On The Probabilities of Pokémon

Und zis is when you PONT.

Hey SixPrizes. This article is going to be all about the probabilities of pulling the cards you need when you need them. You see, Pokémon is different from many card games in just how much you play through your deck. With access to Supporters, your whole deck is at your fingertips, but you need to know when to fish for what you need, and when to play it safe.

Take poker (ex: Texas Hold ‘Em) for instance. Though bluffing and mind games are a major part of poker, a proper understanding of probabilities is near essential to become a truely competitive player. As Kenny Rogers taught me, You gotta know when to hold ’em, know when to fold ’em, know when to walk away, know when to run. Pokémon is actually fairly similar.

With Pokémon, you need to know when to play it safe, when to not even bother trying, and when to go for it. An example would be the question posed recently and addressed briefly in Jay’s article. When should you PONT, and when should you Juniper? When should you play the PlusPower + Supporter to try for the KO, and when should you just Catcher and take a cheap prize? That’s what this article is going to be all about.

To start off, a huge thank you to my friend Travis for helping me out with the probability side of things. Travis pretty much gave me a refresher crash course in probability in order to write this article, so you can thank him for this whole article pretty much.

Before I begin, I’ll also just say a couple things. First, in preparing to write this article, I really needed to make sure things were approachable. After all, numbers can scare people off sometimes, especially if you try and explain how you got them.

Done! So it takes 240701 Slugmas to screw in a lightbulb.

So I’ll just be saying right now, don’t worry! I’m only going to explain my work once, and I’ll include a link to all of my work at the bottom of the article if anyone is interested in verifying everything. And second, I think there are 3 things I’m hoping for people to get out of this article.

One is to get an idea of exactly how probable it is that you pull off the combos you need. This can really affect how you make decisions in-game, between when to go aggressive and when to play conservatively. The second is to provide you with reasonable scenarios that you actually might find yourself in, and be able to advise on when to make what play.

And lastly, I hope this article can provide you with a base you can rely on. You probably won’t have time (nor the ability) to run mental math like this, but hopefully you can think back and say “well that scenario was only so likely, so mine is probably about this likely.”

Crunching the Numbers

The situations we’ll be looking at today can be summarized into 4 main categories.

  1. Start of the game
  2. Early game
  3. Mid game
  4. Late game

And in each category we’ll be looking at 3 different sub-categories.

  1. Looking for 1 card to complete a combo
  2. Looking for 2 cards
  3. Looking for 3 cards
Fun fact, that “+” in the background is really… a T !!!! *gasp*

So, doing the math… anyone? Anyone? That’s 12 different situations we’re going to be looking at. Each at different points of the game, and each will be fishing for different combos of cards to pull things off.

Obviously, most all “unknowns” where we make decisions in which we’d be interested in the probability of A or B working, come from playing Supporters. Supporters give us cards we can’t know, so we make guesses about how likely it is to get what we need by playing the Supporter. Now… in writing this article there is one card in the format that I’d love to look at in detail, but it just gets far too complicated. I’m talking about Smeargle CL.

If you’ve been stuck under a Graveler for the past year or two, Smeargle’s “Portrait” Poké-Power lets you look at your opponent’s hand and use the effect of one Supporter card you find there as the effect of Smeargle’s Poké-Power. This means you can essentially play two Supporters in a turn. How I’ll reconcile this is that you can simply look at each “Supporter” separately. So if you’re looking for a total of two cards, you can look at the situation as “what are the odds I get 1 card,” and after that, “what are the odds I get the other card with the second Supporter.”

Without further ado… let’s dive in shall we? I’ll add, to see just how good of an insight you have, I’m going to encourage people to try and ballpark what the odds of success of these situations are. Try it out! I bet it’ll be fun. I know I had fun doing it before I actually calculated the probabilities. If you want a challenge, try to be accurate within 5%.

1. Start of the Game

Why does start of the game deserve it’s own category? Donks of course. It’s a difficult decision to make at the start of the game. “Should I overextend myself or should I play it safe?” This category is likely going to be the most directly applicable to everyone and every deck with the capability of a first turn donk, since it’s the easiest to simulate.

You start by drawing 7 cards, and one for your turn to make 8. That means there are 52 unknown cards in your deck and Prize cards. If you can search your deck (very possible), you would be able to distinguish what is in your Prize cards and what is in your deck. But for the purposes of this article, we’ll say you can’t.

If you can search your deck though, then you can just adapt the probabilities listed here from the probabilities listed in the “early game” section, and find yourself a happy median.

A. Looking for One Card

pokemon-paradijs.com
Making donks possible.

Alright, here’s a likely scenario for any ZekEels, CMT or Darkrai/Tornadus EX player. You’re about to pull off the T1 donk or at least T1 KO, but you’re 1 card short. In this scenario, let’s just say that card is a Double Colourless Energy for Tornadus EX’s Blow Through attack (or Mewtwo EX’s X Ball). Through some circumstances, you’ve managed to get a Tornadus EX active with a Stadium in play, but are missing the DCE.

Your remaining hand is a Professor Juniper, a PONT and a Sage’s Training. I’m including Sage’s Training here to just run it through the probability grinder and show how it stacks up against the other 2 draw Supporters. If you wanted to replace it with something like a Catcher, then the issue at hand becomes “PONT and keep the Catcher?” or “Juniper and go for the better odds of KO?”

So, if we have 4 Double Colourless Energies in deck, what are the odds of getting one by:

  • Juniper’ing our remaining hand
  • PONT’ing our hand back
  • Sage’ing through 5 cards looking for the DCE

I’ll only go through this once, so no worries. The other situations get a bit more complicated anyway. So if we’re looking to calculate the probability of getting one of 4 cards from a 52 card deck, by simply drawing 7 new cards via Juniper, the probability can be expressed as:

Pr(Getting at least 1 DCE via Juniper) = 1 – Pr(Not getting even 1 DCE via Juniper)

Or the probability of getting at least one DCE off the Juniper is equal to 1 minus the probability of not getting at least one DCE off the Juniper. This just makes it easier to look at, since there are numerous scenarios where we could draw 1, 2, 3, or even 4 DCEs off of the Juniper, and calculating the probability of each scenario and adding them up individually would be a pain. So, the probability of not getting even 1 DCE off of a Juniper is:

The Hand: PONT, Juniper, Sage’s Training

Pr(Not getting even 1 DCE via Juniper) = (48C7)/(52C7)

= 0.550355527

Or in English…

pokemon-paradijs.com
Go on, throw away your other Supporter. I’m all you’ll ever need.

