Deck size & Probability - A case for (slightly) bigger deck

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Originally Posted by Cruxx

Sure, as a good old min/maxer I still would argue the point that there might be 2 cards you do not need that desperately to make room for those you mentioned.

I might agree in cases where your deck only supports say 2 or 3 overall goals, supported by 20 to 13 cards each. In such a case it's less important to keep to the absolute card minimum since your chances of drawing your goals are still very high, but most decks don't work this way in my experience.

€dit:

It just means that the 2 points decrease from 93% to 91% mentioned in your example shouldn't be neglected (It's almost 30% more likely to draw the card going from 91% to 93%). That's why I gave the example of 5 points around the 50% mark not having the same value as the 5 points around the 90% mark.

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Erm, you still lost me there. Why would a 2% change equates to 30% more likely to draw the card? Do we understand probability differently?

Anycase, cruxx, i seen ur article abt the rule of 6, and i really like it as a framework for deck designing. It helps me to review my thinking abt the card.

However, my emphasis in deck construction is on resource curve: the probability of me drawing a certain card at T2-T5. I see T2 and T5 as the make-or-break turns for every game (though this differs with deck, e.g. a zhanna deck prob can afford to see T7 as the breaking point). In most games, i don't get to draw all my cards which also means that not all the deck goals will be achieved during the game.

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Originally Posted by Atomzed

Erm, you still lost me there. Why would a 2% change equates to 30% more likely to draw the card? Do we understand probability differently?

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Ok, let's retrace our steps here.

We want to show that 1 additional point of percentage has different benefit, depending on the total value we are starting from.

5 point increase around the 50% mark:
47,5% -> 52,5%

We now want to look at the "miss" chance, that we do not draw our card.
100% - 47,5% = 52,5%
100% - 52,5% = 47,5%

This gives us a ratio of
52,5 / 47,5 = 1,11
-> It is 11% more likely to draw the card compaired to the previous value.


5 point increase around the 90% mark:
90% -> 95%

We now want to look at the "miss" chance, that we do not draw our card.
100% - 90% = 10%
100% - 95% = 5%

This gives us a ratio of
10 / 5 = 2
-> It is 100% more likely to draw the card compaired to the previous value.


2 point increase around the 90% mark (your decrease example):
91% -> 93%

We now want to look at the "miss" chance, that we do not draw our card.
100% - 91% = 9%
100% - 93% = 7%

This gives us a ratio of
9 / 7 = 1,29
-> It is 29% more likely to draw the card compaired to the previous value.

-> The higher the total value is, the more important becomes an additional point of percentage.
-> 1 additional point of percentage has different benefit, depending on the total value we are starting from.

QED

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Originally Posted by Atomzed

Anycase, cruxx, i seen ur article abt the rule of 6, and i really like it as a framework for deck designing. It helps me to review my thinking abt the card.

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Glad to see others make use of and benefit from it as well. :)

I don't want to disprove or argue anything you brought up. I just want to get the perception out there that percent points lost in the 90% + area shouldn't be dismissed lightly, since the value lost is bigger than assumed at first glance. The trade-off needs to meet this sacrifice (+devaluation of the other cards/goals). That's all.






€dit on the general topic of deck building:

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However, my emphasis in deck construction is on resource curve: the probability of me drawing a certain card at T2-T5.

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Definitely very important and that is where the refinement part of the Rule of Six kicks in. I don't know if you know the latest version. The Rule of Six has also Six different steps now. ;)

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I see T2 and T5 as the make-or-break turns for every game (though this differs with deck, e.g. a zhanna deck prob can afford to see T7 as the breaking point).

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I agree these are very important turns in many cases, in the case of Moonstalker though especially, you can just put up your "YOU SHALL NOT PASS" sign and work around what you got in your hand.

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In most games, i don't get to draw all my cards which also means that not all the deck goals will be achieved during the game.

