# Do You Feel Lucky? — Randomness, the Pokemon TCG & You

This CFB Pro article has been published publicly to celebrate the season; happy holidays everyone!

Have you ever lost a game because of bad luck? Of course you have. Anyone who’s played any game with any amount of randomness has felt the despair of losing a game to a series of unfortunate coin flips, an opponent top-decking the only card that could save them, whiffing an Energy card (in Pokemon’s case) for three turns in a row, or something else of that sort. I have too! I still remember losing my first game at Worlds 2013 because my opponent got a series of heads on flippy cards like Roller Skates, which was immensely frustrating to me.

Yet, when I’m asked which advice I’d give to a beginner or intermediate player looking to get better, my first answer is always: “Don’t blame luck for your losses.” What’s my deal?

First, a little bit about me. My background is in mathematics. I started a PhD, didn’t finish it because I then decided to be a teacher, and then taught math in high school before becoming whatever I am now. (Even now, Pokemon is not a full-time activity for me – I’m still teaching math on the side.)

More precisely, my specialty was probability and statistics: fields that deal with randomness and our understanding of it.1 As such, I’ve spent a lot of time thinking about randomness and luck in the game that means so much to me, the Pokemon TCG. On several occasions, I’ve tried to vocalize these thoughts, but I never wrote them down. This essay is my attempt at a convergence of my expertise as a Pokemon TCG player and my knowledge as a mathematician. Hopefully, by the end of the article, you’ll have a better understanding of the nature of luck. That said, this article isn’t only theory: I will also discuss some practical tips on how to manage the luck component of the game, to get better at it.

1 These words can mean different things in everyday language, but in math, the field of probability studies the results of random processes (for example : “if I flip a fair coin four times in a row, how likely is it that I’ll get heads four times”), while statisticians try get information on randomness by looking at the results of a process (for example: if I get heads four times, how likely is it that the coin was fair”).

While, as its name indicates, this article is aimed at Pokemon TCG players, and many of my examples will come from situations in the game, I think the bulk of this article can also be applied to other competitive games. After all, in my experience playing and/or watching other TCGs, Pokemon VGC, and more, complaining about luck is hardly exclusive to one community!

## What Is Luck?

It is very important to differentiate between luck and randomness.2

2 Some people also talk about RNG (aka Random Number Generation), which is a slightly different thing. RNG is mainly used to describe ways that computers simulate randomness. People misusing that term is a pet peeve of mine. Basically, anytime someone says RNG, they just mean randomness (or luck).

The Pokemon TCG has elements of randomness in it. When you play a Crushing Hammer, the result (heads or tails) is random. Drawing a card at the beginning of your turn is also a random process. Now, you could argue that the result is not actually random: the card that’s on top of your deck is set. An omniscient observer (or a cheater) would know which card is there. What makes it random is the fact that, if the deck was randomized beforehand (and there wasn’t an effect such as Oranguru which allowed you to manipulate which card is on top of your deck), that card is unknown.

Despite its name, randomness is something that can be studied mathematically. We can’t predict the results of a random process, but if we know the process, we can give the probability of any of its outcomes. This, in turn, allows us to make rational decisions.

Luck, on the other hand, is much more nebulous and subjective. That’s not a controversial statement, at first glance: if you topdeck the perfect card at the right time, that’s lucky for you, but your opponent will probably feel unlucky.

Less obvious is the following: luck is not only subjective in whether it is good luck or bad luck, but also on whether something is luck at all.

Consider the following situation: you start watching a game in progress. “What’s happening?” you ask. Someone explains to you: “Right now, Alice has two coins left to flip, and she needs to hit heads twice to win, otherwise she loses.” She flips. Heads, heads. Wow! That was lucky! After all, the probability of hitting heads twice was only 1/4 (25%).

Later, you talk to someone about that game, but they don’t feel like Alice was particularly lucky. It turns out that on that last turn of the game, she had four coins to flip, and needed to hit two heads out of four (the probability of this happening is 11/16, or 68.75%). The first two coins she flipped ended up on tails, but the last two were heads. So, while it looked to you like an unlikely turn of events, from the perspective of someone who saw the whole turn, Alice winning wasn’t particularly lucky, it was only expected. You only felt differently because you had incomplete information.

