ryanvergel
New Member
I want to discuss, analyze, and argue for the important of consistency in lists, especially at this specific point in the season.
First, we must explain what it is we mean by consistency. We will be using our friend Webster's third definition for the word:
agreement or harmony of parts or features to one another or a whole
This is a very important concept to grasp. The whole of a deck is its purpose, intention, or main strategy. My viewpoint is similar to the designers of the 20th century- form follows function. The form of the deck, which cards are chosen to be in it, must follow the function of the deck, its strategy or goal.
For a deck like Dialga G X and Garchomp C X, usually called DialgaChomp, its main strategy would be to build a defensive and disruptive pokemon and heal it to deny prizes. It does this by including special metal energy, Garchomp and Poketurn to heal, Warp Energy to manipulate the field of play, and many trainer cards to search out specific pokemon to facilitate this basic strategy. Sometimes people use ancillary pokemon like Uxie LA or Spiritomb AR to help speed up the process of achieving the main strategy.
The dominant principle here is that a deck's contents should be at their best agreement or harmony possible to produce the desired whole and deck strategy. This means a number of things, and what we will discuss here is that it means your deck must be as consistent as possible, without becoming a hindrance.
I think a lot of people on the PokeGym and at tournaments fail to take this into account, and a huge amount of losses can be attributed to this flaw in deck construction that is never adequately argued for. People typically speak of jargon and non-sense when they talk about consistency. People throw the word around easily, and don't understand why it is important, or how it is actually achieved well.
If we take consistency to be important because it advances the goal of the deck, and thus the achieves the purpose and nature of the deck more fully, then we must try to achieve this principle as well as possible. To do this, we need to consider a lot of probability and tournament structures. There are obvious trends and certain threshhold probabilities that you would want to seek, or can rationally conclude to seek, and I will try to showcase those specific areas.
The first area we will discuss is the most basic one, and this is of energy. Many decks in the past commonly had one fourth of their contents devoted to energy, which was the resource needed to attack and retreat. Pokemon had higher attack costs, higher retreat costs, and there is a one-attachment per turn clause in Pokemon, making it very detrimental for a deck to not take full advantage of this. Attaching an energy every turn is important, and is a main contributor to losing. A single energy drop can mean a missed turn of attacking, and one turn is often all that decides the outcome of a game.
How do we know how many energy to run in order to attach an energy every turn?
That number will depend on a lot of factors, such as how expensive your Pokemon's attacks and retreats are, as well as what kinds of energy they can run. However, with that said, there is a large trend towards contemporary lists to run around 12 energy. Let's look at how this compares with probabilities, specifically drawing an energy in your opening hand.
With 12 energy, you will open with one 81% of the time. If you play 15 energy, you will open with one about 88% of the time. This is a jump in about 7%. However, if you only ran 9 energy, you would only open with an energy 70% of the time. The pattern in this progression is not geometric- as more energy are added, there influence on the odds of starting with an energy decrease. Eventually there is a point where the cards are not adding enough influence to the probability of opening with it compared to how other cards might bolster consistency. That is a kind of threshold that I noted earlier, and is what we want to hit and maintain. There is usually a certain margin that allows for relatively large gains in starting with an energy, and allowing for just enough starts with energy so that your deck can perform well in a tournament without having too many energy devoted and squandering otherwise precious space in a deck.
There are many Pokemon odds calculators, and I have tried to do basic math for opening information around the forum, so I will only go into the examples that I deem fitting and I think will be appropriate to convey the message. There are a billion exceptions to the ideas I will be putting forth, but it does not affect that overriding argument of the thread, which is based purely on rationality. With decks like Jumpluff and Gyarados existing, previous standards of energy devotion are quite different.
So how do we create our range and threshold of what is acceptable for starts?
We do this by looking at the particular tournaments we will attend, and how well we want our deck to perform.
Let's take a Battle Roads and Nationals as two comparisons.
The Tournament Operation Procedures gives this table for top cuts:
Players per age division /// Swiss Rounds /// Single Elimination (Top Cut)
9 rounds with a top 32 will typically mean that 7-2 and above will make it into the cut, depending on how many are actually in the tournament.
