Discussion The Math on Talonflame

2

21times

Aspiring Trainer
Member
Hello fellow beach bums,

By my calculations, the math on getting Talonflame in your opening hand is a 40% chance:

Non TF cards | Total number of cards | Chance of NOT pulling TF
56 | 60 | 0.933333333333333
55 | 59 | 0.932203389830508
54 | 58 | 0.931034482758621
53 | 57 | 0.929824561403509
52 | 56 | 0.928571428571429
51 | 55 | 0.927272727272727
50 | 54 | 0.925925925925926

60.05% chance of NOT getting in your opening hand.
 
Underrated post. You da real mvp
 
But its not just about getting Talonflame in your hand, you also have to account that you don't get any other basic Pokemon which would result in a mulligan. So these percentages have to be unique for each # of basic pokemon a deck might run.
 
Not really. You can still play Talonflame as your active and Bench a basic like normal.
 
PMJ said:
Not really. You can still play Talonflame as your active and Bench a basic like normal.
Click to expand...

No, you're missing the point. Although you have 60% chance of not getting Talonflame in your hand, what really matters is the chance you don't get Talonflame and do get another basic. A deck with only 4 Talonflames has a 100% chance to start with Talonflame.
 
In theory that is true, but you cannot run a deck with no basics and 4 Talonflames.

Mulligans don't increase your odds of drawing a specific card.
 
gracebond said:
In theory that is true, but you cannot run a deck with no basics and 4 Talonflames.

Mulligans don't increase your odds of drawing a specific card.
Click to expand...

True, you must have 1 basic. Some rough math, if you had a deck with 1 basic and 4 talonflame, you're 4x more likely to draw a talonflame if you choose only 1 card. All other hands are mulliganed if you got neither the basic or talonflame. Isn't that scenario then a 80+ % chance you'll start with talonflame?
 
dbussert said:
No, you're missing the point. Although you have 60% chance of not getting Talonflame in your hand, what really matters is the chance you don't get Talonflame and do get another basic. A deck with only 4 Talonflames has a 100% chance to start with Talonflame.
Click to expand...
That's not what the question is. The question is, what are the odds that I get Talonflame in my opening hand?

It doesn't matter what the other six cards are; only that at least one of them is Talonflame.
 
dbussert said:
True, you must have 1 basic. Some rough math, if you had a deck with 1 basic and 4 talonflame, you're 4x more likely to draw a talonflame if you choose only 1 card. All other hands are mulliganed if you got neither the basic or talonflame. Isn't that scenario then a 80+ % chance you'll start with talonflame?
Click to expand...

That is true, but it's a fickle strategy to do so. You can only ever cheat in one Talonflame. At that point it is a 2 Pokemon deck.
 
Yay for numbers (although I'm not too hot on the statistics thing)!

My view has always been that Talonflame is not worth it, because if you don't start with it then it's somewhat of a waste, and if you do start with it and go second your opponent can just hit the N and ruin your day. Although if we're going pure theory here, I guess the "competitive reality" doesn't have much weight, but another quick point in that vein would be that cutting down to minimum numbers of Basics makes absolutely no sense at all.

So returning to theory... if no Basics isn't possible, and low numbers of Basics makes no sense, then we can assume that we'll have somewhere between five and ten Basics in a standard deck? Doesn't this actually further cut the odds of getting Talonflame in your opening hand, as you have an equal / higher chance of hitting another Basic in your opening hand, and once you have that hypothetical hand Gale Wings is useless. (If anyone want to give me a quick statistics lesson as well as a schooling on Pokémon theory, I would not object.)
 
50 to 60% failure rate is where the game should run. Unfortunately, we have been playing in a climate of 5 to 10% probability of failure rate. Right now 40% is a hard sell, after worlds it might not look so bad. My suggestion is to re-post this after worlds. There might be different opinions. Don't know, but after worlds a 40% success rate might not look so bad.
 
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One example would be say Greninja that doesn't run octillery there are only 4 basic pokemon on the deck (4 froakie). A common problem is getting benched out (donked), or mulligan too many times. With talonflame you have a better opportunity to get greninja setup even in the face of an item lock and you can start with a 130 hp body instead of a 60 hp one.

If you ran 2 talonflame then 2 out of your 6 'basics' are talonflame so it would be safe to say that a minimum of 33% of starts could be with talonflame (not accounting for hands that contain more than 1 basic).