To complicate matters, in a TCG or any other game with incomplete information (for example, you don’t know which cards are in your opponent’s hand or deck), sometimes what someone sees as luck is not actually luck. I remember a City Championship (basically a League Cup) in which my friend Caroline beat a guy in Top 4 by top-decking an Energy. He started ranting to his friends about how he would totally have won next turn, but he was so unlucky because she just happened to draw what she needed at that time. (As one does.) Caroline later confided to me that she already had an Energy in hand and had only pretended to need the topdeck. So, from Caroline’s opponent’s perspective, he was a victim of bad luck, but the truth is that he had already lost and didn’t know it yet.3

3 I wanted to write “the truth is, the game was rigged from the start,” but I didn’t want to imply that any actual cheating happened. (Please still give me credit for the cool Fallout: New Vegas reference.)

There’s a framework that explains all of this in a consistent way, though. All we need is a little bit of math.

## An Introduction to Conditional Probability

Wait, don’t run away!

People sometimes ask me if having studied so much mathematics has helped me as a Pokemon TCG player. Truth is, that it has rarely benefited me directly, it’s not like there’s a secret theorem I can apply to help me get better results. However, being familiar with math has given me a better understanding of abstract things, like patterns in the game. This section is my attempt at passing on this kind of knowledge.

If you’re truly allergic to math, you can skip it and still get the rest of the article just fine. That said, I think it provides a useful tool here to explain what’s going on, and I’m going to do my best to explain it in an accessible way. I’ll also simplify some stuff in order not to get lost in detail that aren’t important for our purposes, so if you’re well-versed in math and you notice something slightly incorrect, just assume that I didn’t want to lose most of my audience by going into details. (If it’s just the vocabulary that’s a bit off, it might be a legitimate mistake, though; I’m far more used to talking and writing about math in French.)

Let’s start with a few definitions. A random experiment is a process which has some possible outcomes. For example, drawing a card at random in the most insane deck to ever win a major event (Xander Pero’s Naganadel Checkmate) is a random experiment. In this case, the outcomes of that experiment are the 60 possible cards you can draw in the deck.

An event is a set of outcomes. In our example above, we can define the event, “drawing a Pokemon card.” Since there are 25 Pokemon cards in the deck, that event (let’s name it A) has 25 outcomes in it (the outcomes corresponding to each Energy card).

We often want to know about the probability of an event, which is a number between 0 and 1. An event with probability 0 (for example, “drawing a Fire Energy”) never happens (since there’s no Fire Energy in the deck), while one with probability 1 is sure to happen.4 In the case of our event A (“drawing a Pokemon card”), its probability is pretty easy to calculate in our case. Out of the 60 possible outcomes of our experiment, 25 of them realize the event, so the probability of A (which we write P(A)) is 25/60 (or 0.4166…; we can also write is as the percentage 41.666…%).

4 Yes, I know, “almost surely.” (I did say that I would simplify some stuff!)

All good so far? Now, if you have two events A and B, the conditional probability of B given A (written P(B|A) is the probability that B happens, given that A happens. In other words, we assume that A is happening; what is the probability that B is also happening? For example, let’s consider our event A above (“drawing a Pokemon card”), and the event B: “drawing a Pokemon-GX.”

To calculate this probability, we assume that event A is happening, so the card we’ve drawn is a Pokemon. Now, among these 25 Pokemon, there are eight Pokemon-GX in Xander’s deck. Once again, every card is just as likely to be picked as any other, so the probability that the Pokemon we’ve picked is a Pokemon-GX is 8/25 (eight Pokemon-GX, 25 total Pokemon). That can be written as P(B|A) = 8/25 (or 0.32, or 32%).

(If you’re curious, the probability of A given B is simply 1. If B happens, the card drawn is a Pokemon-GX, so it must be a Pokemon, so event A must happen as well!)

Conditional probabilities are a very useful tool and they’re used a lot in random experiments that involve a succession of random procedures. For example, let’s say you have a six-sided die and a 20-sided die. You pick one of the dice at random and roll it and record the result of that roll. What is the probability that you end up with a result of 1?