Pr(Not getting even 1 DCE via Juniper) = (Total potential hands without a DCE) / (Total Potential hands)

The (xCy) stands for “x choose y.” It’s the number of combos of cards you can get drawing y cards from a total of x cards. Now we just take 1 and subtract our answer to find the probabilities of getting at least 1 DCE.

Juniper

Pr(Getting at least 1 DCE via Juniper) = 1 – 0.550355527

= 0.449644473

= 45.0%

So we just found out that the odds of getting at least one of 4 DCEs from drawing a straight 7 off of a Juniper is about 45% with 52 cards left in deck. How do PONT and Sage’s Training stack up? Remember, for PONT we’re shuffling 2 extra cards back into the deck, so we increase the numbers we’re choosing from compared to Juniper by 2.

PONT

Pr(Getting at least 1 DCE via PONT) = 1 – (50C6)/(54C6)

= 1 – (0.615)

= 0.385

= 38.5%

Sage’s

Pr(Getting at least 1 DCE via Sage’s) = 1 – (48C5)/(52C5)

= 1 – (0.659)

= 0.341

= 34.1%

pokemon-paradijs.com
I’ve seen a Sage where the 5 cards were 3 Junk Arm and 2 DCE.

There we go! You’re through! You don’t have to worry about any more math. The evil decimals are gone and friendly percentages are all that remain. For the rest of the article, I’ll just explain the process in English. If you’re interested, I’ll be including a file for download with all my work at the end.

So, looking through that, we just found that a Juniper gives you about a 45.0% chance of getting yourself the DCE you need, a PONT is about 38.5% and a Sage’s Training is a 34.1%. Not that anyone runs Sage’s Training much anymore, but it is interesting to know that straight draw 5 has a worse probability of fishing out the 1 card you need than a PONT, N or Copycat shuffling back for 6. Looks like everyone stopped running Sage’s Training for a reason.

So now if we reflect on that for a brief moment, remember that if that 3rd card were something like a Catcher, you’re now armed with the knowledge that using a Juniper only increases the odds of getting that 1 card for the KO by 6.5%. That’s not too too much, but if you as the player deem it worth it, then go for it. You will be getting 6-7 more donks every 100 chances you get than someone else who uses PONT.

But the question then becomes, how many games did you play where you whiffed a Catcher? There’s no way I could simulate that, but you’re now armed with the ability to assess whether you think it’s worth it.

In Summary

  • Juniper: 45.0%
  • PONT: 38.5%
  • Sage’s: 34.1%

B. Looking for Two Cards

Alright, since it’s simple and a common occurrence, let’s continue with the Tornadus EX example. This time, let’s say I don’t have the Stadium in play and still need both a DCE and a Skyarrow Bridge (SAB). So we have a PONT, Juniper and a third card (this time let’s say Junk Arm for fun). We still have 4 DCE in the deck, but we only have 2 Skyarrow Bridge in the deck. We still haven’t been able to look at our prizes.

tcgwithhats.blogspot.ca
My 1337 paint skillz

This time, we’ll be taking the same approach, finding the probability that we don’t get the combo we need. We can think of it kind of like a Venn Diagram in a box. We combine the probabilities of the DCE and the SAB and the instance where we don’t get either is where the two circles cross over. Looking at the equation in English…

Pr(Getting at least one of both a DCE and a SAB) =
1 – Pr(Not getting at least 1 DCE)
+ Pr(Not getting at least 1 SAB)
– Pr(Not getting either a DCE and a SAB)

The reason you subtract the probability of not getting either of them is because in the Venn Diagram, that’s the part that overlaps. Since we added both circles together, and both circles had the part that overlaps, we’ve actually added it twice, so we have to subtract it once.

What we’re looking to do is get the whole area of the Venn Diagram, which represents situations where we don’t get both together, and then we’re going to subtract that from 1 again, to get the probability of getting both together. Think of it kind of like the area in the box not taken up by the Venn Diagram is the area we’re interested in.

So, if we run the numbers, they look something like this:

The Hand: PONT, Juniper, Junk Arm

Juniper

Pr(Getting at least one of both a DCE and a SAB with Juniper) = 1 – [(0.550) + (0.747) – (0.400)]

= 0.103

= 10.3%

PONT

pokemon-paradijs.com
Crummy

Pr(Getting at least one of both a DCE and a SAB with PONT) = 1 – (0.615) + (0.788) – (0.475)

= 0.072

= 7.2%

Pretty crummy odds right? That’s just because the odds of drawing the SAB alone are already only about 21-25%. It’s pretty hard to fish 1-of 2 cards out of 50+ from your deck. That said, as you can see, Juniper’ing away your Junk Arm only gives you 3.1% better odds of the T1 KO than using the PONT. In this scenario, I’d probably advise using PONT since both odds are pretty low anyway. No sense in wasting resources.

The only argument against this is if you are looking to do more that turn (like play additional basics), in which case, it might be justifiable to use Juniper to get yourself an extra card to play with that turn (e.g. a potential Dual Ball or Tynamo).

C. Looking for Three Cards

Alright, so you probably know how improbable this scenario must be now. If looking for 2 cards, which you ran 4-of and 2-of, only has at best a 10.3% chance, then 3 cards can’t be very good at all. But hey, let’s look at a situation I ran into during my Battle Roads. So my opponent in round 4 had a Mewtwo EX active, and needed to attach a DCE, get a PlusPower, and then get another PlusPower or a Junk Arm.

I’m going to assume he ran 4 DCEs and 4 Junk Arms, but he told me he only ran 2 PlusPowers. He has 52 cards left in deck. We’re taking the same approach where we’ll find the odds of not getting what we want, and just subtract that from 1.

This one gets complicated though, since in order for the Junk Arm to work, you first need to draw a PlusPower. So I’ll just avoid the explanation and say that I did the probability of getting 1 DCE and 2 PlusPowers and the probability of getting 1 DCE, 1 PlusPower and 1 Junk Arm and combined them conditionally for the solution.

