Discussion The Math on Talonflame

Just to refocus back to the original question - not considering Greninja or how many other basics you might be running - just referring to the simple question:

What is the chance I will get a Talonflame in my opening hand?

It looks like zevkyogre's number is about the same as my number, about 40%. I think tehsquirrel's is about 26%?

Either way, it's pretty clear that it's going to be less than 50% of the time, meaning that if you're basing a strategy off getting TF in your opening hand, you're hoping to get lucky.

It's like in baseball, they use the stat "Wins Over Replacement." You have to ask yourself, are there 4 other cards that would give me more wins than TF? For example, if I ran 4 Lysandre instead of TF, then would that help me win more than TF? If I ran 4 enhanced hammers or 4 team flare grunt instead, would that help me win more than TF?

And there's no math equation that will solve that problem.
 
Mine was 39.09 ignoring the odds of going past 3 Mulligan. It is correct and I used a card probability calculator for the combinations and permutations.

My method is using discrete math to avoid a probability tree as it is not necessary.

@21 times,. You could run 1 basic and 4 talonflame but that doesn't seem competitive. I think it most helpful as an addition to a deck that runs 5 or less small basics.

With N so prevalent it doesn't really help build combos...
 
21times said:
Just to refocus back to the original question...
What is the chance I will get a Talonflame in my opening hand?
It looks like zevkyogre's number is about the same as my number, about 40%. I think tehsquirrel's is about 26%?
Either way, it's pretty clear that it's going to be less than 50% of the time, meaning that if you're basing a strategy off getting TF in your opening hand, you're hoping to get lucky.
Click to expand...

Actually, you are incorrect. Read my stats again. You're saying 40% is the cap at success, but it's not - you run 4 Talonflame, all of the time. You have to, the strategy almost demands it if you are building a deck centered around Talonflame set-up (this is why we got off-topic a tad bit - because there's a discussion of value running non-max count Talonflame.)

Of the 386 million combinations, 115-177 million combinations are ignored because they are mulligans.
Of the non-mulligan combinations, with up to 5 non-Talonflame basics, assuming you run 4 Talonflames in the deck, Talonflame has a 57%-73% probability of showing up and being played.

It is NOT less than 50% success at all. That's a VERY BIG difference, because you failed to account for mulligans, and your probabilities are completely messed up.
You failed to account for the fact that you could get more than 1 Talonflame.
You failed to account for the fact that you have 7 chances to get the 1 Talonflame - which would be 56/60*55/59* etc.

Your math also cited the probabilities with more than4 Talonflame cards in the deck, which is illegal to begin with (56 non-Talonflame cards is the minimum.)

Like I said, Techsquirrel is not off by a lot (he said 37%-39%, I said 40.8%,) but the spreadsheet allows for us to see all of the considerations, which is the only reason I calculated, ran, and uploaded it, and all of the probailities are accounted for.

If you want to consider the viability of running a deck that hinges on Talonflame starting, THIS is the spreadsheet's use (though you can see, that if you run 3 Talonflame with 4 basics, you still have a 52% success rate that the deck has done what it's designed to do.)
 
My calc was correct for 4 froakie and 2 talonflame. I even show the general way of how the probability progresses which was the whole point of my post. Initial impressions in the thread did not account for difference with Mulligans. Your spreadsheet might be a major resource for talonflame players.

I never mentioned running more than 4 talonflame.


[edited post: Misunderstood ZevKyogre's intentions and apologized]

I thought that ZevKyogre was talking about my post in places where he was discussing 21times post. 21times posted a few things that are incorrect, which is ok and happens sometimes, its just important to be able to see that. It was really cool that 21times started the thread because this will be the go-to resource for those looking to optimize talonflame numbers in competitive decks.

I do think talonflame will find a niche in the meta but like I said I think it will be in decks that would typically run 5 or less small basics that could be supported by some setup. Greninja players (I've played at least 25 games in league and online with greninja and probably just as many against it) often end up sacrificing a froakie or frogadier anyhow in the effort of getting setup.
 
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So let me just say this: your analysis is fantastic. Your analysis is far better than what my limited skill set could provide, which was to simply identify what the probability was of getting TF in your opening hand. Your very first hand. I'm going to stand by my math and logic on that. I feel confident that 40% is the probability of that. I don't care about mulligans or other basics, I'm just looking for the chance of getting TF the first time I look at my 7 cards.

My initial analysis intentionally ignored basics and mulligans because, as you have exactly identified, there are literally millions of different possibilities involved in factoring those in. And, again, you have done an absolutely top notch job of analyzing those possibilities. I may have started the ball rolling, but you certainly took it to its fullest extent, something that I do not have the knowledge to be able to do. Your analysis is far superior than mine, and it is far more valuable overall. Mine is certainly very limited, and yours is far more inclusive and useful. Thank you for taking the time and effort for expanding on my limited calculations.
 
What's done is done. But it certainly now lays the foundation for expanding discussion, given what are chances are that talonflame is successful:

Is Talonflame worth it? And what other decks do we see synergy for this reckless set-up followed by 3 completely useless cards?

In a thread elsewhere, people were mentioning fun decks with Talonflame + Archie or Maxie, and 4 Greedy Dice just to see HOW LUCKY they are. It would be interesting, but I think Archie/Maxie tactics are dead post-rotation.

Talonflame set-ups can also be useful for Vespiquen decks - not that Vespiquen needs support (though many argue she does,) but that Talonflame's 3-4 "useless" copies are no longer COMPLETELY useless (combine Talonflame, Klefki, Unown, Combee, Vespiquen, Gible, and maybe the Oddish line as a potential deck list.) The problem is that, once you go to 10 basics other than Talonflame as we cited, the chances of success DO go down to below 50%, so the synergy there is REALLY weak. And then it becomes a crapshoot that we DON'T want to base our deck around.

But, most competitive decks have 8 basics overall, which still leaves Talonflame at a coin toss or better, which is viable to set your deck around as a convenient or expedited set-up. I think anything that relies on 55% success rate or better is fine, which limits you to 4 Talon + 5-6 basics (which is why Frogadier is ideal with Water Duplicates expanding our definition of basic- or basic-counted, because you DON'T need froakie.)
 
Totally agree that Maxie's / Archie's has become worthless. So many other cards that are much more valuable.

I'm running TF in a Vespiquen / Regice / Glaceon EX deck, and I'm seeing TF starts at 41%, 9 in 22 test matches but I have 16 basics. If I start it, great, if not, it's ultra ball fodder.
 
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