To start with, let’s name our events: S is “picking the six-sided die,” T is “picking the 20-sided die,” and O is “getting a 1.” What we’re looking for is P(O). You might think that this depends on the die we pick, but that would not answer the question; the part where we choose one of the dice is a part of our random experiment, not something outside of it; we need to take it into account in our result too.

That remark does provide a good starting point for our reflection, though. If we picked the six-sided die, the probability of getting a 1 is, very logically, 1/6, whereas if we picked the 20-sided die, the probability of getting a 1 is 1/20. These are conditional probabilities and can be described with the events S and T. What I just wrote is simply: P(O|S) = 1/6 and P(O|T) = 1/20.

But since we pick the die at random, we’re equally likely to pick the six-sided or the 20-sided die. That means that P(S) = P(T) = 1/2.

So how do we calculate the probability of the event O? Well, we have a 1/2 chance of picking the six-sided die, and in that case, we have a 1/6 chance of getting a 1. So, by multiplying these numbers, we get a probability of 1/2 * 1/6 = 1/12 of picking the six-sided die and getting a 1. We also have a 1/2 chance of picking the 20-sided die, and then a 1/20 chance of rolling a 1 with it, so our probability here is 1/2 * 1/20 = 1/40.

Finally, rolling a 1 (realizing the event O) can happen with either with the six-sided die or the 20-sided die, so we add these two probabilities together. Our result is P(O) = 1/12 + 1/40 = 13/120 (or 10.8333…%).

Confusing? This can be made much clearer with a probability tree like this one:

In this beautiful diagram I drew with my expert graphics skills, each branch of the tree corresponds to a possible event. First, either S or T can happen (we either pick the six-sided die or the 20-sided die), and then, whether we’re in the S branch or the T branch, we can either roll a 1 (event O) or not. On each branch, we note the probability of following that branch. The probability of a path (for example “S then O“) is the product of the probabilities on the branches of that path. To find out the probability of event O, we look at all the branches that end up with O happening (the ones in green), and we add their probabilities. That gives us what is ultimately the probability of O happening. (This whole formula we use to calculate P(O) is known as the law of total probability.)

## The Feeling of Luck

Welcome back to those of you who skipped the previous section!

So, what does this all have to do with Pokemon? Well, if you exclude all the decisions that players make (let’s assume for a second that at every point in the game, there is one line of play that’s optimal, and that players are perfect and will always recognize and choose that line of play), a game of Pokemon is just a random experiment. A very long, very complicated random experiment, that incorporates everything random that happens in the game: drawing the opening hands, setting up Prize cards, every time a card with a random effect is played (not only flippy cards like Crushing Hammer, but something like Great Ball where you look at the seven top cards of your deck is also random, because the seven top cards of your deck are random).

Such a game can, in theory, be represented with a probability tree like the one above, but a much, much larger one. Instead of two branches that each branch off into two more branches for a total of four paths, you would have 60 branches that each branch off into 59 branches, that each branch off into 58 branches, and so on… Repeat until you get to the seventh repetition, where each of our previous paths branches off into 54 new branches. And that doesn’t represent a whole game, just the drawing of the opening hand. For only one of the two players. (And it doesn’t cover the case of a mulligan.)

In the finals of Worlds 2010, Michael Pramawat faced off against Yuta Komatsuda. I wasn’t there, and games weren’t streamed or recorded at the time, so what I know about that match is only what I read of it, so it’s possible that my story is not perfectly accurate. Nevertheless, from what I understand, here is how it ended. In game three, Pramawat had Komatsuda to a point where he would win on the next turn. There were about 20 cards left in Komatsuda’s deck, and only one could save him: Uxie LV.X. Komatsuda drew his card for the turn: Uxie LV.X. He won the game and became World Champion.

A common reaction, especially if you’re a fan of Michael Pramawat, is to feel bad for him. Out of Yuta Komatsuda’s 20 possible draws, only one could save him. That means that Michael Pramawat’s probability to win was 19/20 (95%). How unlucky!