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Disagree to a degree. A goal is presented by multiple cards (at least 6 when using my principle), thus giving you a very good chance of drawing cards that support that specific goal you are counting on during T1-T5.

That's a different topic though and I don't want to derail your thread. We can gladly continue it elsewhere, e.g. the Rule of Six thread.

oh great, thanks for contributing towards the discussion.:D

I didn't view it in the form of miss %. What u did was to look at % miss and compare before and after. So the impact may be greater than what I originally think.

I decided to play around with the notion of consistency.

Imagine you have a deck with a dream play of a 2 drop, 3 drop and 5 drop right on time. To make this happen you include 10 2 drops, 8 3 drops, and 8 5 drops. If you compare 41 cards to 39 cards:

The odds of a perfect hand are 69.2% vs 72.9%. Seems pretty close.

But now calculate the odds of hitting that perfect hand at least 2 games out of 3 in a 4 round tournament:

35.9% vs 45.0%. By keeping your deck down to 39 cards you greatly improve your consistency.

Of course there are lots of simplifying choice I made in these calculations, including assuming the player goes first every game :) I'll try for something more complicated later.

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Originally Posted by Ringel

Atomzed:

I'm playing around with the calculator and I'm getting different results than in your OP. Are you sure you aren't mixing sample size (number of cards drawn) and number of successes (number of cards of the right kind in the deck) up?

(Or am I the one who is getting these wrong)

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http://stattrek.com/Tables/Hypergeometric.aspx

Population size = Deck size
Number of successes in population = Amount of specific card in the deck
Sample size = How often was drawn? 6 for 1st player in T1, 7 for 2nd player in T1, 7 for 1st player in T2...
Number of successes in sample (x) = Set to 1 if you want to know the "normal" probability
Last line = That is the % we are looking for, don't excactly know why it isn't the first result line, but you can easily verify with some examples.

Yeah, I don't know what was going wrong, but I was in error. But my edited post should be correct.

The problem with percentages is that every percentage point is a different size.
I think a more accurate representative would be a ratio.
Lets look at how often you will draw what you want.
96% chance of getting what you want is the same as for every 24 games that you draw your card, 1 game you wont
95% chance of getting what you want is the same as for every 19 games that you draw your card, 1 game you wont.
90% chance of getting what you want is the same as for every 9 games that you draw, 1 time you won't
85.7% is 6:1
80% is 4:1
75% is 3:1

I am by no means an expert with any of this, but I don't understand why people don't use ratios..
Ratios can be easily calculated 'on the fly' during a game, and give a more accurate representation.
(I think...)

This article is a horrible, horrible idea. Don't do it. Adaptability is strictly worse than consistently. The only reason you should ever need to adapt to many different gamestates is if you're already losing, and that's because control really doesn't exist in SE. The MOST important thing in any tcg is consistency. Every deck has a plan to win and loses when that plan doesn't pan out, so why would you EVER make it any less likely to get what you need when you need it? If this is the kind of bull being tossed around behind A1, no offense to you guys, but I'm glad I'm not a part of it.

@dndfreak, for the record, i'm not a MtG player. I play yu-gi-oh casually on the console. So I don't have the wealth of experience you have.

I will hold my hand and say that I'm wrong if/ when others point out my error in calculations. And question the assumptions (which Crux and Ringel did).

I'm not sure why you have to drag A1 into the picture though. I mean, just like in the Lands article that you wrote, there were differing opinions, did anyone insult your guild along with it?

But then, if you are happy that you are not in A1, purely bec of this 1 article that 1 member wrote, then go ahead. Personally, I would have like you to be in A1 but time and space wasn't right. Bluejet and Juggernaut was fortunate to have you.

(and you can carry on with your bashing if you want)

Look mate, you start your article by saying or at least implying that it's generally accepted behind closed doors at A1. That's what I have to go on, and that's why I said what I said. I would say the same no matter who decided to slap their name in my sig first. So there you have it.