The Hand: PONT, Juniper, 5 Cards no one cares about

Juniper

pokemon-paradijs.com
X Attack for the TCG

Pr(AUBUC) = Pr(A) + Pr(B) + Pr(C) – Pr(A∩B) – Pr(A∩C) – Pr(B∩C) + Pr(A∩B∩C)

Pr(AUBUC)*Pr(A1UB1UC1)= (0.952)

1 – (0.952) = 0.048

or…

Pr(Getting at least 1 DCE, and 2 PlusPowers or 1 DCE, 1 PlusPower and 1 Junk Arm) = 4.8%

So the odds of pulling off the DCE, double PlusPower with Juniper that turn were less than 5%. If you’ve ever discarded something important chasing after 3 cards, I implore you to reconsider. The odds that a PONT works are even less, so I’ll just label both Supporters as less than 5% (or <5%).

In this situation, given the choice… I would PONT. Exceptions of course, are if you’re discarding cards you want to discard (like Energies for acceleration later).

2. Early Game

With many decks hitting at full power as quick as turn 2, this section will be looking at how to play on the second or third turn. To set up the sort of situation we’re in, we’ll say we have about 40 cards left in the deck/prizes. Why 40? Well, if you started the game with a draw Supporter like Juniper, that would already bring us down to 45 cards at the start of the second turn.

We draw, and bring it down to 44. It’s also very common to be able to search out cards from the deck, so we should be able to lower that number from 44 to even less.

Finally, with search, we should have been able to see our prizes. Now, if we count seeing our prizes, I’d argue the most useful number to look at is really closer to 35-38 cards left in deck. But since accounting for every type of prize situation would be a boatload of work, and we wouldn’t even get much out of it, I’ll pass and say 40 cards left in deck.

If you’re playing a fast deck, by turn 2 you’re probably looking for a KO. As such, the cards of interest on this turn are mostly cards that help us get a KO. I’m going to say that we haven’t had the fortune of discarding Trainers to make them Junk Arm targets yet.

pokemon-paradijs.com
Gimme yo’ Bench-sitters!

After all, the scenario of wanting a Catcher from the deck on your 2nd turn, and having had a first turn where you discarded or used a Catcher, doesn’t happen all too often. So it’s probably more useful to look at these situations like you’re still trying to fish your first copies for use out of the deck.

A. Looking for One Card

So here’s our situation. I’ve got a Darkrai EX out (or whatever attacker you set up by T2) and am looking to grab a Catcher to KO my opponent’s benched Eel, Smeargle, Celebi etc… This Catcher could easily be re-labeled as a Dark Patch in this situation, since both are cards that Darkrai is often fishing for on it’s second turn.

But we’ll say it’s a Catcher so that if instead you’ve got a Zekrom BLW out, it makes no difference (not that it really makes a difference anyway, just trying to emphasize that the numbers are what’s important here, not the exact situation).

Alright, so we’re looking for a Catcher. We have 4 remaining in the deck, and a PONT and Juniper in our hand (amongst other cards). We’ve got 40 cards left in the deck/prizes. Again, if you have searched your prizes and can effectively cut down the number of cards in your deck, feel free to ballpark between this scenario and the “Mid Game” scenario for your likely probabilities.

Let’s say our hand is a PONT, Juniper, Shaymin UL and a Super Scoop Up. What are the odds that we can draw one of our 4 Catchers by just Juniper’ing away our hand? What are the odds of doing so while saving the Juniper, Shaymin UL and SSU for later by shuffling back with PONT?

The Hand: PONT, Juniper, Shaymin UL, Super Scoop Up

Juniper

Pr(Getting the Catcher by using Juniper) = 1 – (0.448)

= 0.552

= 55.2%

PONT

Pr(Getting the Catcher by using PONT) = 1 – (0.535)

= 0.465

= 46.5%

pokemon-paradijs.com
Who you gonna call? Ghostbusters!

It seems the gap has grown a bit! With fewer cards in the deck, but still fishing for at least 1-of four cards, the odds of getting one with Juniper are 8.7% better than the odds of getting one with PONT. That’s a full 2.2% wider gap than the “Early Game – Looking for 1 card” scenario. So, the decision comes back to the player. Do you think it’s worth discarding a Shaymin UL and a Super Scoop Up (not to mention 1 draw Supporter) to get 8.7% better odds of the T2 KO?

I’ll add, if you’re curious. If your hand contained only 2 cards instead, a Juniper and a PONT, then PONT only closes the gap by 1.8%. That means that shuffling back with PONT would still leave you with about a 7% worse chance of getting the Catcher that turn. I’ll also add that Sage’s Training is still worse than both at only 42.7% chance of success.

This scenario is totally up to you. It has a lot to do with what is in your hand, and how important that Catcher KO is. If I felt like the right path was to go aggressive and forget about Shaymin, then I’d Juniper. If I felt Shaymin would be valuable later on, I’d PONT. If the cards in my hand were different, I’d have to look at whether or not I wanted them in the discard pile to be Junk Arm targets, or if I wanted them in my deck so I could use more of them that game.

And of course, depending on how important I feel that Catcher KO would be, I might just say that giving me the extra 7-9% chance of pulling it off is worth more than whatever is in my hand.

B. Looking for Two Cards

Alright. Let’s go with the same sort of scenario. We’re looking for a Catcher to get a good KO this turn. But I’ll look into two vastly different possibilities here since both occur pretty frequently. The first possibility is that you need a Catcher and an Energy card for your attachment this turn.

Let’s say our deck runs 4 Catchers, 4 DCE and 9 basic Energy of some sort. This sort of Catcher/Energy line is pretty standard, so no matter what deck you’re running, this line should be applicable. For the purposes of this scenario, I’ll say we’ve only attached 1 Energy so far. We’re looking to attach from our hand to finish things off. In ZekEels or Darkrai decks, a similar situation occurs quite often when you say… Used a Juniper on the first turn to get an Energy in the discard pile, but came out with an Energy-less hand.

