 

[Kal]

I'm not sure I understand what it is that you are calling "the theory" if it is anything other than the explicit use of numerical utility estimates. What you describe in the "In Game Applications" is exactly how people tend to think about mixups already (ie in vague intuitive terms).

Uhh I don't really want to type up a whole explanation of Bayesian decision theory but you can start by reading something like this, which does a pretty good job I think. If you still have questions after I would gladly answer them.

I'm sorry if I came off as being overly abrasive; That was not my intent. I really like what you're trying to do in principle, but I think your approach is a little too unrefined at this point.

Sorry, I'm still not seeing how you would apply Baye's Theorem in the example you mentioned. I'm familiar with applications of Baye's Theorem to things like the following:

1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

But I do not see how it applies to what you mentioned. As for "the theory" I am simply being careless with my words. I mean "The Probabilistic Model" I have outlined in the first post.

This topic can be summed up as:

Notice your opponent's habits so that you can narrow down the options you have to watch for. The less options you have to consider, the more likely you are to be successful in picking the correct one.

This is a gross misunderstanding of what I've said. I didn't mention anything about narrowing options so that your guesses are more likely to be correct. In fact, this model (in theory) applies regardless of the likelihood of being correct (if, for example, your opponent did 1000 different things .1% of the time, this model would still apply).

 

[Acryte]

TLDR: When reading your opponent and choosing a response in a given situation, make sure you are factoring in the risk/reward of your options.

hmmm I have some issues with this, mainly as I feel smash cannot be reduced to or by mathematical equations persay (as fun as it might be to try and do so, and if you can certainly not in this manner).

When reading an opponent, the idea would be that you generally choose the option that maximizes the probability of success... however by doing such, unless the situation is 100% successful then you allow the opposing player to know what you will choose to do. Armed with such information they are able to counter your tactic. This is because if there was no counter strategy then there is no reading necessary other than reading the situation. You aren't reading the other player because his response doesn't matter. If you know that they HAVE to throw rock then throw paper. BUT if they can throw whatever they want, and you have decided that paper is least risky and has the most reward (obviously through some sort of weighted rules, maybe a betting system idk) and you use it most often then he will throw scissors.

You must be stating then that you should either, at a higher percentage of the time choose the highest reward option or the least riskiest option that promises substantial reward and the choice should be at random (Now you're just doing standard reads without factoring in behavior blindly). Or remove the random choice and read his behavior to determine your choice of which 70% of the time you will be upsmashing (now you are just doing standard reads)

Or maybe you are just saying that when faced with an option where you have multiple choices, you should decide whether the risk is worth the reward when it comes to guaranteed damage, KOs, risk (combo/single hit/grab/KO), and stage position... arent the smart choices what they will be using already? It seems that the EXTREMELY situationally effective responses will only be used extremely situationally and therefore less often. Don't risky players already know the risks of being risky?

I mean, that whole concept is competetive smash in a nutshell. I don't see how the outlined formulas have really done anything or shed light on any internally active concepts in the metagame. The only thing it really accomplishes is providing visual information on how risky and rewarding something is before the match even starts, as just general information. That might be useful maybe if they didn't realize how risky "option A" was and how little it actually worked vs "option B" that covered multiple responses even including the "option A" as well. Then they could say "WOW. I should probably start using Option B instead".

It could help you have the right knowledge of a scenario in your head before the match, but without reading what the opponent's habits are you are wasting your time. And since his habits will change based off of your habits, you can't pin it down with a formula like that. The only constant in your formula is the risk value but not the input percentages or the output.

Let me put it into perspective by rewording and adding to your example:

Let's suppose that you are shiek, and that you dthrow your opponent. Your opponent has a tendency to tech in place (which you have observed as habitual data through playing him and/or watching him play). In fact, he techs in place 70% of the time, apparently regardless of his and your stage position, your previous responses, how often he gets away with it, and/or his damage percentages. He doesn't adjust because he is a poor player. He chooses to tech in place regardless of the fact that if you were to upsmash him 100% of the time, he will still allow himself to die to the upsmash 70% of the time instead of rolling or adapting instantly to the change in your responses. He can't adapt because if he did then the formula's input percentages and therefore the outputs will change with every iteration of this situation. If the output changes with every iteration then nothing holds constant and the formula provides no useful output to the player applying it.