This means that you can afford to take two losses to make it into the top cut. If you lose your first round, you have to win 7 out of the next 8 rounds to get into the tournament. Well, let's say that you could lose any of the 9 rounds due to poor luck or a bad opening hand. If you have one of those situations occur, and you lose because of your very poor set up, then you have to win 7/8 of the other games.
Can you reasonably expect your deck to do well without adequate consistency?
What if you lose 2 of your games because your set up was slow? You must reasonably expect your deck to then "win out". It is hard to avoid problematic or slow starts, but you must account for them when building a consistent deck. If you have a deck that is allowing too many losing starts, you will have an immense burden for your deck when it does set up. Do most decks even win 7/7 games when they reasonably set up? Not usually.
With this in mind, we want to avoid having bad opening hands, because the first 2-3 turns usually determines the outcome of the match.
What is a bad opening hand?
A bad opening hand is one that does not allow for the deck to achieve its goals. This means that the player is unable to establish its core strategy and begin to succeed in winning. If the player cannot set up an attacker, or attach energy to attack, or have enough pokemon in play, the player will usually and eventually lose. A player has to get set up to win, and in this format people are not taking the proper considerations to do so.
If we play a deck with 6 basic energy, and use 3 roseanne's research, we can calculate the odds of being able to attach an energy turn one. With 6 energy, you are attaching energy going first a little over half of the time. Even with a roseanne's research, you must go second to use it, so only 50% of the time does it increase your opening odds from 6 to 9. With this in mind, if a deck you run must use 2+ energy attachments to attack (like Gardevoir), and you need to attack by turn 2-3 to maintain early game power, then you need to attach an energy turn 1 as often as possible without hurting the space for other needed and assisting cards. A deck like Gardevoir would be best running at least 13-14 energy, so that on average they will be able to open with an "energy out" 90% of the time or so. This means that in a tournament like Nationals, you will admit one time to not drawing an energy and being behind, and possibly losing etc. Any higher than 10% and you will begin to drift into having this happen more than once a tournament. If it begins to lean towards twice a tournament, then your two losses are already accounted for, and you are expecting your deck to perform perfectly which is unreasonable.
Different decks need different energy considerations, but it is important to know the odds of drawing energy, drawing outs to it, and what your ideal odds of drawing them are to be.
With that in mind, one would need to begin to think of the set up in general.
It is important not only to attach energy, but to set up your attacking pokemon. With this kind of information in mind, it is important to play enough pokemon search cards to consistently get out your attacking pokemon in order to maintain your strategy. Cards like Roseanne's Research, Bebe's Search, Call Energy, Pokemon Communication, Pokemon Collector, and Luxury Ball remain some of the best trainers and cards in the game because of their ability to precisely search from the deck desired pokemon, sometimes with exact specificity, and other times with more vague but numerous application.
Something that I dislike seeing is people using less than the maximum number of allowable cards for something that is very strong and consistency boosting. The best card in the format, Luxury Ball, is argued to be the best card because it should be included in every deck.
With only a minor drawback- the inability to search out level X pokemon, the non-supporter trainer can get any other pokemon, basic, legend, stage 1, and stage 2 without any other implications. In this way it has a huge function range with little drawback. One should be in every deck.
Yet I see decks without this card. I see decks that run stage 2 pokemon that only run 3 Rare Candy. I see decks that need a t1 energy drop every game to truly be successful play less than 10 energy and not attach one turn 1 25% of the time. These people are not building their decks properly. These are often the same people who complain about poor luck. The truth is, unless your deck is filled with consistency-boosting cards, you will not have enough outs or probability to set up properly and fulfill the function of the deck. When my opponent is playing Gengar, and prizes 3 Gengar and doesn't play Azelf- he is at fault. Attributing this poor circumstance to luck is not possible, because there exist cards that can usually overcome this difficulty. Azelf LA is such a card for us.
Similarly, if my opponent has all of his Gengar prized, he cannot get them into play. If one does not have the sufficient energy or pokemon in play- which are obtained by consistency-boosting trainers and energy, then one will be operating similarly as not playing an Azelf LA. Much of the luck is in our control. I get tired of people complaining about situations, only to hear that they didn't use call energy, or only ran 3 Bebe's Search, or cut the Rare Candy down to 3.
