The Payoff Matrix: Useless Theorymon, or a Valid Approach to Prediction?

[mtr]

Lol, first time I've posted in Stark Mountain in a while.

Anyways, I've been thinking about prediction, and I was wondering what you guys thought of taking a "payoff matrix"-oriented approach to prediction, rather than predicting aggressively or conservatively. In this path, you would assign certain outcomes high or low payoffs, and use them to make your move, or decide if you wanted to predict to begin with.

Here's an example: The enemy team, an offensive Ubers team, has a Scizor and a Kyogre (who is Scarfed, btw). You, the stall player, have a Blissey and a Forretress. Stealth Rock is up on both sides. Right now, it's Kyogre v. Blissey on the field. The Kyogre poses no substantive threat to Blissey, since it is Scarfed.

You have two choices: switch to Forretress or use Wish. The opponent also has two choices: switch to Scizor or use Surf.

So let's make a payoff matrix for this situation.

You switch, Opponent switches: Very High payoff for you. 1 layer of Toxic Spikes can mean gg against a stall team in Ubers.
You switch, Opponent attacks: Very Low payoff for you. After all, you just got Forry butchered.
You use Wish, opponent attacks: Medium Payoff. The opponent might try to get in Scizor on your Protect, you can switch next turn to heal Forry, blah blah blah. Basically, nothing happened this turn, what matters happens next turn.
You use Wish, Opponent switches: Low payoff. I mean, the opponent can use U-turn on your switch to scout out your team and do residual damage, or get a sweeper in for free.

So what should you do? Well, if you switch, you can get a good or a bad payoff. If you don't, the net result is a poor payoff. So the matrix would advise switching.

But how about this: let's make it Scizor+Kyogre vs. Groudon+Blissey. Remember, Stealth Rock is already up. Therefore, the payoff of getting Groudon onto the field is lessened by far, since he can't do anything besides a weak attack.

So the revised payoff matrix dictates that you should stay in with Blissey, since switching doesn't give you any good payoff, and a potential for a very bad one (Kyogre using Surf on Groudon).

Criticisms of this model:
-Your opponent might also run this matrix, and thus predict your outcome, thus leading to a prediction game anyways and defeating the purpose.
-This payoff matrix approach only works in relatively simple situations, or in endgames.
-There are many external considerations, such as stall-based teams deriving generally lower payoffs than offensive teams for good plays.

So what do you think? Is it useless, or somewhat helpful to approach games from this perspective?

 

[YJiang]

You also have to take into account the probabilities that the other player will do each associated outcome, and weight your matrix with the expectations. This is much more difficult that you might think, since it also depends on his assigned probabilities to your actions (and so on) until you reach an equilibrium state based on your mutual minimax strategies.

 

[BuddyBlueBomber]

I think that this model is hurt by the fact that individual players make different choices depending on what plan, or backup plan, they chose to execute. Now, in this situation, you can almost bet that Kyogre would switch because it holds no threat to Blissey. However, the player may chose to attack instead, if they feel like testing the waters and see what the opponent will do in the situation. If they stay, then it's a good indication that they probably will try and stall out, if not, then you just grabbed a free kill.

You should view cues on how reckless or conservative the opponent is, as well as their play style and temperament are before making any paramount decisions.

 

[FlareBlitz]

The primary problem I see with this approach is that your opponent will be able to examine the same situation from your side, see what the "ideal" option is, and then play such that your ideal option leads you to a disadvantage. In the above situation, for instance, any competent battler will switch to Kyogre out to Scizor to avoid Toxic/Thunderwave. However, knowing this, a good player can merely keep Kyogre in to scout a switch and do massive damage to Forretress. This is especially the case if both sides know the other side's team; if I'm using a team with quickstall mewtwo and giratina and stuff I know you have a toxic spiker, I will do everything in my power to make sure it doesn't get a free turn, including those sorts of "stupid" or suboptimal moves. This in turn forces YOU to make suboptimal moves in prediction of my suboptimal moves, thus rendering the entire matrix pointless. The only way it would work is if we could assign discrete probabilities to all outcomes in the matrix which, given the nature of Pokemon, is impossible.