But you need another for the attachment this turn (and will be relying on your draw Supporter for this). CMT can run into this scenario easily as well, with the only difference being that you used a Forest Breath to get the extra attachment rather than discarding the Energy.

So for this example, we’re going to say that we’ve removed 2 Energies from the deck (likely basic Energies), by attaching or discarding them. Nonetheless, we’re just looking for 1-of 11 Energy cards now remaining in the deck, as well as 1-of 4 Catchers. For now, let’s go with the ZekEels example. In our hand we have a PONT, 2 Junipers, and a Mewtwo EX. Bring in the age-old question. PONT? or Juniper? A reminder, we have 40 cards left in our deck/prizes.

The Hand: PONT, Juniper, Juniper, Mewtwo EX

Juniper

pokemon-paradijs.com
I’m no scrub. I only run 1st edition Base Set Energies.

Pr(Getting at least one Catcher and one Energy via Juniper) = 1 – [(0.448) + (0.084) – (0.026)]

= 0.494

= 49.4%

PONT

Pr(Getting at least one Catcher and one Energy via PONT) = 1 – [(0.535) + (0.149) – (0.062)]

= 0.378

= 37.8%

Wowee! There’s a wide spread. Almost a full 12% difference in the probability that you get at least one of your 4 Catchers and one of your 11 Energy cards. Why is this spread larger than the spread we saw earlier when we were searching for 2 cards? Well, to put it simply, since we’ve got less cards in deck, we have a greater individual probability of drawing the cards we need. i.e. We have a better chance of drawing just a Catcher, or we have a better chance of drawing just an Energy.

When you consider that Juniper lets us draw 1 more card from the deck, and doesn’t shuffle cards irrelevant to the combo back into the deck, it makes sense that the gap would widen. We’re drawing one more card with an already-increased probability of getting what we need!

Still, in the above scenario, that might be harsh; Losing 2 Supporters and a Mewtwo EX (or being forced to bench the Mewtwo prematurely). The odds are ONLY 11.6% worse after all. The aim of this article isn’t to definitively say “PONT now!” or “Juniper now!” You’ll come across a situation similar to this eventually, and when you look at what’s in your hand and what’s on the field, you’ll have to decide what you want to do. Personally, if the KO was important, I might just bench the Mewtwo and Juniper.

The second scenario is that you need a Catcher and something like 1-of 2 PlusPowers (or an alternate example being Level Balls, say you needed an Eel to get the extra Dynamotor this turn). This time, instead of fishing for 1-of 4 cards and 1-of 11 cards, we’ll look at how the gap differs when you’re fishing for 1-of 4 cards and 1-of 2 cards.

The Hand: PONT, Juniper, Juniper, Mewtwo EX

Juniper

pokemon-paradijs.com
Remember when Pokémon in the TCG actually had levels?

Pr(Getting at least one Catcher and one PlusPower via Juniper) = 1 – [(0.448) + (0.677) – (0.289)]

= 0.164

= 16.4%

PONT

Pr(Getting at least one Catcher and one PlusPower via PONT) = 1 – [(0.535) + (0.738) – (0.381)]

= 0.108

= 10.8%

Less than half the gap of looking for an Energy as the second card. That’s a pretty drastic drop. The gap thinned from 11.6% to 5.6%. Of course, also of note is the fact that the odds are just significantly worse overall. I’d say this situation would be almost a no-brainer to PONT back the extra 2 Junipers and the Mewtwo. Personally, the risk of losing 2 draw Supporters and benching a Mewtwo prematurely for only a 16.4% chance of success just simply wouldn’t be worth it, much less worth it over a less detrimental option.

C. Looking for Three Cards

Unlike the “Start of the game” situation, this time when we’re looking for 3 cards, it’s much more likely that the 3rd card in the equation is Junk Arm’able. Examples of useful “3rd” cards that could be in the discard already in this situation would be cards like Dark Patch (Darkrai), Ultra Ball (ZekEels/Darkrai) or Switch (Darkrai/CMT). Each of these cards works to accelerate Energy or allow for acceleration to occur, so it’s understandable that we’d be interested in fishing them out in the early game.

Since we can effectively increase the number of cards of interest in our deck using Junk Arm, perhaps the probability this time around won’t be so pitifully small that it will be worth comparing Juniper to PONT. Let’s take a look shall we? The combo we’re going to be going for this time will be Catcher, Energy, and one of the three example cards.

Let’s say Dark Patch. If you want a more plausible idea of how this turn could play out, let’s say you had a Tornadus EX active that hit for 60 the first turn. You started the turn by Ultra Ball’ing 2 dark Energy into the discard pile to grab your Darkrai. You use one Dark Patch, and are left with a PONT, Juniper and Junk Arm.

So, to finish your combo, this turn you want to Catcher out a card of interest (Smeargle, Eelektrik, Celebi etc…), use another Dark Patch, and attach an Energy from your hand. If we run 4 Catchers, 13 Energy, 4 Dark Patch and 4 Junk Arm, what is the probability of pulling off this combo?

pokemon-paradijs.com
And it was decreed, Dark Pokémon shall be tier 1.

Well, we now have one Dark Patch in the discard, and 3 Energy cards in play. That leaves us with 4 Catchers, 10 Energy cards of interest, and 6 potential Dark Patches (7 if we PONT our Junk Arm back). We still have about 40 cards left in deck.

Again: Pr(AUBUC) = Pr(A) + Pr(B) + Pr(C) – Pr(A∩B) – Pr(A∩C) – Pr(B∩C) + Pr(A∩B∩C)

I include this more as a reminder to myself than anything :P

The Hand: PONT, Juniper, Junk Arm

Juniper

Pr(Pulling off this godly combo via Juniper) = 1 – (0.448 + 0.109 + 0.289) – (0.035 + 0.109 + 0.019) + (0.004)

= 0.3134

= 31.34%

PONT

Pr(Pulling off this godly combo via PONT) = 1 – (0.468 + 0.125 + 0.249) – (0.044 + 0.097 + 0.018) + (0.004)

= 0.3131

= 31.31%

There’s a result that I bet was difficult to see coming. That’s right. Pulling off this three card combo is almost just as likely with PONT as it is with Juniper. Their odds are practically equal. So… provided the math is correct (it is… trust me), why is this the case? Well, even if the 3rd card in our hand was some card other than Junk Arm (thus meaning we wouldn’t discard a potential Dark Patch), the odds of a Juniper working only increase by about 3%.