One must remember that in cutting consistency cards for other 'tech' cards, one is making a small sacrifice towards the ability of the deck to achieve its entire function. If you don't set up, that tech card will be useless. Finding the individual balance and harmony for a deck is extremely difficult, and usually requires extensive playtesting, and I think- analysis of probabilities and tournament structures.
I know at a 9 round nationals where I need to go 7-2 that I will want to attach an energy turn 1 8/9 or more of the time, and I will likely want a card to get basics or an evolution once my basic attacker is obtained 8/9 of the time or more. I can only reasonably allow my deck to accept one loss to poor set up, trying to reduce it further will usually hurt the overall power of the deck by marginally increasing the consistency, and trying to reduce it less will allow too many losses to do well at this large event. I must take this into account, and so should you. When you see a deck that runs no call energy, yet has colorless attack costs, or a deck without luxury ball, or a deck that is using cards like Pokedex or Pokeradar at the expense of having enough precise-search cards like Pokemon Communication, Bebe's Search, etc. to get out the attacking pokemon early and effectively you should CRINGE like I do.
Too many people blame luck more than themselves. In this format, we have an absurd number of cards to allow for optimal consistency. If you don't take advantage of them, or consider them properly, then you will not reasonably do well.
Thanks to R_A for reminding me of what I like to do here- help the community and try to improve things. Trust me, you will have a lot more fun at Nationals if your deck is able to achieve its function, and you need to be willing to dedicate enough cards to achieve such a goal. The number and ratios are up to you to find, but don't be lazy. I want to see more Call Energy and Pokemon Communication out there in the Deck forum, and less Pokedex Handy 910.
Sample Calculations:
Odds of starting with an energy
So, probability of energy= 1-odds of NOT having an energy
NOT having an energy is determined for each of the 7 cards we have.
If we start with 6 energy, then on the first card we draw, there is a 54/60 chance of it not being an energy, but as each card is drawn, this probability slightly boosts. We multiply them all together to get the collective chance of the entire 7 card hand NOT having an energy.
So, if we start with 54/60, when we draw another card- if we assume no energy, it is 53/59, and so forth, until you get:
1 - (54/60)*(53/59)*(52/58)*(51/57)*(50/56)*(49/55)*(48/54)
So, if the probability of NO energy is 45.9, then the probability of YES energy is 1-45.9 or about 54%.
Odds of a LONE 30HP starter in a Jumpluff deck
The deck has the following basics:
4 Hoppip
3 Baltoy
2 Crobat G
2 Uxie LA
1 Azelf LA
1 Regice
1 Unown G
1 Unown Q
1 Luxray GL
It has 5 pokemon with 30HP- 4 Hoppip and Unown Q. The odds of not drawing a HOPPIP/Q is (55/60)*(54/59)*(53/58)*(52/57)*(51/56)*(50/55)*(49/54) = .525437
So, the odds of starting with a HOPPIP/Q in the hand is 1-.525437, or 47.45%.
However, starting with the HOPPIP/Q doesn’t mean that you must play it active, or that you don’t have outs thereafter. You could also start with another pokemon.
Now, we have to figure out the odds of not drawing another basic.
In this list, there were 11 other non-HOPPIP/Q basics, so that’s 11 outs.
The odds of no "out" in the remaining 59 cards in the deck (since we are assuming one of our cards is a HOPPIP/Q) out of the 6 cards left to draw:
(47 / 59) * (46 / 58) * (45 / 57) * (44 / 56) * (43 / 55) * (42 / 54) = 0.238308366
So, the odds of NOT getting an ‘out’ with our HOPPIP/Q is .238, or 24%.
The combined odds of this event (HOPPIP/Q& no other starter/out) would be multiplying the two likelihoods together.
Simply, it is .4745 * .238 = 0.112931
So, it’s about 11.3% chance of getting a lone HOPPIP/Q start.
We SHOULD consider the fact that the deck might mulligan, So, let’s continue the math. The odds of not drawing a basic from a deck with 16 basics would be
(44/60)*(43/59)*(42/58)*(41/57)*(40/56)*(39/55)*(38/54)= 0.0992228933
The deck will mulligan 10% of the time since it plays 16 basics, meaning the deck WON’T mulligan 100-10, or 90% of the time.