There’s no question that were I in Pramawat’s place at that moment, I would feel completely and utterly crushed. This is not in question. However, I believe the statement that “his probability to win was 19/20” is wrong. 19/20 was the probability to win at that specific point in the game. In other words, it is the conditional probability to win, given everything else that happened before in that game; not the actual probability to win the game. It’s the probability of some small branch at the far end of the immense tree that represents that game. The actual probability for one player to win the game would be calculated by considering every possible path, not just one. By the law of total probability, that 19/20 probability would have to be considered, but it would only appear as a very small part of a formula far too complicated to write, let alone calculate.

To put it another way, you’d need to account for luck at every point in the game, and not on that last turn. After all, if you’re looking back on the game, there’s no reason to just assume that everything before that last turn is set in stone, and randomness only occurred in the very last turn. Only looking at the last turn is arbitrary. Think back to Alice and her four coin flips: that would be like only looking at the last two coin flips.

I want to be extremely clear that if you lost a game because of an unlikely event happening, it’s perfectly fine to complain about your lack of luck (to your friends after the game, not to your opponent). It’s a perfectly valid feeling! But it’s precisely this: a feeling. Luck is not an objective truth; it’s how you feel about a random event after the fact. It’s normal to be frustrated about an opponent’s perfect topdeck, but unless you’re also considering everything else in that game, starting with the opening coin flip, including every draw in the game (and you probably don’t know all your opponent’s draws, so you don’t have all the information), you’re not doing any objective analysis. Again, it’s not a bad thing, if you understand that you’re proceeding from emotion, not reason.

Therefore, I strongly recommend against blaming luck for your losses. It might feel good to remove any responsibility from yourself and attribute it all on some nebulous force outside of your control, but the truth is, most people don’t really understand randomness and would, without even noticing it, conflate the probability of winning the game with the much less significant probability of winning the game at some specific point. More importantly, blaming your losses on luck means you never think back on your games and try to figure out what you could have done differently.

Multiple times, I’ve seen players, especially beginners, point at some unlikely event that happened in their game and blame a loss on it. “I would have won if only they didn’t draw Cheryl to heal their damaged Pokemon on that specific turn!” Usually, they’re not entirely wrong, and something unlikely and bad for them did happen. However, often, what they’re missing is that they could have played in a different way and avoided any risk at all. It’s not wrong for them to feel unlucky, but it prevents them from recognizing their mistakes, and it means they’re likely to these mistakes again.

It’s misguided to look back at random things that happened and wonder about their probability, because the questions you’re asking are informed by what already happened. Regularly, I see people saying things like: “I just lost a game where my four Single Strike Urshifu V were prized! What are the odds!?” And sure, the odds of prizing all four Single Strike Urshifu V are very low (about 1/38550, in a deck that plays 12 Basic Pokemon including four Urshifu). So, on average, in your next 38550 games with that deck, only once will all four Urshifu be prized.

But people only ask this question when they just got out of a game where they had such a circumstance happen. The probability of prizing four Urshifu might be 1/38550, but the probability of prizing four Urshifu given that you’re asking this question is very close to 1!

Asking the specific question “what are the odds of prizing all four Urshifu in a game” is not innocent, it’s informed by what already happened. Usually, people ask this when they’ve already played dozens of games with the deck, so they could just as well ask “what are the odds that, in 20 games of Single Strike, I’ll prize all four Urshifu at least once.” Which is still a very low probability, but much higher than the one above. Or they could ask “what are the odds that I’ll be unable to play the game because of my Prizes,” which would include other possible Prize combinations (like prizing all four Houndour or all four Single Strike Energy). Again, still very low odds, but higher. By asking “what are the odds of prizing all four Urshifu in a game,” they implicitly suggest that this specific, unlikely event has some special significance, like if it was the only way they could lose. But it’s not.

Unlikely events happen all the time. If you’re playing Jolteon VMAX and your opening hand is Sobble, Quick Ball, Speed Energy, Boss’s Orders, Marnie, Elemental Badge and Quick Shooting Inteleon? That’s extremely unlikely to happen. But it’s also completely unremarkable. If you got this hand, you wouldn’t ever think to ask what the odds of it happening were. You wouldn’t talk about it after the game. In fact, you would probably forget about it by your second turn.