This is because the probability of drawing cards individually from each scenario is fairly high already. In the “Looking for two cards” scenario, drawing 1 additional card off of Juniper gave us a much better chance of getting that 1 additional card we needed. Well, this time we need a combo of 3 cards. So, while drawing the 1 additional card is beneficial, it’s not going to go too far in the three-way interaction of these probabilities.

I included the specific numbers here to illustrate this point. In the equations above, the second bracketed group after “1 minus” contains the probabilities of not getting at least one of either of 2 of the 3 cards we’re interested in. Even I find myself re-reading that sentence, but really, it makes sense. As we can see, the probabilities there are only 0.035, 0.109, 0.019, 0.044, 0.097, 0.018 for not getting 1-of either of each potential 2 card combo. Thus, if we were looking for 1-of either a Catcher or an Energy, we’d almost be guaranteed to get it regardless of Juniper or PONT.

pokemon-paradijs.com
Makes your deck oodles more consistent.

This is the impact that adding a 3rd card into your combo can have over a combo of only 2 cards. It actually acts as a sort of “equalizer” making PONT the obvious choice provided you want to keep the additional card in your hand, not to mention the Juniper for later. And as I mentioned, even if we weren’t discarding a Junk Arm (and therefore potential Dark Patch) using Juniper, and had some other random card in our hand, the PONT is still approximately just as good, with only a 3% difference between the two.

3. Mid Game

At this point (turn 4 to turn 6) the field has been pretty well established and both decks are firing on all cylinders. You should often be able to pull 2-3 cards out of your prizes by this point of the game, meaning that the prizes are even less of a concern for our calculations. That said, you should now also have an intimate knowledge of your prizes, and can ballpark these probabilities accordingly.

You’ve also likely been able to discard at least one of each of the main Trainers you run in your deck (ex: Catcher, Dark Patch, Dual Ball, etc… anything where you run at least 3). That makes them available as Junk Arm targets (and also complicates the math… bleh). Furthermore, you’ve been using Supporters for many turns now, and have likely shuffled back hands at least a couple times, potentially restoring the deck or at least not depleting it as much as say, staight-drawing off of Juniper does. Still, your deck/prizes are now probably sitting around 25 cards total.

Let’s say you’ve got a decent-sized hand to start the turn (4-6 cards) since you hopefully didn’t have to leave yourself without options for the next turn. The reason I bring this up is because you’re more likely to have access to at least one part of your combo thanks to Junk Arm or just having it in hand. Nonetheless, we can look at a 3 card combo scenario for the sake of interest. But I’ll pose a different type of scenario to you. First things first…

A. Looking for One Card

Alright, the odds are you’re running Pokémon Catcher in your deck, and it’s time for the web gun to shine. But alas! It isn’t in your hand. And neither is a Junk Arm! On top of that, you’ve already used/discarded two Pokémon Catchers, leaving only 2 in your deck. You’ve also used 1 Junk Arm leaving 3 in your deck. What’s more is that you’ve taken 2 Prize cards, while your opponent has also taken 2, leaving you with a difficult choice.

Your hand has 4 cards remaining in it, PONT, Juniper, N and some Trainer you’d like to keep for later rather than discard (PlusPower might make a good example). You’ve got your field set up and are ready to take 2 Prizes off of a beefy EX, but just need to pull that Catcher.

pokemon-paradijs.com
Am I worth it?

Obviously Juniper gives you the best odds of pulling it, but you know that PONT should also be pretty good, and can keep Supporters in your deck as well as PlusPower. But what about N? You could drop your opponent’s hand (let’s say he/she took a prize last turn and has a decent-sized hand, likely to have what they needs for next turn) to only 4 cards by using N, but that leaves yourself with only 4 cards-worth of refresh.

You also know that after this turn, N won’t be very useful since you’ll only kill your own hand with it, so you might as well use it now. Should you risk it? Let’s look at the probabilities…

The Hand: PONT, Juniper, N, PlusPower

Juniper

Pr(Getting at least 1 Catcher or Junk Arm off of Juniper) = 1 – (0.161)

= 0.839

= 83.9%

PONT

Pr(Getting at least 1 Catcher or Junk Arm off of PONT) = 1 – (0.268)

= 0.732

= 73.2%

N

Pr(Getting at least 1 Catcher or Junk Arm off of N) = 1 – (0.432)

= 0.568

= 56.8%

I don’t think there were any real surprises there. The more cards in deck, and the less cards you draw afterward, the lower your chances of success are. It’s pretty simple to predict the general trend when we’re only interested in 1 card. That said, the odds are interesting to know. Juniper being at 83.9% is a practical guarantee of pulling off the Catcher, while N leaves you with a decent 56.8% chance of pulling it off.

pokemon-paradijs.com
Can they print a gold Gust of Wind?

Of course, N is also diminishing your opponent’s hand, which should make the play more appealing. And for the players who like to play it safe and find a nice middle ground, PONT offers a good degree of certainty, while keeping Supporters and that extra Trainer for later in the game.

I probably wouldn’t N considering the chance of failure though. Depending on how many draw Supporters I had left, and how the field was set up, the decision is really down to “PONT or Juniper.” Nothing much to talk about here, make the play you think is best. Let’s move on to scenario #2.

B. Looking for Two Cards

Let’s say the situation hasn’t changed much. We still have the same hand (Juniper, PONT, N, PlusPower) and same number of cards left in deck (25). We’ve still taken 2 Prizes to match their 2, and are still looking for the Pokémon Catcher to get our 2 Prize KO. But we’ve hit a snag. We need the Energy attachment per turn to make it happen.

To turn this into a more plausible scenario, let’s say you’re playing ZekEels and they’ve started playing aggressively with a Mewtwo EX. Your opponent also benched a Mewtwo EX last turn and attached 1 Energy to it pre-emptively, putting them in a good position for a Mewtwo war.

