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Thread: How many Blue cards are needed to support Force of Will?

  1. #1
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    How many Blue cards are needed to support Force of Will?

    Im currently playing 18 blue cards including forces, but im wondering if I need more? is 18 enough? what is the minimum ammount?
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    Nah, more like OJ Simpson being an expert on collectibles and leather gloves. Tiger was just suffering the ill effects of a golf club to the dome.

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    Re: How many Blue cards are needed to support Force of Will?

    Seventeen blue cards is about the minimum you need to reliably Force once; 20-22 blue is roughly the number of blue cards you need to double-Force. IMO, 18 is a little low for my taste, but it should be fine, depending on the deck.

  3. #3

    Re: How many Blue cards are needed to support Force of Will?

    I dunno, I wanna say something like 18 should be fine IF you have something like Top to support it/dig that blue card in the time of need.

    But yeah, generally what Bardo said is right.

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    Re: How many Blue cards are needed to support Force of Will?

    well the deck I play is Team america, and iv changing things to try to get an edge on aggro, and ended up with 18 blue cards. im just wondering if 18 is a good number. i was running 20, but figured that 2 less wouldnt hurt.
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    Quote Originally Posted by umbowta View Post
    Nah, more like OJ Simpson being an expert on collectibles and leather gloves. Tiger was just suffering the ill effects of a golf club to the dome.

  5. #5

    Re: How many Blue cards are needed to support Force of Will?

    18 Counting Force of Will itself is what I think.

  6. #6
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    Re: How many Blue cards are needed to support Force of Will?

    I look at FoW's most important duty as being pulled in the first turn.

    # of Blue cards in a 60-card deck (Including 4x Force of Will): Approximate chance to open with Force of Will + a blue card (including one of the remaining FoW's)

    15: 31.4%
    16: 32.6%
    17: 33.6%
    18: 34.5%
    19: 35.3%
    20: 35.9%
    21: 36.5%
    22: 37.0%

    Remember that you have a 40% chance to open with at least one FoW. Subtraction will show you the percentage of hands where you open with an FoW but no other blue card.

    There are diminishing returns to adding more blue cards for the sake of opening with an active FoW. Moving from 15 to 16 blue cards increases the odds by ~1.2%, but moving from 21 to 22 blue cards increases the odds by ~0.5%.

    That is far from answering your question (which will be deck and metagame specific), but it is a decent starting point.





    peace,
    4eak

  7. #7

    Re: How many Blue cards are needed to support Force of Will?

    The number of blue cards needed is precisely Summation on i[Floor[Exp[Floor[Log[Log[Gamma[18 Union 19]]]]]]!!!!/(2^i)]

  8. #8

    Re: How many Blue cards are needed to support Force of Will?

    Quote Originally Posted by pi4meterftw View Post
    The number of blue cards needed is precisely Summation on i[Floor[Exp[Floor[Log[Log[Gamma[18 Union 19]]]]]]!!!!/(2^i)]
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  9. #9

    Re: How many Blue cards are needed to support Force of Will?

    I've always have been told 16. I believe the initial builds of AfFownity had 16 blue cards to support FOW.
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  10. #10

    Re: How many Blue cards are needed to support Force of Will?

    16 is a very, very low amount. Anything below 16 is just way too unstable, and even 16 will leave you with an inconsistent card.

    18 is enough to get by, though you will run into a lot of situations where you don't have blue.

    20 is comfortable.

    22+ will not only let you Force with a great amount of consistency, but will also give you options in case you have an important blue card you don't really want to pitch.

    A lot of people stop at 18 and think they're "ok" in regards to Force. This has to be taken in context though. For example if you are playing a TFK/Welder synergy deck, and your hand is Force/TFK/S.Titan, you *can* pitch Force but you will probably be crippled by it.
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    Re: How many Blue cards are needed to support Force of Will?

    Quote Originally Posted by Rico Suave View Post
    16 is a very, very low amount. Anything below 16 is just way too unstable, and even 16 will leave you with an inconsistent card.

    18 is enough to get by, though you will run into a lot of situations where you don't have blue.

    20 is comfortable.

    22+ will not only let you Force with a great amount of consistency, but will also give you options in case you have an important blue card you don't really want to pitch.