(.9/.125) * (.1/x)
X=HOPPIP/Q start after mulligan
.9x=0.0125
x=.0125/.9=.01389
So, the odds of a mulligan and then a lone HOPPIP/Q are 1.4%
So, combined:
The odds of not mulligan and getting a lone HOPPIP/Q are 11.3%, and the odds of mulligan and a lone HOPPIP are 1.4%
So, combined, it is 12.7% of a truly, lonely HOPPIP/Q start.
----
tl;dr:
You can't expect to do well at a tournament unless you provide your deck enough consistency, and the consistency you do use must be practical in terms of its space consumption and actual probability of assisting in the deck achieving its main strategy.
tl;dr: DON'T RUN 2/3 CLAYDOL. RUN FOUR CALL ENERGY.
First, we must explain what it is we mean by consistency. We will be using our friend Webster's third definition for the word:
agreement or harmony of parts or features to one another or a whole
This is a very important concept to grasp. The whole of a deck is its purpose, intention, or main strategy. My viewpoint is similar to the designers of the 20th century- form follows function. The form of the deck, which cards are chosen to be in it, must follow the function of the deck, its strategy or goal.
For a deck like Dialga G X and Garchomp C X, usually called DialgaChomp, its main strategy would be to build a defensive and disruptive pokemon and heal it to deny prizes. It does this by including special metal energy, Garchomp and Poketurn to heal, Warp Energy to manipulate the field of play, and many trainer cards to search out specific pokemon to facilitate this basic strategy. Sometimes people use ancillary pokemon like Uxie LA or Spiritomb AR to help speed up the process of achieving the main strategy.
The dominant principle here is that a deck's contents should be at their best agreement or harmony possible to produce the desired whole and deck strategy. This means a number of things, and what we will discuss here is that it means your deck must be as consistent as possible, without becoming a hindrance.
I think a lot of people on the PokeGym and at tournaments fail to take this into account, and a huge amount of losses can be attributed to this flaw in deck construction that is never adequately argued for. People typically speak of jargon and non-sense when they talk about consistency. People throw the word around easily, and don't understand why it is important, or how it is actually achieved well.
If we take consistency to be important because it advances the goal of the deck, and thus the achieves the purpose and nature of the deck more fully, then we must try to achieve this principle as well as possible. To do this, we need to consider a lot of probability and tournament structures. There are obvious trends and certain threshhold probabilities that you would want to seek, or can rationally conclude to seek, and I will try to showcase those specific areas.
The first area we will discuss is the most basic one, and this is of energy. Many decks in the past commonly had one fourth of their contents devoted to energy, which was the resource needed to attack and retreat. Pokemon had higher attack costs, higher retreat costs, and there is a one-attachment per turn clause in Pokemon, making it very detrimental for a deck to not take full advantage of this. Attaching an energy every turn is important, and is a main contributor to losing. A single energy drop can mean a missed turn of attacking, and one turn is often all that decides the outcome of a game.
How do we know how many energy to run in order to attach an energy every turn?
That number will depend on a lot of factors, such as how expensive your Pokemon's attacks and retreats are, as well as what kinds of energy they can run. However, with that said, there is a large trend towards contemporary lists to run around 12 energy. Let's look at how this compares with probabilities, specifically drawing an energy in your opening hand.
With 12 energy, you will open with one 81% of the time. If you play 15 energy, you will open with one about 88% of the time. This is a jump in about 7%. However, if you only ran 9 energy, you would only open with an energy 70% of the time. The pattern in this progression is not geometric- as more energy are added, there influence on the odds of starting with an energy decrease. Eventually there is a point where the cards are not adding enough influence to the probability of opening with it compared to how other cards might bolster consistency. That is a kind of threshold that I noted earlier, and is what we want to hit and maintain. There is usually a certain margin that allows for relatively large gains in starting with an energy, and allowing for just enough starts with energy so that your deck can perform well in a tournament without having too many energy devoted and squandering otherwise precious space in a deck.