 

[DevilinDenial]

In my opinion this seems like overthinking a situation. In the ST9, the finalists both overpredicted and ended up losing a Pokemon. In cases like this I find it useful to make the most logical choice.

This only applies to a match of equals: if you realized earlier in the match that the opposing player is "better at prediction", you may want to do the exact opposite of the predictable, in order to catch your opponent off guard. If you've been on your game, though, it's a good idea to predict on them. This all changes if your opponent is doing the same.

Prediction is key to Pokemon, Jumpman once said the best move in the game is probably Switch. Being as trigger-happy with that move as the villian in a western will only get yourself shot.

All this thinking got me confused as to whether or not I'm making sense lol.

 

[JeffreyLebowski]

Well, as a wifi player, i can say that this is a somewhat accurate model of prediction. This is how prediction works. All the "problems" i see are just oveprediction, which is part of prediction. Whenever you predict, you risk overpredicting. This doesn't mean the model doesn't work.

 

[ARandomDude]

The problem with applying game theory and payoff matrices to prediction is that many things can't be quantified into terms like $$profit or jail time. For example, scarftar vs latias, what's the payoff if you switch out of crunch to lucario, but they have gyarados and scarftom waiting in the wings? The most quantitative way to measure things (IMO) is by %HP of your total team, but many things can't accurately be converted that way.

If using a non-quantitative method (e.g. play to minimize losses), that's just conservative play.

 

[TheValkyries]

I don't really see this as working the way you want it. Quite frankly Pokemon and prediction is like playing poker. You're opponent could be bluffing or they could have an excellent hand. They also have the choice of when to play aggressively or conservatively. The matrix will fall for the bluff every single time. And with the amount of bluffing that goes on just makes it useless.

 

[capefeather]

I think that good players consider the risk-reward factors anyway. What you do about it entails prediction. Pokémon is like an iterated, weighted version of Rock, Paper, Scissors, i.e. you play RPS with the opponent several times and winning with each move results in different payoffs.

Say Rock is the "best" move. You want to win with Rock. But your opponent knows that you want to win with Rock and considers using Paper. But you know that your opponent knows that you want to win with Rock, and so you consider using Scissors. But then your opponent knows that you know that your opponent knows that you want to win with Rock, and so he considers using the original "best" move Rock. That's where prediction comes in, really. So risk-reward factors do matter, but that doesn't mean that you or your opponent has to follow the prisoner's-dilemma solution, because it's iterated.

This is a good read.

 

[Ice-eyes]

The problem with converting via HP % in pokemon is that a lot of games aren't won by that kind of attrition. It doesn't matter how many pokemon with whatever health you have if I've taken out your Gyarados and your Jirachi and I have a Lucario waiting in the wings.

Long-term thinking can't be factored into simple mathematical calculations like this. In terms of the matrix you would have to take into account the relative importance of each of your and your opponents pokemon. That's one of the main differences between pokemon and Sirlin's game, Kongai - in Kongai it's almost impossible to sweep as we know it in pokemon. One character will almost never beat two to three characters in a game situation.

 

[Destiny Warrior]

The problem is, this assumes that the opponent does not predict your prediction.

Besides, however hard you try, it is pretty much impossible to put a real-life event(the battle in this instance) in terms of mathematical equations, unless it is also heavily based on mathematics. You can only do it upto a certain point, after which it relies on factors beyond your control, which you cannot manipulate(like the RNG, or your opponent's calibre).

 

[ginganinja]

I had a similar situation posted in the OP (I should have warstoryied the battle) where I had a mix Dialga and a CM Lugia vs a Wish Bliss and a Choiced Garchomp. My opponient had SR up and it was currently Lugia vs Blissey. It went on for a cycle as we switched and double switched and Lugia and Blissey both kept healing. When it was finally Dialga vs Blissey I had to choose either Draco Meteor or Brick Break. Brick Break would have KO'd Bliss but Draco Meteor would not have. I ran a little matrix and had to use Draco Meteor even though if Garchomp came in on Brick Break it was GG for me. It was a 50/50 shot as if I used Draco Meteor and he brought Garchomp in I win, however if he brings Garchomp in on brick break I lose as Blissey just stalls out Lugia. No doubt my oppoinient was also predicting and saced Blisey to the Brick Break, revenged Dialga and Lugia survived the Outrage by about 2% and KO'ed with Ice Beam.