    A lot of people stop at 18 and think they're "ok" in regards to Force. This has to be taken in context though. For example if you are playing a TFK/Welder synergy deck, and your hand is Force/TFK/S.Titan, you *can* pitch Force but you will probably be crippled by it.
    Data?

    15: 31.4%
    16: 32.6%
    17: 33.6%
    18: 34.5%
    19: 35.3%
    20: 35.9%
    21: 36.5%
    22: 37.0%
    You say that 31.4 is just way too unstable, and 32.6% is the minimum, and then 34.5% is enough to get by and 37% is very consistent? You could scroll up and see that your post added absolutely nothing to 4eak's analysis other than wild speculation and misinformation.

  12. #12
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    Re: How many Blue cards are needed to support Force of Will?

    I've heard numerous things. I think 16 excluding Force is fine. The problem with running less than 18 or 20 total blue cards is that you sometimes just don't have the colors you need or end up blowing it on things that are important. What I mean is like FoW removing FoW or a Brainstorm that you want. If you have more blue stuff, it opens up your options.

  13. #13

    Re: How many Blue cards are needed to support Force of Will?

    This is only meaningful if you actually do the math. Anything else is wild speculation. Unless you do the math, it's ludicrous to say: 31%: too low. 32%, good enough, yay!

    But who wants to do the math? If you don't though, then you'll never find the true minimum. It's a continuum (well up to the discreteness of 1 card in 60), if you're looking to approximate then you might as well just recognize that and pick a number.

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    Re: How many Blue cards are needed to support Force of Will?

    For the record, what we're interested in isn't the odds of having Force + blue card, it's the odds of having another blue card assuming you have a Force. That would be something close to - but maybe not exactly - the aforementioned percentages multiplied by 250% (which is the inverse of 40%, which is the odds of drawing a Force). That would keep the relative difference between different numbers of blue cards the same, but magnify the absolute differences. (It's mostly just a difference of perception, but I think that's a better way to look at it.)
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    Re: How many Blue cards are needed to support Force of Will?

    @ pi4meterftw

    I will gladly admit that the true solutions are clearly mathematical. I disagree with the claim that the math isn't meaningful without the full set of computations though.

    Math will give us some perspective.

    Too many people think they can "feel" the difference between single card choices (X blue cards or X+1 blue cards, for example) when the truth is that they'd need a sizable sample size of testing to validly feel it; and even then, the differences are so small that only someone who had kept perfect records could honestly justify finding a difference. Cognitive science warns us about trusting experience when it comes to understanding randomness--a facet of the world which the human brain is not fit to understand; we see illusions of patterns in randomness all too often. Even Paul Erdos was confused (and originally went ballistic when he found out he was wrong) about the Monte Hall problem--this stuff is not intuitive.

    Math is more than a language here or some ultimately unsolved magic-thought-experiment. Math is a context-anchor for the conversation, hopefully preventing people from making claims they probably shouldn't be making. Math is a simple way to say, "hmm..most of you have never really played enough games (testing each alternative) to validly answer this question". I was originally trying to be diplomatic. I don't think the language (essentially hyperbole) I've seen regarding this question (in several threads) is acceptable given the context. That might go for magic conversation in general. I know I'm guilty of it. We should all be much quicker to admit our ignorance and much slower to claim detailed knowledge (this isn't a crack against absolute truth; I despise relativism).

    As I said in my above post, the answer to this question is context specific. You need to provide the deck, pilot, metagame, etc., and only then can you honestly make a decision (or even an educated guess).


    @ Illissius

    For the record, what we're interested in isn't the odds of having Force + blue card, it's the odds of having another blue card assuming you have a Force.
    Why would this be the best way to look at it?





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    Re: How many Blue cards are needed to support Force of Will?

    Quote Originally Posted by 4eak View Post
    Why would this be the best way to look at it?
    Because you can't change the odds of drawing Forces by including a different number of blue cards in your deck. What you're interested in is the percentage chance that you'll be able to cast the Force of Will which you draw.
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  17. #17

    Re: How many Blue cards are needed to support Force of Will?

    in that case, wouldnt you use the hypergeometric distribution?
    assuming you have at least one FOW in your opening 7,
    probability of being able to use your fow in the first turn is 1-hypgeomdist(0,6,n,59) <-excel has a built-in function
    where n is the number of blue cards in your deck, excluding the 1 fow already in your hand.

    i got the following: (note that a "15" means 16 blue cards)
    15 0.843332274
    16 0.864696055
    17 0.883575675
    18 0.900207721
    19 0.914811469
    20 0.927589749
    21 0.938729788
    22 0.948404032

    probability seems quite high, am i missing something?