You still have 2 Eelektriks on board thankfully, and can return KO their Mewtwo easily by benching yours. But, to help set up your board position for later game, you’d love to take out their benched Mewtwo instead, leaving an easy Mewtwo KO for your last 2 Prizes. You could PlusPower before shuffling back to be safe and ensure that with even 1 Electric Energy you can still KO. But you also don’t want to waste a PlusPower if you’re just going to attach a DCE anyway.

To read more into the situation, it’s pretty probable that your opponent is planning to N you, so it’d be nice to pull the N on them first, while you can still refresh decently off of it. There is currently 1 DCE and 4 L Energy in the discard pile, and you’re running 4 DCE and 9 L Energy.

How risky is this play, and what are the odds of success with each of your Supporter options? As per usual, let’s find out! You’re looking for a Catcher or Junk Arm (5 total in deck) and an Energy (8 left in deck). Your deck has 25 cards left. For now, we’ll say you’ve played the PlusPower to ensure your KO as much as possible.

The Hand: PONT, Juniper, N, PlusPower

Juniper

And I’ll use Psydri… haha no… just kidding. X Ball yo’ face!

Pr(Getting at least 1 Catcher/JA and 1 Energy off of Juniper) = 1 – [(0.161)+(0.040)-(0.002)]

= 0.800

= 80.0%

PONT

Pr(Getting at least 1 Catcher/JA and 1 Energy off of PONT) = 1 – [(0.252)+(0.092)-(0.010)]

= 0.666

= 66.6%

N

Pr(Getting at least 1 Catcher/JA and 1 Energy off of N for 4) = 1 – [(0.417)+(0.221)-(0.057)]

= 0.419

= 41.9%

Those combos eh? Because pulling an Energy is so likely, and you’re drawing so many cards (7 in total) off of Juniper, the odds of getting what you need are pretty much the same as just needing the Catcher. But if you PONT back into your deck, you conserve a Juniper which might come in handy for that N that you know is coming. Unfortunately, this drops your odds to almost a literal 2/3 shot. I hate gambling, but this time it might be worth it.

Then we have N. In our 1 card scenario, drawing only 4 cards wasn’t so terrible. We still at least had over a 50% chance of pulling off our play. But here, we only leave ourselves with a 41.9% chance, and a burned PlusPower. Fortunately, you also kill your opponent’s hand a little and are still able to KO that active Mewtwo anyway.

I wouldn’t say I’d recommend this play, but if you think your opponent won’t recover from a 4 card hand (I’d always assume they would) then be my guest and try your luck.

C. Looking for Three Cards

pokemon-paradijs.com
I love the nights where you’re flipping like… 1 for 20 with these guys.

For consistency’s sake, we’ll stick with the same scenario. This time though, you don’t have the Mewtwo in hand. You do have 2 Dual Ball in the discard pile and 2 in deck though, so they are Junk Arm’able. You also have 1 Mewtwo EX in deck (the other is prized/discarded).

However, for calculating this scenario, I won’t include the situation where you use 2 Junk Arms off of a Juniper, since that would leave you without a hand and would likely be a grievous mistake. This means you are looking for a Catcher, a Dual Ball, and an Energy attachment to take out the opposing benched Mewtwo.

The combos you can use to pull this off are that you draw at least 1 of the Catcher or Dual Ball, and a Junk Arm for the other, along with an Energy. Unfortunately, this leaves N in an unfortunate position since your hand will be too small to use even 1 Junk Arm.

What this means is you have 5 potential Catchers (2 real, 3 Junk Arm), 8 Energy, and 6 potential Mewtwos (1 real, 2 Dual Ball, 3 Junk Arm). Since Junk Arm can serve as two cards, we’ll do the potential hands separately. I’m going to cheat a bit here, but it shouldn’t effect the final probability much.

The extra conditional probabilities that Junk Arm creates are a mess on paper, so I’ve simplified it by making minor assumptions which I know to be false, but likely inconsequential. I’ll also factor in the Dual Ball 25% fail rate in these probabilities.

The Hand: PONT, Juniper, N, PlusPower

Juniper

Pr(AUBUC) = Pr(A) + Pr(B) + Pr(C) – Pr(A∩B) – Pr(A∩C) – Pr(B∩C) + Pr(A∩B∩C)

Pr(Pulling off this 3 card combo with Juniper) = Sum of Probabilities of individual potential hands

= [(0.369) + (0.299)]/2

= 0.334

= 33.4%

PONT

Pr(Pulling off this 3 card combo with PONT) = Sum of Probabilities of individual potential hands

= [(0.229) + (0.184)]/2

= 0.207

= 20.7%

Bee my Pokémon?

And as I said, N doesn’t even get to use Junk Arm, so the probability is incredibly slim. Even a good ol’ fashioned PONT is barely hitting above 20% chance. The point here is that N will not get you the KO on the benched Mewtwo (so don’t burn your PlusPower going for it), and isn’t great for disrupting the opponent either (4 cards is plenty).

And though you may be Juniper’ing three draw Supporters, you at least increase the odds of a KO that turn by a respectable amount over PONT. The choice is yours, but hopefully it’s not N.

4. Late Game

Entering this article, I couldn’t ignore the most crucial part of the game. That being the last couple turns. After all, the winner is decided in these two turns, so it’s most prudent to talk about them. However, at this late stage in the game, not only do you have few cards left in deck (nullifying the difference between PONT and Juniper to some extent), but you also likely don’t have a choice between the two.

And even if you did, since this may be the last turn of the game, your decision is best made based off of what is in the discard, what is in deck, what is in your hand, and whether or not just going for a better probability (Juniper) is worthwhile.

Because of this, my standard approach for the above situations probably wouldn’t yield much applicable knowledge. After all, after you’ve been N’d to a 2-3 card hand (after your draw for turn), you probably aren’t going to be mulling over whether to PONT, Juniper or N.

So what are you mulling over at this point in the game? You’re likely trying to size up how you can finish the game this turn, or if not, how you can not lose the game next turn. As such, it’s these kinds of scenarios I’m going to explore. I’ll start off with an example so you can better understand what I mean.

pokemon-paradijs.com
I wonder if it’s awkward to paint with your tail…

I’m going to describe a pretty specific situation here to help everyone appreciate what I mean, but in the scenario analysis, I’ll try and generalize it a bit more. Say we have a Pokémon Catcher in hand, a PONT and a random card (Tynamo, Junk Arm etc…). We’re playing a ZekEels mirror, and we have a Smeargle active, a SAB in play, and a Mewtwo EX on the bench without Energy on it. This turn, we can Catcher and KO an opponent’s Eviolited Mewtwo EX with 2 Energy on it for our last 2 Prizes.