The number of basics matters when calculating talonflame beyond just drawing it into your opening hand, especially when the deck runs a low number of basics. In order to closely calculate the odds you have to take into account the potential to mulligan a few times (after that it becomes statistically less significant) and then draw it. Since you shuffle the same cards and draw the same number when you mulligan then it looks like this:

(Odds of getting talonflame in opening hand) OR (odds of mulligan which is basically odds of not getting a basic in opening hand AND odds of getting talonflame) OR ( odds of mulligan AND odds of mulligan AND odds of getting talonflame)

in greninja RUNNING TWO TALONFLAME this is:

(22.14%) + (45.86% * 22.14%) + (45.86% * 45.86% * 22.14% )
(22.14%) + (10.15%) + (4.66%) [ + 2.14% if you calculate the 3rd mulligan, but any other deck with > 4 basics it doesnt really matter ]

36.95 or really a minimum of 39.09% in Greninja.

In a deck that runs a more typical count like 10 basics:
(22.14%) + (19.06% * 22.14%) + (19.06% * 25.86% * 22.14%)
(22.14%)+ (4.22%) + (.8%) + [ 0.15% with 3rd mulligan...]
27.16% or a minimum of 27.31% with 10 basics and 2 talonflames...
 
I am playing around with Talonflame in the TCGO and when I draw Talonflame but no basics on my first hand the game forces me to mulligan. So how is the ruling? Do you mulligan if Talonflame is your only pokemon or is the game wrong?
If the game is working as intended, the card seems kinda worthless as a 0-0-4 to me...
 
badIuck said:
I am playing around with Talonflame in the TCGO and when I draw Talonflame but no basics on my first hand the game forces me to mulligan. So how is the ruling? Do you mulligan if Talonflame is your only pokemon or is the game wrong?
Click to expand...
PTCGO is wrong in all kinds of ways. If Talonflame is the only "basic" in your hand, you may start with it, or you may mulligan. It should be your choice.
 
You know what talonflame is good for though? Expanded vespiquen
 
I'm bumping this because of Worlds. I posted this on the TCGO Forums page. Slightly modified)

Before reading this post, please review or learn from another site what permutations and combinations are, and you should know basic probability.

We have seen in Worlds that Talonflame's use has been limited to...Greninja decks. I have not seen them in any other matches, and I don't see any decklists that have Talonflame.

The new Talonflame from Steam Siege allows you to play the Stage 2, free-retreat, one-energy attacker down as your facedown active Pokemon - not on the bench, no use if it is picked up in Mulligan.

The opening hand has 7 cards, pulled from a 60 card deck: 60C7 = 386,206,920 different combinations. EXCEPT that some of those cards are duplicates obviously (2 BREAKS, 4 Frogadier, 4 Greninjas either as 1-3 or 2-2, energies, etc) and you have 4 Talonflame in the deck.

We don't care, believe it or not - it is still 386.2 million combinations possible. Cool!

How many combinations have at least 1 Talonflame, considering we have either 0, 1, 2, 3, or 4 Talonflame?

The answer is...not as simple as I (and the original posters) originally posted. It actually depends on how many basics you have aside from Talonflame.

For 2 non-Talobasics (2 Froakies) - About 177 million give Mulligans. Another 54.8 million more give non-Talonflame starts. About 29 million give Talonflame + 1 other starter. 122 million give you one Talonflame, and the rest of the cards not playable. (This leads to an unfortunate situation where you could land your 2 Froakie in the prize cards, which you don't want.)

But ignoring Mulligans because you reshuffle your deck, you have 209 million combinations that I count for the stats.

About 1 in 4 - 26.2% chance of all 4 Talonflame being dead-weight in a deck.

BUT, if it works, you have a chance to set up Froakie, you have free-retreat, you have a chance to pick off a REALLY weak basic AND pick up any 2 cards you need (And then have them N'd next turn
ohmy.png
)

It is still better than having any other basic in the deck, where they might go out in play, and give you a dead hand with something cruddy like Regice, or Articuno, or worse - a free 2-prize hit off of Shaymin
sad.png


(Can anyone with a better understanding of probability confirm that I didn't oversimplify by ignoring duplicates in the deck?)

I actually have a GoogleSheet that will show you the hard numbers. https://drive.google.com/open?id=1qEpLS7HleRsHqCSMYQoFdmuklYMNtei5jYwR9BiM-ZE If I'm allowed to link.

HOWEVER, because I actually calculated this, I'd like to post it as an article, be a featured article of the month or whatever, and get a booster box, if people think it's good.