  18. #18

    Re: How many Blue cards are needed to support Force of Will?

    Quote Originally Posted by libingboy View Post
    in that case, wouldnt you use the hypergeometric distribution?
    assuming you have at least one FOW in your opening 7,
    probability of being able to use your fow in the first turn is 1-hypgeomdist(0,6,n,59) <-excel has a built-in function
    where n is the number of blue cards in your deck, excluding the 1 fow already in your hand.

    i got the following: (note that a "15" means 16 blue cards)
    15 0.843332274
    16 0.864696055
    17 0.883575675
    18 0.900207721
    19 0.914811469
    20 0.927589749
    21 0.938729788
    22 0.948404032

    probability seems quite high, am i missing something?
    You're okay getting raped 15% of the time?

    @4eak

    I don't see how you can avoid, for one thing, a discussion based on feelings, experiences, and biases without doing the math. Besides the fact that this is a math problem, I see that as an issue with your perspective. What I don't see as an issue with your perspective is your hatred of relativism. I'm surprised anybody is stupid enough to espouse such a misinformed philosophy as relativism.

  19. #19

    Re: How many Blue cards are needed to support Force of Will?

    Quote Originally Posted by Forbiddian View Post
    Data?

    You say that 31.4 is just way too unstable, and 32.6% is the minimum, and then 34.5% is enough to get by and 37% is very consistent? You could scroll up and see that your post added absolutely nothing to 4eak's analysis other than wild speculation and misinformation.
    My data is thousands upon thousands upon thousands of games worth of experience.

    If you want to look at it from a percentage point of view, think of it this way.

    ~40% chance to have Force of Will in opening 7.

    % chance to have a blue card with that Force:

    15: 31.4%
    16: 32.6%
    17: 33.6%
    18: 34.5%
    19: 35.3%
    20: 35.9%
    21: 36.5%
    22: 37.0%

    What we're concerned about is having a Force of Will and not being able to use it. What % of the time will we have Force of Will and nothing to fuel it?

    With 15 blue cards, we'll have Force about 40% of the time and Force with a blue card about 31.4% of the time. This means that about 21.5% of the time we draw Force in our opener it will not be castable. In other words Force is only reliable about 78.5% of the time in the opening 7.

    With 22 blue cards, we'll have Force about 40% of the time and Force with a blue card about 37% of the time. Force will not be castable about 7.5% of the time with this approach. Force jumps from a 78.5% chance of being reliable up to a whopping 92.5% chance.

    The consistency and reliability of Force jumps by a full 14%. In a 20 game stretch, which would a reasonable expectation in a tournament, with 22 blue cards you'll see Force being useful in about 3 games that a build with 15 blue cards would not have a useful Force. That's like an entire match right there, and the difference between making top 8 or scrubbing out (they call it scrubbing out for a reason...).

    So yea, I'd say I am spot on and I wasn't spouting misinformation or wild speculation.

    Furthermore, math will never be a complete answer for this because there are simply way too many factors to take into account. Card manipulation, not using Force on the first turn but perhaps the 2nd or 3rd turn, possibly hard casting Force later in the game, and various other things will contribute to the effectiveness of the card.

    Don't be so quick to discount first hand experience, especially when that experience isn't given as a cold hard fact but rather as a general guideline for others to make their own decisions.
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  20. #20
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    Re: How many Blue cards are needed to support Force of Will?

    @ Illissius

    Because you can't change the odds of drawing Forces by including a different number of blue cards in your deck.
    Clearly, this just isn't entirely true (although it is almost always true of the opening hand). It really depends on what blue cards you're choosing to use. Cards like Brainstorm, Ponder, Fact or Fiction, Standstill, Ancestral Visions, Fathom Seer (ya rly ;P), Silvergill Adept, Solidarity's list of interesting draw effects, Fire/Ice, etc. all affect the odds of drawing Forces throughout the game as well.

