This question, like nearly every TCG "what are the odds..." question, is a Hypergeometric Distribution. There is no range associated with the results of this function.
The probability of exactly 1 of 2 possible cards from a 60 card population (a deck) being in a 6 card sample (Prizes) is ~18.3%. The probability of exactly both being there is ~.8%. The probability of at least one being there is ~19.1%.
You can run your own distributions easily in Excel or a Google Doc spreadsheet using the HYPGEOMDIST function. Keep in mind that this function is non cumulative. If, for example, you want to find the result of getting "at least 4 Energy cards in my starting hand" you would need to sum the results of 4, 5, 6, and 7, as HYPGEOMDIST(4,7,12,60) will only tell you the result for exactly 4.
You still fail to understand how the 3-1 line does not have an upper hand on the 2-2 line through pokemon rescues.Since you guys are hung up on yourflawed math skills, lets take this from someone who actually gets paid for it:
With a 2-2 build each half has a 18.3% chance of being prized (roughly 1 in 5). With 3-1 + Azelf, there is only a .8% chance of both Azelf and the 1 being prized.
In the 2-2 build if you have 2 halves prized, you can run 1 Legend with Azelf.
In the 3-1 if 2 halves are prized, you can run 2 Legends with Azelf.
As to the dreaded "Power Spray your Azelf" situation it seems a lot want to lean on, a smart player is going to search their entire deck when they Collector on T1-2. If they find that the 1 is prized, they'll pull out their Azelf and use it BEFORE their opponent can get 3 SPs in play thus avoiding the Spray entirely.
It also sets up quicker and more reliably playing a 3-1. Again to all you neigh-sayers I invite you to try it out before offhandedly dishing on a concept you obviously don't understand and havent tried. It's like you're AFRAID you will see it for yourself how wrong you are.
The chances of both pieces being prized is .8%, not 18.3%, the 18.3% is the chances of one of those cards being prized.
I see what you're saying, you meant that each half has a 18.3% of one card of one half being prized. At first it looked like you were saying that both cards of one half had a chance of being prized at 18.3%.That's for both being prized when there are only 2 in your deck. It has nothing to do with 2 being prized when there are 4 in your deck. The odds are higher on 2 out of 4 (as in 4 Legend pieces)than they are on 2 out of 2 (as in the 1 and Azelf exclusively in this case). You are seeing only what you want to see.
Was entirely wrong. If anything the 2-2 line would allow you to potentially run a legend more often than a 3-1 line would if 2 pieces were prized. In a 3-1 line there are only 3 combinations of what can be prized, and allow you to play a legend without relying on azelf. In a 2-2 line there are 4 combinations. And through this since both 3-1 line, and 2-2 line both have the same possibilities of getting 2 pieces prized, but the 3-1 line has a lower amount of combinations in which you can run a legend line without relying on azelf, the 2-2 line would run more consistently.In the 2-2 build if you have 2 halves prized, you can reliably run 1 Legend with Azelf.
In the 3-1 if 2 halves are prized, you can reliably run 2 Legends with Azelf.
That's for both being prized when there are only 2 in your deck. It has nothing to do with 2 being prized when there are 4 in your deck. The odds are higher on 2 out of 4 (as in 4 Legend pieces)than they are on 2 out of 2 (as in the 1 and Azelf exclusively in this case). You are seeing only what you want to see.
[a bunch of ridiculously large type]
One second...
http://en.wikipedia.org/wiki/Gambler%27s_Fallacy
And did you see my Pythagoras comment earlier? Trust the math.
Otherwise this thread is heading for 'OMG someone is WRONG on the Internet!' territory.
Well, I tested out 3-1 and 2-2 and found that 2-2 was a much smoother, more consistent line to play.
Did that change anything?
FWIM
Results can never change probability. If you flip a coin 100 times, do you expect it to give you 50 heads and 50 tails? No, right? It'll probably be slanted one way or the other. You could easily get something like 60 heads and 40 tails. But no matter how many times you flip a coin, and no matter how often a coin will flip up heads or tails, will that ever change that you have a 50/50 chance for getting heads or tails? Results have nothing to do with probability.Still doesn't change the way it works in actual game play. Try it. Until then you have no actual experience with which to compare the 2 models. Just a bunch of blah blah blah theory. You are taking first hand experience from several different players and totally dismissing it based solely on your conjecture theorem that in no way factors in every aspect of a complete deck.
What he's expecting to happen is specifically called Reverse Gambler's Fallacy, its on the wiki.One second...
http://en.wikipedia.org/wiki/Gambler's_Fallacy
Admittedly, Gambler's Fallacy is a little off of what you're talking about, but it's about the same thing, instead of expecting the odds to even themselves out, you expect them to not even out, which is even more erroneous.
And did you see my Pythagoras comment earlier? Trust the math.
Because the results don't actually tell you what is more likely to work consistently. It won't predict accurately as probability, what's more consistent.Instead of all the headache-inducing maths and science, why doesn't anyone come back and say 'well, I tested out 3-1 and 2-2 and found that 2-2 was a much smoother, more consistent line to play'? I could relate to that.
I mean, if you are playtesting a Legend deck anyway, why not?
Otherwise this thread is heading for 'OMG someone is WRONG on the Internet!' territory.
No, results don't affect probability. How are you not understanding how the coin flip example of results not accurately depicting the actual chances of what will happen? Saying "We aren't flipping coins." has nothing to do with it. If there's a die with 4 sides blue, and 2 sides red, you roll it 100 times, and you end up rolling red more often than blue. From these results, per your take on this situation, we would have to say that red has a higher chance of coming up than blue on this die. I mean red came up more often right? So it must be more likely to come than blue most of the time. We tested it right? That has to be the probability.That's the best you have? Gambler's Fallacy? LOL! There comes a point after hundreds of games that yield the same overwhelming results that what you claim just doesn't apply. I've read the coin flip thing that you and Sabett have trolled all over this and other threads over and over again. We aren't flipping coins. At what point of if I do A B C then X Y Z happens will you stop beating that dead horse?
If testimony from at least 3 different skilled players who have run decks both ways many, many times and which all point to the same conclusion, isn't enough for you to think 'hmm... maybe i should give it a try and just see' then you have real superiority issues that I can't help you with.
It works better. Period. 'Nuff said. I'm done with it. Argue with yourself.
In the event that it does.EDIT: Why are we arguing about something that never will be above tier 3??
That's the best you have? Gambler's Fallacy? LOL! There comes a point after hundreds of games that yield the same overwhelming results that what you claim just doesn't apply. I've read the coin flip thing that you and Sabett have trolled all over this and other threads over and over again. We aren't flipping coins. At what point of if I do A B C then X Y Z happens will you stop beating that dead horse?
If testimony from at least 3 different skilled players who have run decks both ways many, many times and which all point to the same conclusion, isn't enough for you to think 'hmm... maybe i should give it a try and just see' then you have real superiority issues that I can't help you with.
It works better. Period. 'Nuff said. I'm done with it. Argue with yourself.