There are many Pokemon odds calculators, and I have tried to do basic math for opening information around the forum, so I will only go into the examples that I deem fitting and I think will be appropriate to convey the message. There are a billion exceptions to the ideas I will be putting forth, but it does not affect that overriding argument of the thread, which is based purely on rationality. With decks like Jumpluff and Gyarados existing, previous standards of energy devotion are quite different.
So how do we create our range and threshold of what is acceptable for starts?
We do this by looking at the particular tournaments we will attend, and how well we want our deck to perform.
Let's take a Battle Roads and Nationals as two comparisons.
The Tournament Operation Procedures gives this table for top cuts:
Players per age division /// Swiss Rounds /// Single Elimination (Top Cut)
6-7 /// 2 or 3 /// None
8 /// 2 or 3/// Top 2
9–15 /// 3 or 4/// Top 2
16 /// 3 or 4 /// Top 4 or 2
17–31 /// 4 or 5 /// Top 4 or 2
32 /// 4 or 5 /// Top 8, 4 or 2
33–63 /// 5 or 6 /// Top 8, 4 or 2
64 /// 5 or 6 /// Top 16, 8, 4, or 2
65–127 /// 6 or 7 /// Top 16, 8, 4, or 2
128 /// 6 or 7 /// Top 32, 16, 8, 4, or 2
129–255 /// 7 or 8 /// Top 32, 16, 8, 4, or 2
256 /// 7 or 8 /// Top 32, 16, 8, 4, or 2
257-511 /// 8 or 9 /// Top 32, 16, 8, 4, or 2
512 /// 8 or 9 /// Top 64, 32, 16, 8, 4, or 2
As far as a Battle Road will go, you will often see 32 and less competitors, which means you will probably have 4 or 5 rounds, or even 3 rounds if it is small in attendance. In these events, the ratio of wins to losses to get into a top cut is much smaller. For example, if there is a top 4 with 16 people, one person will be 4-0, and another three will be 3-1, so you know you need to win 3 games if you lose one to get into the top cut. As we move along the numbers, primarily into the 257-511 range, the numbers expected for each pod in Masters at US Nationals, we will have our 9 rounds as the tournament announcement specifies, and top 32 cuts for each of those pods.8 /// 2 or 3/// Top 2
9–15 /// 3 or 4/// Top 2
16 /// 3 or 4 /// Top 4 or 2
17–31 /// 4 or 5 /// Top 4 or 2
32 /// 4 or 5 /// Top 8, 4 or 2
33–63 /// 5 or 6 /// Top 8, 4 or 2
64 /// 5 or 6 /// Top 16, 8, 4, or 2
65–127 /// 6 or 7 /// Top 16, 8, 4, or 2
128 /// 6 or 7 /// Top 32, 16, 8, 4, or 2
129–255 /// 7 or 8 /// Top 32, 16, 8, 4, or 2
256 /// 7 or 8 /// Top 32, 16, 8, 4, or 2
257-511 /// 8 or 9 /// Top 32, 16, 8, 4, or 2
512 /// 8 or 9 /// Top 64, 32, 16, 8, 4, or 2
9 rounds with a top 32 will typically mean that 7-2 and above will make it into the cut, depending on how many are actually in the tournament.
This means that you can afford to take two losses to make it into the top cut. If you lose your first round, you have to win 7 out of the next 8 rounds to get into the tournament. Well, let's say that you could lose any of the 9 rounds due to poor luck or a bad opening hand. If you have one of those situations occur, and you lose because of your very poor set up, then you have to win 7/8 of the other games.
Can you reasonably expect your deck to do well without adequate consistency?
What if you lose 2 of your games because your set up was slow? You must reasonably expect your deck to then "win out". It is hard to avoid problematic or slow starts, but you must account for them when building a consistent deck. If you have a deck that is allowing too many losing starts, you will have an immense burden for your deck when it does set up. Do most decks even win 7/7 games when they reasonably set up? Not usually.
With this in mind, we want to avoid having bad opening hands, because the first 2-3 turns usually determines the outcome of the match.
What is a bad opening hand?