    My problem is that assuming force is in your hand really doesn't represent what is actually happening in the game. We would be overestimating the value of Force if we assumed it was in our hand in every opener, and this would certainly change how we value the cards which support it. I definitely prefer adding (rather than removing) context to this problem.


    @ pi4meterftw

    You're okay getting raped 15% of the time?
    Why should we not say you are getting raped 68% of the time instead? If they have the turn 1 kill (or eventual game-winning bomb) on you, then you either have FoW+Blue card, or you don't.

    I don't see how you can avoid, for one thing, a discussion based on feelings, experiences, and biases without doing the math.
    Assuming that no one can solve all the math, then you are assuming that we must use feelings/experience/biases, right? We are forced into that position. I didn't say I wasn't interested in anecdotal evidence and experience that hadn't done all the math--but I'm uninterested in some claims which I know can't be made because of the math I do have (you said much the same above). I just think we should be more careful about the conclusions we draw. I think math is more useful than you implied, even if only it helps us to weed out improper, hyperbolic claims.

    I think with enough testing (and proper recording of results) you may be able to arrive at some conclusions. My point was that nobody had done enough testing to answer this problem, and as they hadn't solved the entire math problem (which includes so many more factors), then we probably should be more careful with our language. Some people talk about "the blue count for force" as if they are dealing with the facts instead of outright admitting these are guesses, that was my problem.

    Of course, the entire math problem is far too difficult to solve. Yes, we can solve some pieces of the puzzle, and as both you and I have pointed out in this thread, that isn't enough to really arrive at the perfect answer. The math might still be a guide though. So, while we don't know the answer, we at least do have a way to gauge (from the math) some details about the value of experience and how much testing (at a minimum) might be required to draw certain conclusions.

    My response to your post was that the math, indirectly, was more useful than you implied. Not much more really; I agreed with the rest of your post =).


    @ Rico Suave

    My data is thousands upon thousands upon thousands of games worth of experience.
    Wait, you tested thousands of games at each: 15 blue cards, 16 blue, 17, 18, 19, etc.? You kept great records of this? Are you sure you aren't being just a little biased? These aren't large percentages we are talking about -- 1 or 2 card differences, especially for an event which we don't necessarily pay perfect attention to throughout our testing and experience, is not very easy to 'feel'.

    What we're concerned about is having a Force of Will and not being able to use it.
    If reliability is understood in terms of the opening hand (which I will admit, there is more to the card), then we cannot understand its value by assuming it is in your hand and discounting the times it wasn't in your opening hand--which is what you've done.

    The reliability of FoW in the opening hand begins at a 40% ceiling. You can't make it more reliable than that, it only goes down from there.

    Take a different example:

    If I only have 1 Battle of Wits added to my 299 Island deck, I can't really understand the reliability of casting Battle of Wits by assuming it was already in my opening hand. I must understand it in a broader context, I need to account for the odds of drawing that Battle of Wits itself. Likewise, we need to take into consideration the odds of drawing FoW itself to help us understand how we should go about supporting it. Unlike Battle of Wits, which actually wins the game, FoW may or may not be as useful (compared to the rest of our deck) in helping us win, and with only a 40% chance to see it in the opening, we must give thought to the other cards in the deck. Perhaps slots which would have supported FoW could have been used more wisely for other functions that don't support FoW.

    Don't be so quick to discount first hand experience, especially when that experience isn't given as a cold hard fact but rather as a general guideline for others to make their own decisions.
    I'm sorry, you aren't offering just "general guidelines". I agree when you say say this:

    This has to be taken in context though. For example if you are playing a TFK/Welder synergy deck, and your hand is Force/TFK/S.Titan, you *can* pitch Force but you will probably be crippled by it.
    However, you extended your anecdotal evidence too far. Your language included:

    very, very low amount....way too unstable....enough to get by....spot on....That's like an entire match right there, and the difference between making top 8 or scrubbing out (they call it scrubbing out for a reason...)
    This was the problem. These aren't general guidelines. You setup a blue count list, and ran through them like these were facts, not anecdote and your experience.

    The more I play this game (and think about it), the more I realize how much I don't (and will likely never) justifiably know.





    peace,
    4eak

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