EDIT: the link has been updated with a new uploaded spreadsheet. With this link, you can actually see the combinatorics in the calculation, and it was hard to copy and paste the data on down with the modifications. https://docs.google.com/spreadsheets/d/1HTfq8DomTMpOaoI243SyTF5MFqExrYirtB8SNo-m698
Sheet 1 has 4 Talonflame and up to 5 other basic Pokemon. Due to a request / conflict of numbers in other forums, I also did up to 10 non-Talo basics (sheet 2,) and up to 10 non-Talo basics with only 3 Talonflame (sheet 3,) 2 Talonflame (sheet 4,) and with only 1 Talonflame (sheet 5.)
 
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I'm updating my post to reflect that it is 21times that has his math oversimplified.

I don't know if you're wrong, techsquirrel - but I will look through the math (you are a bit off)
But it's almost pointless to run non-max count Talonflame, when you are relying on it as much as the Greninja decks are.
I'm sure I can run the Spreadsheet again.


Edit: I DID run through the numbers, really simple edit, I can upload another one.

Running 2 Talonflame, 4 Froakies (you don't have to run this many with Water Duplicates and Splash Energy, but I'll run it on your conditions):
Of the 386 million hand combinations, 209 million are not mulligans (177 million are).
Of those 209 million non-mulligan combinations, 59% of the hands will come up without a Talonflame. 26% will have only Talonflame, while just under 14.7 % will have Talonflame + 1 other-basic at least (Froakie in your case, or maybe a Jirachi in another variant).
 
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One thing to consider is running more talonflame run into diminishing returns. There are those times where you start with one and then run into or draw into them through the game (or have 2 in opening hand for instance). My first guess for a good number was 2 but I guess it was fairly popular at worlds, I still don't know if I would run more than 3. I guess you could go 3 froakie and 3 talonflame which would make it reasonably easy to get froakie going while being more likely to start talonflame. TBH it's not that amazing as they have printed 130 hp basic non ex with similarly powered attacks taking into consideration it never hits for weakness and you gotta either be dedicated or start it. The best thing is the free retreat, too bad it can't wear a FFB!
 
ZevKyogre said:
I'm bumping this because of Worlds. I posted this on the TCGO Forums page. Slightly modified)

Before reading this post, please review or learn from another site what permutations and combinations are, and you should know basic probability.

We have seen in Worlds that Talonflame's use has been limited to...Greninja decks. I have not seen them in any other matches, and I don't see any decklists that have Talonflame.

The new Talonflame from Steam Siege allows you to play the Stage 2, free-retreat, one-energy attacker down as your facedown active Pokemon - not on the bench, no use if it is picked up in Mulligan.

The opening hand has 7 cards, pulled from a 60 card deck: 60C7 = 386,206,920 different combinations. EXCEPT that some of those cards are duplicates obviously (2 BREAKS, 4 Frogadier, 4 Greninjas either as 1-3 or 2-2, energies, etc) and you have 4 Talonflame in the deck.

We don't care, believe it or not - it is still 386.2 million combinations possible. Cool!

How many combinations have at least 1 Talonflame, considering we have either 0, 1, 2, 3, or 4 Talonflame?

The answer is...not as simple as I (and the original posters) originally posted. It actually depends on how many basics you have aside from Talonflame.

For 2 non-Talobasics (2 Froakies) - About 177 million give Mulligans. Another 54.8 million more give non-Talonflame starts. About 29 million give Talonflame + 1 other starter. 122 million give you one Talonflame, and the rest of the cards not playable. (This leads to an unfortunate situation where you could land your 2 Froakie in the prize cards, which you don't want.)

But ignoring Mulligans because you reshuffle your deck, you have 209 million combinations that I count for the stats.

About 1 in 4 - 26.2% chance of all 4 Talonflame being dead-weight in a deck.

BUT, if it works, you have a chance to set up Froakie, you have free-retreat, you have a chance to pick off a REALLY weak basic AND pick up any 2 cards you need (And then have them N'd next turn
ohmy.png
)

It is still better than having any other basic in the deck, where they might go out in play, and give you a dead hand with something cruddy like Regice, or Articuno, or worse - a free 2-prize hit off of Shaymin
sad.png


(Can anyone with a better understanding of probability confirm that I didn't oversimplify by ignoring duplicates in the deck?)

I actually have a GoogleSheet that will show you the hard numbers. https://drive.google.com/open?id=1qEpLS7HleRsHqCSMYQoFdmuklYMNtei5jYwR9BiM-ZE If I'm allowed to link.

HOWEVER, because I actually calculated this, I'd like to post it as an article, be a featured article of the month or whatever, and get a booster box, if people think it's good.
Click to expand...
This is actually very cool. I for one would be happy to see it published
 
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