When we ignore all the times when unlikely events happen that don’t affect us a lot, and only think back about the unlikely events that happen that hurt us, we end up with the impression that we’re unlucky, but it’s our selection bias that makes us think so. This is how every competitive game community ends up with a high number of people complaining about how they lost because of luck.

## Skill versus Luck

After Yuta Komatsuda’s win at Worlds 2010, there were some takes arguing that Michael Pramawat should have won, or that he deserved to win, or that Yuta didn’t deserve to be champion. And that’s a strange opinion, to me. If you’re making claims about who deserved to win Worlds, you need to be looking at the whole tournament, not just the finals, not just game three of the finals, and certainly not just last turn of game three of the finals! It would be very arbitrary to assume that everything should have happened the same, except for that last turn. Was there no other unlikely event that “shouldn’t” have happened in the whole tournament? As I just explained, unlikely events happen all the time, though we don’t notice them most of the time, so that’s not the case either.

However, it does raise an interesting question: what does it mean to deserve to win? Imagine that in the next Regionals, someone wins just by donking their opponents. Every single game of every single match, from round one to the finals, their opponent bricks, draw-passes, and loses on turn one or two. That scenario is so unlikely that I would be confident betting that it will never happen, but it is still theoretically possible. If it were to happen, most of us would probably say that that victory was just luck. And I just wrote that it’s bad practice to look back at something and try to find the part of luck in it, but this scenario does feel different to the ones discussed previously.

That’s because, in our miracle donk run scenario, our donk champion didn’t express any skill: victory just fell into their lap, so to speak. Even if they did play perfectly, it’s hard to say they outplayed their opponents when said opponents didn’t get to play the game.

Therefore, the question of who deserves to win ties into that old debate about whether Pokemon is a game of skill, or luck.

Now, the obvious answer to that question is 10% luck, 20% skill, 15% concentrated power of will, etc.5 Beyond that, though, it’s an interesting question, but one can be asked in very wrong ways.

5 There’s an unwritten law of the Internet that whenever someone asks the question “what is love,” the author must immediately allude to Haddaway, otherwise their audience will do it for them. Similarly, I believe that every time the skill vs luck debate comes up, Fort Minor’s “Remember the Name” should be quoted.

This essay is long already without diving into this debate, so I’ll only say this. There’s merit to asking if the game rewards skill enough, or if randomness plays too big a role (i.e., if it’s likely that someone playing badly can still beat someone playing better if random effects go in their favor enough). But that only makes sense when considering the Pokemon TCG as a whole (or at least, say, a specific format, or maybe a matchup). If you’re looking at a specific game, you can’t separate parts that are “luck” from parts that are “skill.” That’s partly because, as I explained above, luck is mostly a feeling that we get from the results of specific random processes.

But it’s also because skill can’t be meaningfully separated from luck. The winner of a game of Pokemon TCG is not whoever some official council decides played better, abstracted from any random elements. Randomness is a part of the game and playing well means taking that into account. Managing randomness is a core skill of every TCG, both when playing and when building a deck. A corollary of this is that when several players made a perfect deck choice and play as well as they can, luck is often the defining factor.

Take any event, whether it’s a League Challenge or Worlds, you can make a case that luck was an important factor in the winner’s success. I won NAIC in 2018, and I’m proud of it. I think I played well! Still, I’m aware that luck played a role in that victory. Had my hands been worse, I could have lost my Top 8, a perfect mirror match, against Fabien Pujol. Had the Top 8 bracket been arranged differently, I could have been eliminated by the remaining Zoroark-GX / Garbodor player. I don’t think this means that I didn’t deserve the win. I can simply imagine other scenarios in which other players would have won, and they would have been just as deserving.

Therefore, it’s more important to focus on the big picture, on the number of wins and Top 8s, than on any specific event. There’s a reason that qualifications for Worlds, for example, happen over a whole season, and not a couple of specific events! The more tournaments and games are played, the less likely it is that some outlier event happens.

## Managing Randomness

To recap, here are some important points I’ve made so far.

• Randomness is a part of the game and becoming a better player means learning how to manage it.
• Probability theory is a useful tool to understand randomness, but it can’t be applied to explain the past. You need to focus on the future.
• Luck is a subjective feeling, and if you blame your losses on it, you’ll miss the ways you can improve.