However, if we fail to get an additional Energy to make our damage output high enough, then Catcher’ing out Mewtwo will just let them take their last prize the next turn with a Catcher. Thus, we’re also considering using a Pokémon Catcher on an Eelektrik to stall the turn, since we can try to Catcher out the Mewtwo later instead.

Deck details: We’ll say that after we use the Pokémon Catcher, we have 1 left in deck, and 1 Junk Arm left. Our deck has 15 cards left. We also know our opponent has used 3-4 Junk Arms this game, 3-4 Double Colourless Energy and 2 Switch. Thus, it’s unlikely that they just Switch or retreat the Eelektrik if we do Catcher it, making this a real option.

We luckily have 2 Eelektriks online, so our choice really forms a dichotomy between whether or not we want to look for 1 card as a win-condition with a potential loss, or if we want to look for 2 cards as a win-condition without a potential loss. We can Catcher the Mewtwo and only have to look for 1 Energy for the win, or we can Catcher the Eelektrik and look for 2 cards for the win. One Energy and an additional Pokémon Catcher/Junk Arm.

I’ll still do the odds for both a PONT and a Juniper though, since it is good to know both even if you’re not likely to have a choice between the two. After all, if I didn’t, you might be interested in whether the decision you’d make in this situation would be different based off of your draw Supporter.

A. Looking for One Card

So we’ve chosen to Catcher the Mewtwo EX and are now fishing for 1 extra Energy for the win. We have 15 cards left in deck. For the sake of comparison, I’ll look at the situation where we have 2 Energy left in deck, and the scenario where we have 3 Energy left in deck. What are the odds of getting 1 extra Energy this turn for the win? I’ll add that we have 1 more Pokémon Catcher in deck, which will come into consideration later.

The Hand: Pokémon Catcher, PONT or Juniper, Junk Arm

Juniper

nytix.com
Spin for the win!

Pr(Getting at least 1-of 3 Energy off of Juniper) = 0.877

= 87.7%

PONT

Pr(Getting at least 1-of 3 Energy off of PONT) = 0.786

= 78.6%

Juniper

Pr(Getting at least 1-of 2 Energy off of Juniper) = 0.733

= 73.3%

PONT

Pr(Getting at least 1-of 2 Energy off of PONT) = 0.625

= 62.5%

As you can see, the odds are pretty good that you’re about to win. However, with only 2 Energy left in deck, that PONT value of only 62.5% might seem disconcerting. So, say you didn’t get the Energy there. What are the odds that you’ll at least get a Catcher/Junk Arm to undo your prior one? You did just shuffle the Junk Arm back in after all.

Well, the odds of getting at least 1 Catcher/Junk Arm OR 1 Energy are 94.2% for the PONT for 1-of 2 Energy scenario. So you are likely pretty justified in Catcher’ing the Mewtwo first, rather than Catcher’ing the Eelektrik hoping to stall.

Of course, this would leave you with only 1 more Catcher option in the deck, which becomes your sole win-condition if you fail to get the Energy. If you Juniper’d the Junk Arm away, you would be left without a win condition after Catcher’ing away the Mewtwo. So you’re just relying solely on the Energy card being in your hand. And you do have a 73.3% chance of that, so you’re probably pretty set.

So if that’s the case, how bad are the odds really, of pulling off the win when you Catcher the Eel instead?

B. Looking for Two Cards

pokemon-paradijs.com
Quick! It’s evolving! Hit B!

Alright, so we’ve Catcher’ed the Eelektrik and have PONT’ed or Juniper’d our hand looking for 1-of 3 or 1-of 2 Energy, and 1-of 2 Catcher cards. What are the odds we pull off the win this turn? Keep in mind, though this scenario is likely to yield worse odds of winning this turn, we’re also assuming it helps guarantee that you don’t lose the game on the next turn as well. Something to consider.

The Hand: Pokémon Catcher, PONT or Juniper, Junk Arm

Juniper

Pr(Getting at least 1-of 3 Energy off of Juniper and 1-of 2 Catcher cards) = 0.629

= 62.9%

PONT

Pr(Getting at least 1-of 3 Energy off of PONT and 1-of 2 Catcher cards) = 0.598

= 59.8%

Juniper

Pr(Getting at least 1-of 2 Energy off of Juniper and 1-of 2 Catcher cards) = 0.518

= 51.8%

PONT

Pr(Getting at least 1-of 2 Energy off of PONT and 1-of 2 Catcher cards) = 0.468

= 46.8%

Now we know. So consider this. I’d say if you had 3 Energy left in the deck, the choice to Catcher the Mewtwo is obvious. Additionally, with 2 Energies left in deck, to Juniper is also the obvious choice. Not only because the chance of the win is 73.3% but because as I mentioned, you leave yourself without a win-condition for the game, so it’s an all-in gamble.

But if you had only 2 Energy left in the deck and a PONT, then the choice becomes interesting. Only a 62.5% chance of victory that turn, and a veritable guarantee that you can at least prevent the Mewtwo from KOing you the next turn. But this also leaves you fishing for only 1 Catcher card in a deck of 10 cards the next turn.

I will not make a Bart Simpson reference. I will not make…

However, if you Catcher the Eel, you still have a 46.8% chance of victory, and also have a veritable guarantee of not losing. You’re also left fishing through your deck for 2-of 10 cards instead of 1-of 10 next turn, if you whiff on either the Energy or the Catcher (you should get at least one of them).

That said, I’d probably advise Catcher’ing Mewtwo in the first 3 scenarios, but I’m reserved on the third scenario. If it meant I could be really sure I wouldn’t lose the next turn, I would Catcher the Eel first. But if they could either Switch or DCE retreat the Eel somehow, and odds didn’t seem improbable, I would Catcher the Mewtwo and go for the 62.5% instead.