A bad opening hand is one that does not allow for the deck to achieve its goals. This means that the player is unable to establish its core strategy and begin to succeed in winning. If the player cannot set up an attacker, or attach energy to attack, or have enough pokemon in play, the player will usually and eventually lose. A player has to get set up to win, and in this format people are not taking the proper considerations to do so.
If we play a deck with 6 basic energy, and use 3 roseanne's research, we can calculate the odds of being able to attach an energy turn one. With 6 energy, you are attaching energy going first a little over half of the time. Even with a roseanne's research, you must go second to use it, so only 50% of the time does it increase your opening odds from 6 to 9. With this in mind, if a deck you run must use 2+ energy attachments to attack (like Gardevoir), and you need to attack by turn 2-3 to maintain early game power, then you need to attach an energy turn 1 as often as possible without hurting the space for other needed and assisting cards. A deck like Gardevoir would be best running at least 13-14 energy, so that on average they will be able to open with an "energy out" 90% of the time or so. This means that in a tournament like Nationals, you will admit one time to not drawing an energy and being behind, and possibly losing etc. Any higher than 10% and you will begin to drift into having this happen more than once a tournament. If it begins to lean towards twice a tournament, then your two losses are already accounted for, and you are expecting your deck to perform perfectly which is unreasonable.
Different decks need different energy considerations, but it is important to know the odds of drawing energy, drawing outs to it, and what your ideal odds of drawing them are to be.
With that in mind, one would need to begin to think of the set up in general.
It is important not only to attach energy, but to set up your attacking pokemon. With this kind of information in mind, it is important to play enough pokemon search cards to consistently get out your attacking pokemon in order to maintain your strategy. Cards like Roseanne's Research, Bebe's Search, Call Energy, Pokemon Communication, Pokemon Collector, and Luxury Ball remain some of the best trainers and cards in the game because of their ability to precisely search from the deck desired pokemon, sometimes with exact specificity, and other times with more vague but numerous application.
Something that I dislike seeing is people using less than the maximum number of allowable cards for something that is very strong and consistency boosting. The best card in the format, Luxury Ball, is argued to be the best card because it should be included in every deck.
With only a minor drawback- the inability to search out level X pokemon, the non-supporter trainer can get any other pokemon, basic, legend, stage 1, and stage 2 without any other implications. In this way it has a huge function range with little drawback. One should be in every deck.
Yet I see decks without this card. I see decks that run stage 2 pokemon that only run 3 Rare Candy. I see decks that need a t1 energy drop every game to truly be successful play less than 10 energy and not attach one turn 1 25% of the time. These people are not building their decks properly. These are often the same people who complain about poor luck. The truth is, unless your deck is filled with consistency-boosting cards, you will not have enough outs or probability to set up properly and fulfill the function of the deck. When my opponent is playing Gengar, and prizes 3 Gengar and doesn't play Azelf- he is at fault. Attributing this poor circumstance to luck is not possible, because there exist cards that can usually overcome this difficulty. Azelf LA is such a card for us.
Similarly, if my opponent has all of his Gengar prized, he cannot get them into play. If one does not have the sufficient energy or pokemon in play- which are obtained by consistency-boosting trainers and energy, then one will be operating similarly as not playing an Azelf LA. Much of the luck is in our control. I get tired of people complaining about situations, only to hear that they didn't use call energy, or only ran 3 Bebe's Search, or cut the Rare Candy down to 3.
One must remember that in cutting consistency cards for other 'tech' cards, one is making a small sacrifice towards the ability of the deck to achieve its entire function. If you don't set up, that tech card will be useless. Finding the individual balance and harmony for a deck is extremely difficult, and usually requires extensive playtesting, and I think- analysis of probabilities and tournament structures.
I know at a 9 round nationals where I need to go 7-2 that I will want to attach an energy turn 1 8/9 or more of the time, and I will likely want a card to get basics or an evolution once my basic attacker is obtained 8/9 of the time or more. I can only reasonably allow my deck to accept one loss to poor set up, trying to reduce it further will usually hurt the overall power of the deck by marginally increasing the consistency, and trying to reduce it less will allow too many losses to do well at this large event. I must take this into account, and so should you. When you see a deck that runs no call energy, yet has colorless attack costs, or a deck without luxury ball, or a deck that is using cards like Pokedex or Pokeradar at the expense of having enough precise-search cards like Pokemon Communication, Bebe's Search, etc. to get out the attacking pokemon early and effectively you should CRINGE like I do.
