6 April 2017

Competitive Pokemon has been an interesting experience, especially because it has some major differences with most other competitive games. Most competitive games take one of two forms. In the first, players are making actions in real time. Most physical sports fall into this category, along with Starcraft, DOTA, League of Legends, and so on. In the second category, players take alternating turns making moves. This category includes games like Chess, Go, Magic, Hearthstone, and Poker.

In contrast to these games, in Pokemon the players make their decisions simultaneously. Once both players have sent their orders, then those orders get executed and the players begin thinking about their orders for the next turn. As a result, the type of skill needed to play Pokemon differs quite a bit from the skills needed for the other games I mentioned before.

In real time games, there is typically a high amount of mechanical skill, and doing the wrong thing well is often better than doing the right thing poorly. For example, in Golf you could spend a lot of time thinking about the proper club to use, but the decision is meaningless if your swing is bad. In Starcraft, you could have the right unit composition, but if your macro is bad your army will be too small for that advantage to matter.

In the turn-based games, there isn't the pressure of good execution. The decision making and the execution are one and the same. As a result, the focus is on finding the "best" move. Even in games with hidden information, there is typically a theoretically optimal play based on the information that you have, and your goal is to find that play.

Pokemon works entirely differently. In a sense, there is still a theoretically best play, but that play is almost always going to be a mixed strategy instead of a pure one. In other words, given the same position in multiple games, you'll play differently in some than in others. You might say that this is true in other games as well, but the situation is a bit different. In Chess and Go, your opponent is going to see your move before they have to make theirs, so they can respond appropriately. When you play different moves in Chess or Go, it's because you believe they are approximately equally good, or that one is slightly better for the day or opponent. In Poker, you want to create uncertainty for your opponent, but the way you balance betting and folding is by basing the decision on the cards in your hand.

To illustrate, let's look at the simultaneous decision game that everyone knows: Rock Paper Scissors. Rock beats scissors, scissors beats paper, and paper beats rock. It's clear that there's no single move that is the best here. If you were to always play rock, you'd lose to someone who always plays paper. Indeed, the theoretical optimum is to play each option randomly one third of the time (however, in practice opponents are predictable and you can do better by accurately predicting them). But let's change the situation a bit.

Let's play a new game, called Modified Rock Paper Scissors. In this game, rock beats scissors and scissors beats paper, just like before, but if one player plays paper and the other plays rock, then paper wins only two thirds of the time (for example, we roll a die and paper wins if it lands 3 or higher). It's tempting to think, "Why would you ever play paper?" but at the same time it's obvious that if your opponent always plays rock then the proper answer is to always play paper.

In the end, the best strategy still involves playing all three options some portion of the time, but some will be played more often than others. The proper balance will have the property that it has the same chance to win regardless of the opponent's move. For analysis, we'll pretend that a tie is actually a coin flip to win, since of course if our opponent also plays optimally, the rematch will be a 50-50. Let's use \(r, p, s\) to denote the probabilities that we play rock, paper, and scissors, respectively. We know that \(r + p + s = 1\).

  • Against an opponent playing rock, our winrate is \(\frac{1}{2}r + \frac{2}{3}p\).
  • Against an opponent playing scissors, our winrate is \(r + \frac{1}{2}s\).
  • Against an opponent playing paper, our winrate is \(\frac{1}{3}r + s + \frac{1}{2}p\).

Counterintuitively (for me, at least), if you solve this system of equations you get \( r = p = \frac{3}{7} \) and \( s = \frac{1}{7} \). The move that was weakened gets played more than when it was strong! Instead, the move that gets played less is the move that defeats the "bad" move. Once you've seen the result, it makes sense. Playing rock a lot already gives you a decent matchup against paper, so you don't need to counter it with scissors as often. On the other hand, your opponent is going to be playing rock quite a bit, so you'll still play paper a lot to catch that.

Comparatively, Pokemon is like Modified Modified Modified Modified Modified Modified Modified Modified Rock Paper Scissors. Each round leads to a slightly different situation in the future round, and so the calculations to determine the proper mix of moves are very complicated, but the general idea is the same.

In the Pokemon VGC format there are two Pokemon on each side of the field at a time. Pokemon make their moves based on their speed, so fast Pokemon will move before slower Pokemon. Let's call the Pokemon on one side A and B, while the Pokemon on the other side are C and D. It is a very common situation where neither A nor B can knock out C or D on their own, but combined they'd be able to knock one out. If both A and B are faster than C and "double up" onto it to knock it out, then C effectively won't get a turn.

It's usually very powerful to get two moves off while your opponent only gets one, so a newcomer to VGC might wonder why you don't double up every turn. The answer is the move Protect. Protect defends the user from (with a few rare exceptions) any attack that might hit it for the turn. If A and B double up into C, but C used Protect, then A and B did nothing while D got a free turn. Just like getting two moves off while your opponent gets one is strong, so is getting one move while your opponent gets none.

Once you learn the power of protect, it is tempting to ask the opposite question: Why would you ever double up? If you always split your attacks, so say A attacks C and B attacks D, then if they protect one Pokemon you'll still get one hit in. The answer lies in the fact that Pokemon are generally balanced so that fast Pokemon are more fragile or hit weaker than slow Pokemon. So what appears to be a fair one-for-one or two-for-two trade will usually not be so fair: the slower side will tend to slowly gain an advantage this way.

It's difficult to internalize this fact. When you double up into a protect, it often feels like you lost the game on the spot. On the other hand, splitting the attacks feels like the safe play, because even though your opponent might have gained an advantage, you still got something done. In reality, both of those are usually false. Comebacks after a bad turn happen all the time, so the downside of doubling up into a protect are smaller than they appear (and the upside of doubling up while your opponent protects the other Pokemon is massive), and the apparently small disadvantage is often an almost guaranteed loss.

This is the basis for two of the most important skills for high level Pokemon play. The first is the ability to accurately judge situations. Ideally, you'd want to know your exact win probability for each of the various decision combinations. However, you only have 45 seconds to make a move, so such a calculation is going to be impossible. Advice like "Think about your win condition" and "Consider what the threats are on each side" are about judging the situation. It's important to consider the decision from both sides. Just like we saw in Modified Rock Paper Scissors, even though scissors seemed weaker, it is still a very valuable play because it counters your opponent's apparently strong play.

The other important skill is the ability to fall flat on your face, stand back up, and continue walking. Pokemon is full of luck-based mechanics such as critical hits, moves with 85 percent accuracy, moves with a 30 percent chance for a beneficial side effects, and so on. However, even without these mechanics there would be a significant amount of luck created from the mixed strategy dynamic. Even when playing optimally, sometimes you'll get a terrible result. In order to be a top player, you have to be able to move past that and continue making the best decisions possible.