With that in mind, let’s look ahead: how can this new understanding of luck and randomness help you become a better player? Here is my advice:

### During a Game

• The more information you have, the less random the game is. Try to figure out your Prize cards on your first search through your deck. In an IRL event, it’s much harder to figure out all your Prizes than on TCGO, and it’s not very important to know if, say, a Quick Ball is prized. However, you should count the cards that are fundamental to your strategy, as well as any techs (especially one-ofs) that are relevant in the matchup you’re playing. Note that sometimes, some cards are important, but you can wait until a later search for them.
• For example, when playing Single Strike, I’ll quickly take note of how many Houndour, Houndoom and Single Strike Energy I prized. I’ll also see if my Pokemon VMAX are in the deck since I only play two of each (Urshifu and Umbreon). If I plan on using Laser Focus on turn one, I’ll check if my Fighting Energy are prized. If I’m playing against a Darkness-weak deck, I’ll count the whole Umbreon VMAX line. If I play against Zacian or Suicune, I’ll check if my Tool Jammer is here. Urn of Vitality is also a relevant card but it’s okay if I don’t take the time to count them on turn one, because it’s only later that they become relevant.
• You’re allowed to take notes, so if you think you’re going to forget, take a piece of paper and write down your Prize cards! Don’t forget to cross them when you draw them, so at any point in the game, you can check what important cards are still prized. I do this in most major online tournaments.
• Similarly, getting information on your opponent’s hand can help you make sensible decisions. That’s not always easy to do, and it can tend towards psychology more than probability, something I’m infinitely worse at, so I don’t have too much to say about it!
• When playing a turn, think about what you’re trying to accomplish. Often, there’s a safe line and a riskier, but potentially better, line. Unless you’re in a desperate situation in which you need unlikely things to happen, I recommend sticking with the safe plays. What this means is that you should choose the option in which you do something for sure rather than the option in which you might do something better (for example if you draw the right cards off a Professor’s Research), but also risk not doing anything at all.
• Play around what your opponent can do. This especially applies when you’re winning a game. Ask yourself “how can I lose this game” and try to patch the holes, small as they might be, in your plan. I find that this is especially useful in the Expanded format, where there are more options for both players. For example, I was recently playing Coalossal VMAX / Magcargo against Rowlet & Exeggutor-GX / Vileplume in an Expanded event. I was in a great situation but to make sure I couldn’t lose, I had to identify my opponent’s possible outs.
• For example, I would make sure to always have a Path to the Peak in hand so I could counter my opponent’s Silent Lab (which prevents me from using Oranguru’s Ability). At another point, I recognized that the only way I could lose was if my opponent managed to bring a Pokemon in the Active spot and I lost my Guzma, so I made sure to get Guzma in hand with Magcargo and Oranguru’s Abilities, so it couldn’t be discarded by Team Rocket’s Handiwork. Sure, it would be very unlucky that my opponent had Handiwork, chose to play it, discarded Guzma with it and then had their own Guzma on the next turn to stall me. But since this was the only way, I could lose (or at least the only way I recognized), doing all these extra steps was worth it. Had I not done it and lost to that small possibility, I would be the only one to blame.