Too many people blame luck more than themselves. In this format, we have an absurd number of cards to allow for optimal consistency. If you don't take advantage of them, or consider them properly, then you will not reasonably do well.
Thanks to R_A for reminding me of what I like to do here- help the community and try to improve things. Trust me, you will have a lot more fun at Nationals if your deck is able to achieve its function, and you need to be willing to dedicate enough cards to achieve such a goal. The number and ratios are up to you to find, but don't be lazy. I want to see more Call Energy and Pokemon Communication out there in the Deck forum, and less Pokedex Handy 910.
Sample Calculations:
Plug n Chug for odds of occurrence said:
Odds of starting with an energy
So, probability of energy= 1-odds of NOT having an energy
NOT having an energy is determined for each of the 7 cards we have.
If we start with 6 energy, then on the first card we draw, there is a 54/60 chance of it not being an energy, but as each card is drawn, this probability slightly boosts. We multiply them all together to get the collective chance of the entire 7 card hand NOT having an energy.
So, if we start with 54/60, when we draw another card- if we assume no energy, it is 53/59, and so forth, until you get:
1 - (54/60)*(53/59)*(52/58)*(51/57)*(50/56)*(49/55)*(48/54)
So, if the probability of NO energy is 45.9, then the probability of YES energy is 1-45.9 or about 54%.
Odds of a LONE 30HP starter in a Jumpluff deck
The deck has the following basics:
4 Hoppip
3 Baltoy
2 Crobat G
2 Uxie LA
1 Azelf LA
1 Regice
1 Unown G
1 Unown Q
1 Luxray GL
It has 5 pokemon with 30HP- 4 Hoppip and Unown Q. The odds of not drawing a HOPPIP/Q is (55/60)*(54/59)*(53/58)*(52/57)*(51/56)*(50/55)*(49/54) = .525437
So, the odds of starting with a HOPPIP/Q in the hand is 1-.525437, or 47.45%.
However, starting with the HOPPIP/Q doesn’t mean that you must play it active, or that you don’t have outs thereafter. You could also start with another pokemon.
Now, we have to figure out the odds of not drawing another basic.
In this list, there were 11 other non-HOPPIP/Q basics, so that’s 11 outs.
The odds of no "out" in the remaining 59 cards in the deck (since we are assuming one of our cards is a HOPPIP/Q) out of the 6 cards left to draw:
(47 / 59) * (46 / 58) * (45 / 57) * (44 / 56) * (43 / 55) * (42 / 54) = 0.238308366
So, the odds of NOT getting an ‘out’ with our HOPPIP/Q is .238, or 24%.
The combined odds of this event (HOPPIP/Q& no other starter/out) would be multiplying the two likelihoods together.
Simply, it is .4745 * .238 = 0.112931
So, it’s about 11.3% chance of getting a lone HOPPIP/Q start.
We SHOULD consider the fact that the deck might mulligan, So, let’s continue the math. The odds of not drawing a basic from a deck with 16 basics would be
(44/60)*(43/59)*(42/58)*(41/57)*(40/56)*(39/55)*(38/54)= 0.0992228933
The deck will mulligan 10% of the time since it plays 16 basics, meaning the deck WON’T mulligan 100-10, or 90% of the time.
(.9/.125) * (.1/x)
X=HOPPIP/Q start after mulligan
.9x=0.0125
x=.0125/.9=.01389
So, the odds of a mulligan and then a lone HOPPIP/Q are 1.4%
So, combined:
The odds of not mulligan and getting a lone HOPPIP/Q are 11.3%, and the odds of mulligan and a lone HOPPIP are 1.4%
So, combined, it is 12.7% of a truly, lonely HOPPIP/Q start.
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tl;dr:
You can't expect to do well at a tournament unless you provide your deck enough consistency, and the consistency you do use must be practical in terms of its space consumption and actual probability of assisting in the deck achieving its main strategy.
tl;dr: DON'T RUN 2/3 CLAYDOL. RUN FOUR CALL ENERGY.
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