I find the comparison between these two scenarios rather interesting actually. Had I not done the probabilities and been proposed this choice, I might have chosen to Catcher the Eel instead in most scenarios. After all, it sounds better to be safe than sorry. But really, if I had 3 Energy in the deck there’s no way I shouldn’t Catcher the Mewtwo and go for it.

Even with 2 Energy left in deck, I think Catcher’ing the Eel is still a tad silly. If you could guarantee you wouldn’t lose I suppose I would do it, since I would just need a Catcher the next turn or after the Juniper to get the Mewtwo KO. But without knowing for sure that they couldn’t Junk Arm for a Switch, or attach a DCE to retreat, I would definitely bank on a 73.3% chance to win then and there.

C. Looking for Three Cards

Now, the choice above and the calculated probabilities can probably suggest that Catcher’ing the Mewtwo is worth it over Catcher’ing the Eel and chasing 2 cards for the win. I could describe a new scenario to try and make this more applied, but I’m sure you’ll find yourself in a conundrum similar to this at some point (at least in numbers). So instead, I’ll add to this scenario that you don’t have the Mewtwo on bench, and need to draw it from your deck.

Let’s just look at the scenario where you have 3 Energy cards left in deck, since the odds here are going to get low enough that the difference between 2 Energy and 3 Energy shouldn’t matter as much. This time, we’ve Catcher’d the Eelektrik since we can’t guarantee that we’ll be able to get that Mewtwo after our Supporter.

So the combo we’re looking for here is a Mewtwo, an Energy, and a Catcher card (Catcher or Junk Arm). Thus, what I’m calculating here is the probability of drawing into a Mewtwo EX (1 left in deck), an Energy card (3 left in deck) and a Catcher card (2 left in deck, will shuffle back a Junk Arm with PONT). We start with 15 cards left in the deck.

The Hand: Pokémon Catcher, PONT or Juniper, Junk Arm

Believe in the heart of the cards!

Juniper

Pr(AUBUC) = Pr(A) + Pr(B) + Pr(C) – Pr(A∩B) – Pr(A∩C) – Pr(B∩C) + Pr(A∩B∩C)

Pr(Getting Mewtwo, Catcher and Energy off of Juniper) = 0.264

= 26.4%

PONT

Pr(getting Mewtwo, Catcher and Energy off of PONT) = 0.193

= 19.3%

Additionally, you could instead use that Junk Arm for a Dual Ball or Ultra Ball, meaning you’d have to draw the actual Catcher for your 3 card combo to work. But I’m not going to calculate this for Juniper because the probability would be the same as before, except that instead of having 2 Catcher options, you’d have 2 Mewtwo options. So it’s still 26.4%.

The probability for PONT to work increases slightly since you can now draw a Junk Arm instead of the Mewtwo or a Junk Arm instead of the Catcher. But you can’t use two Junk Arms to satisfy this scenario, since you would discard all of the cards in your hand leaving you without the Energy attachment. Still, it’s less than 25% so nothing to write home about.

This scenario and it’s outcomes are only useful however, compared to if you were to try and go for the Mewtwo KO this turn instead of Catcher’ing the Eelektrik. Considering that the probabilities would be worse than the original Eelektrik ones (which were already barely hovering above 50%), it’d probably be best to just play it safe and go for the 3 card combo (provided you were sure they couldn’t retreat the next turn).

Crawdaunt’s Rules

So after all that, I think it’d be good to review a few key concepts you might have been able to pick up. I’ll call these “Crawdaunt’s Rules” for lack of a better term.

  1. The more cards left in your deck, the harder it is to get the card you need.
  2. The more cards you draw, the easier it is to get what you need.
  3. If you’re looking for 2 cards, drawing an extra card in your search makes a big difference.
  4. If you’re looking for 3 cards, drawing an extra card in your search makes little difference.
  5. If a common card like “Energy” is in the combo you’re looking for, your odds of pulling your combo off are only going to be a little worse than if you were just looking for the other card.
  6. This game is built off of playing probabilities, and having a good grasp on them will certainly help your decision-making abilities.
  7. Sage’s Training already gives worse odds than a PONT if you only have a few cards left in hand. Poor Cheren/Bianca.

Point number 7 there is actually an interesting one to consider. Bianca is currently being hyped as the big “replacement” for PONT when the rotation hits. But straight drawing 3-4 cards doesn’t provide very good odds. Personally, I think in the BW-on metagame, I’d search for a deck that had built-in consistency like Empoleon, to supplement my draws.

That’s not to say don’t stock up on Biancas, they will still be the next best Supporter around by being a mini-Juniper. But don’t expect your decks to run as efficiently as they do right now. This will cause the metagame’s pace to slow down a bit, which opens up room for setup decks (like Stage 2 Garchomp/Altaria decks) to start competing.

In Conclusion

smplyskool.ca
All our problems have been solved. Two Ladies and Gentlemen. Two.

The goal of this article is to provide you with various situations similar to ones you might find yourself in, and give the probabilities of success for the choices you might make. Hopefully it’s enlightening to know what the true odds of some of these situations are. I know I found myself being at least mildly surprised by some of the probabilities of some of these certain scenarios.

Did you try ballpark’ing the odds? How close were you? Now that you’ve read through, do you think you would be able to ballpark the odds better in the future?

Try it again! Re-read this article in 1-2 weeks time (with a poor memory) and see if you’re closer than last time. If you are, then hopefully I’ve contributed to some sort of decision-making skill you can draw on in future games. And I also hope that this has been a useful indirect mental exercise potentially, in how to build decks to better maximize your odds of success.

Originally, the idea was proposed that I should summarize the odds in a table at the end, as a quick cheat-sheet type of reference. I thought that would be a great idea, but looking back on it, it probably wouldn’t be useful. The usefulness of this article doesn’t just come from looking at probabilities I’ve listed, but being able to assess your own situations and have an idea when you’re playing on what it is you’re trying to accomplish.

It’s been a great ride! And if you’d like to see more UG articles from yours truly, be sure to give this a +1 and say so in the forums thread! If you don’t want to, tell me why anyway! And if you’re interested in probabilities of situations you’ve run into, post em in the forums thread and I could check em out and I’ll try to give you an answer!

Cheers

~Crawdaunt out

Click here for all my work, if you’re interested.


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