In this senario the matrix helped me weigh up the possiabilities and formuylate my attack. Therefore I believe that the payof matrix can wiork but I would only ever use it in the endgae of a battle in which both opponients had been predicting throughout the battle (in other words very rarely do I use the Matrix)

 

[mtr]

Dialga's Outrage does more than Brick Break. Did you mean Draco Meteor?

Yeah, I realize that there are a number of problems with this model, the most important being that it only works in simple 2-choice situations, or in endgames.

However, it can be a useful teaching tool for beginners and experienced players to learn the basics of when to predict.

 

[ginganinja]

Yep sorry, meant Draco Meteor i'll edit it
And yes the curcumstances are slightly different to your matrix, however it still applies as the matrix implied that attacking was best.

Also this model is rather hard to teach. For example using my senario it was a 50/50 choice as to whoever won out. You just cannot teach that since it is a human (not a computer) making a decision at the other end.

I think that my chess background helped me predict better and the matrix does have some inmpact on my when I play chess (though it obviously requires reworking and the is not the place to discusss chess anyway)

 

[capefeather]

Honestly I preferred my answer over the "you can't calculate love" approach you guys are using. I even intentionally avoided using the convoluted term "payoff matrix" because it just tries to make you sound smarter than you are in "casual" conversations like this one. I've also never played Kongai so I wouldn't know about that. Maybe I read an older version of the article I linked, but the way I remember it it talked about Virtua Fighter and the applications of the "Yomi layer" concept, which I summarized in my previous post.

It's very simple. Pokémon, like most other competitive games, boils down to knowledge and prediction. Being able to gauge risk-reward situations is an example of knowledge. Using that for mindgames is what leads to prediction. Read the archived warstories. On one hand they don't blindly pick the move that they think will beat the opponent without thinking about it. On the other hand they do try to outwit each other, based on what each believes the other is thinking.

 

[Mosh]

Yes, this approach is valid and yes u can calculate what`s the best action to take (it`ll probably be different probabilities of doing different things) assuming that your opponent is complete rational and maximizes the chances of winning the battle which is pretty fair and likely. Problem is: there is no time for u to calculate such thing in the middle of a battle and most important: it is impossible to precisely construct a pay off matrix `cause the pay offs are just too subjective and a hell lot of varieties have to be accounted. And, tbh, good players already think liek this even if they don`t know what a pay-off matrix is. U don`t need to know physics to play pool...

 

[Wikey]

Prediction in Pokémon is basically like poker. You have to balance risk vs. reward with your ability to read your opponent. If you know he's conservative and you're in a match-up that has occurred before in the match that results in him switching to a check. Go for the double-switch or use a move that hurts the switch-in. If you know he's aggressive, keep making the safe move and wait for him to over-predict. That said, even if you feel like you can read your opponent, you have to wait for situations where the reward is worth the risk. Don't go making unsafe moves just because you feel like you know what the opponent is going to do.

My current OU team revolves around this somewhat. My goal is to weaken their team and scout by predicting and bringing in Breloom. I just keep note of who they switch in to take the attack and then start to change it up trying to hit the switch-in or going for a double-switch.

 

[Acritter]

This assumes the probability of each outcome being equal. That is rarely the case. A certain player will be more predisposed to one action than another. However, this is excellent for doing basic checks on actions: the risk/reward scenario. For example, when I've successfully switched in Scizor to Gengar, I almost always Bullet Punch first, as the worst-case scenario is that I deal a bit of damage to another of their Pokemon (or get trapped by Magnezone, but that was a risk regardless of whether I predict correctly) and the worst case scenario for Pursuit is that I lose Scizor and still have a high-health Gengar to deal with. Remember, the best of entrepreneurs never thought in terms of what they could win, but what they could lose.