### Building a Deck

• It’s tempting to try to fit as many techs as you can in a deck to counter every possible situation, but most of the time, having a more consistent deck is better instead. This is because of the same fallacy that I discussed earlier: the human tendency to fixate on some remarkable unlikely events. If you play a tech that beats a certain deck (say, Dusknoir to beat Single Strike), you’ll notice the games you win because of it. If you’re running an additional draw Supporter instead, you won’t notice the games you’ll win because of it, even though draw Supporters are good in all matchups, not only specific ones. It might not look fun to have a cookie-cutter, consistent deck, but it is usually better. After all, it’s Tord Reklev’s specialty, and you can’t argue with his results!
• I don’t mean to say that it’s never worth it to tech against anything. However, there’s a right balance to be found between techs and consistency, and in my experience, newer players tend to stray too far towards the “techs” end of it. If you’re struggling to achieve consistent results, maybe if you’d like to make day two at a Regionals or win a League Cup, I recommend trying a more consistent deck. Force yourself to just copy a standard list without cutting a card to add a cool tech. It’s better to have too few techs than too much; consistency can compensate for the lack of techs in any matchup, whereas techs will only compensate for the lack of consistency in the specific matchups they’re there for.
• On that note, if you’re playing a deck with lopsided matchups, it might be better to switch to something less polarizing. As cool as a deck like Galarian Obstagoon is, and as effective as it can be in the right metagame… pairings are a part of tournaments where randomness occurs. If you’re playing Obstagoon and you’re paired against a lot of Mew VMAX, you’ll be happy. If you’re paired against a lot of Jolteon VMAX, you’ll cry. No matter how good you are, that’s a matchup you’re not likely to win. There are other decks you could play instead that have matchups closer to 50-50, where you’ll have a shot against most opponents. Reduce your odds of losing a match before the game even starts, play a deck with balanced matchups, and avoid thinking “there are plenty of Mew VMAX players; if I played Mew VMAX, why would I make top cut and not them?” Most players’ first break into day two of a Regionals is with a meta-deck, not some rogue concoction.
• Flippy coins like Crushing Hammer are a strange case. Usually, it’s better to not play these cards, because they’re unreliable. If it’s random whether a card will even do anything, and your goal is to reduce the impact of randomness on your games, obviously you’ll want to avoid these cards!
• It’s hard to say that you should never play them. Crushing Hammer has won many tournaments, obviously it’s not bad! However, unless there’s a specific reason in the metagame to play them (for example, in the ADP / Pikarom metagame, Crushing Hammer was often necessary to delay the opponent’s setup by a turn), you can usually cut them for other cards and not be worse for it.
• There’s a rule I’ve seen around which is that you should only play these kind of cards when you would be fine getting only one heads out of four. I don’t think it applies all the time (for Crushing Hammer, the timing of the heads is more important than the number of heads; it was mostly useful on turn one and two to remove ADP’s Energy. After Ultimate Ray, it’s not as good), but it can be worth keeping in mind. A year and a half ago, I won the PokeX Invitational tournament with a Dragapult VMAX list (UPRRCL format) that included four Super Scoop Up. I think this was one of my favorite innovations; in addition to allowing, you to save Dedenne-GX (or re-use its Ability), Super Scoop Up was a way to heal especially in the mirror match, which could be slow as a Dragapult VMAX would only 3HKO another Dragapult VMAX. Healing even once in a game would negate two turns of attacks by the opponent (minus the additional damage counters placed by Max Phantom), which was often enough to turn the game around.

If there is one specific piece of advice to give, it’s the following, very general rule: after a game, always think of what you could have done differently. This applies especially if you feel like you lost due to bad luck. I’m not saying that there is always something that you could have done differently; sometimes you can make no mistakes and still lose. However, often, you’ll find some different line of play that you could have taken. Maybe if you had Knocked Out a Benched Pokemon on that one turn, you could have delayed the opponent’s setup enough? If you had discarded a different card to Quick Ball, you could have used that other card on your next turn? It’s not fun to think back to a game you lost and look for ways to blame yourself for that loss. However, it probably has helped me in my Pokemon career more than anything else. (Generally speaking, I think that being willing to reflect on yourself rather than look for other things to blame is a good life skill in general.)

Be careful not to get too results oriented. Just because something didn’t work doesn’t mean it wasn’t the right choice. Sometimes, in a game, you’ll have to take risks: “Just playing a Boss’s Orders this turn won’t save me, I’m too far behind; I have to Professor’s Research and hope to draw the right three-card combination.” Sometimes these risks don’t pay off, and that doesn’t mean that you shouldn’t have taken them.

Similarly, sometimes you’ll make a line of play which is reasonable, and you’ll lose because your opponent plays some very unusual card or count in their deck. If every decklist you’ve seen of some archetype plays three Boss’s Orders, you probably won’t see it coming when an opponent plays a fourth one. That’s okay. Take note of it and be aware of the possibility. If there was a way for you to play around that small chance of your opponent playing four Boss, then maybe it would have been right to do so; however, most of the time, we can’t play around every card that could theoretically be in our opponent’s deck. Making choices based on what seems likely is not a mistake, even when we lose.