If he is a poor player then just capitalize on his weakness. The player who is making reads will just notice and predict what he thinks the opponent will do based off of the opponent's actions so far. The numbers and calculations aspect that has been applied to things is pointless.

If you start to upsmash in place that 70% will fall to 50%, or 30% or maybe 15%. What will you do? You will start to use one of the other options. This changes with every repetition. You cannot pin any useful percentages to it unless the risk is so low and the reward so great that it will be expected a large majority of the time regardless. It is then that the move will be used except the few instances that the person believes the other player will respond with the one counter option to it. If that counter option exists, he may simply have a middle road option where he can just hold onto the stage control that most likely exists and force them into a separate and equally poor situation.

Also, if a player is extra risky, he knows it... but that usually is based off of an increased chance of KO opportunity and not simply because it can KO. Dr peepee is a perfect example of someone who could take a combo further and possibly overextend in situations but chooses to refrain at times and would rather establish stage control and continue to press his advantages; that isn't to say that he lets any opportunities to end someone's stock slip past either.

Besides, even in the shiek example there are too many options to weight. They could tech left, right, or on the spot; wait and then get up attack with invincibility, or wait and then roll left, right, or get up on the spot. Basically, the formulas are superfluous and the whole thing is just explaining the process that should be going through someone's head provided they are reading their opponent and playing melee on any competetive level.

 

[Kal]

hmmm I have some issues with this, mainly as I feel smash cannot be reduced to or by mathematical equations persay (as fun as it might be to try and do so, and if you can certainly not in this manner).

Over and over people keep mentioning this, as though reading comprehension goes out the window. Like the guide I've written up top is actually titled "A Comprehensive Guide on How to Play Smash: a Mathematical Theory." Sorry, but I don't have the energy to read the rest of your post, because frankly I'm expecting similar gross misunderstandings of what my guide says, and moreover ignorance about how mathematics works in general.

 

[DelxDoom]

the only problem I have is that at some point, looking at the math of it won't always work in a real time game as opposed to turn based stuff like poker [i can say poker has turns, right? lol. poker can seem more fast paced than ... e.g. chess but eh. poker is one of the games where reading is forefront]

alright so yeah. when it comes to real time, reading your opponent has to also happen in a fast amount of time. you say "given infinite time etc" which is all good in theory, but in fighting game cases, there are just some times where making a possibly bad decision fast has a better chance of working than making a "good" decision slowly. I guess this is just what we might call implementation lag.

tl;dr must assimilate the rules of reading the opponent into wherever you have the least implementation lag in order to get maximized results

do i sound extremely condescending yet kal

 

[gm jack]

Why are people finding this hard? It's just a nice way of summing up risk:reward ratios combines with the probability of success.

Simplistic, and of course there are more options, but it makes people stop thinking about reading or predicting in black and white, and lets you think about what combines safety with the greatest reward.

 

[KirbyKaze]

If someone beats you because of a superior numbers game, wouldn't that simply validate that the method works? And there being methods outside of your knowledge doesn't really invalidate any of this. It just means you haven't taken enough into account.

Of course it works. I was just talking about my own personal frustrations with it, and why I don't do it as much as I used to.

I certainly think it's a good way to start playing. Working of educated guesses is much better than just randomly throwing things out.

 

[Kal]

Why are people finding this hard? It's just a nice way of summing up risk:reward ratios combines with the probability of success.

Simplistic, and of course there are more options, but it makes people stop thinking about reading or predicting in black and white, and lets you think about what combines safety with the greatest reward.

This is basically what I'm trying to say. It's not any sort of comprehensive guide to playing smash.