2000 Posts! YAY ME! Moving on....

A lot of people like to deny the fact that Math governs (or at least SHOULD govern) everything we do concerning the Yu-Gi-Oh TCG. I'm going to examine some frequently asked questions, and hopefully answer them once and for all based on the laws of Mathmatics.


1. Should I keep my deck to 40 cards, or is it ok to go over?

It doesn't take a math genius to determine that the fewer cards you have in a deck, the better chance you have at drawing any given card. Is this a good thing?

In a standard CC deck, I would probably say that is really doesn't matter. The strength of a CC deck is that every single card can operate independently reducing the chance of drawing a "dead hand". The deck isn't trying to draw into any specific card, it just works with what it topdecks each turn. If we say that each card is equally important to the deck, it really doesn't matter if you run 40 cards, or more than 40 cards.

Now let's look at Combo Decks. This includes Cyber Stein, Macrocosmos, Dark World, and many more. In these decks, certain cards are reliant on certain other cards to operate optimally. Unlike the CC deck, every card isn't equally important to the deck, at least not at a given point in a game.

40 card CC deck:
After drawing a hand of 5 cards, there is a 35/35 chance that a good card will be topdecked.

60 card CC deck:
After drawing a hand of 5 cards, there is a 55/55 chance that a good card will be topdecked.

In both cases there is a 100% chance that a good card is drawn.

40 card Dark World deck: for the sake of simplicity, we'll assume that only one card that can trigger Dark World effects is main decked.
After drawing a hand of 5 cards, there is a 13% chance that the card needed to trigger Dark World monsters was already drawn, and a 3% chance that it will be topdecked.

60 card Dark World deck: for the sake of simplicity, we'll assume that only one card that can trigger Dark World effects is main decked.
After drawing a hand of 5 cards, there is a 9% chance that the card needed to trigger Dark World monsters was already drawn, and a 2% chance that it will be topdecked.

Obviously, if you are running a Dark World deck, you'd want to run more than one card to trigger them. This would increase all of the percentages porportionally, therefore still giving the 40 card deck the edge.

Are those percentage differences enough to warrant going down to 40 cards? I think that with luck as such as overwhelming factor in this game, it is foolish to not play with the odds as much as possible.

Also note, I'm not advocating running 60 card CC decks, I'm just trying to make the point that running extra cards will affect a CC deck less than a combo deck.
(As a side note, this is why I always laugh when people suggest raising the deck minimum to 50 or 60 cards as a way to fix the game. That "solution" would only further cement the established CC deck.)



2. Why do people always do things the quick and easy way. Why can't people try different combos?

First, we have to establish the two different kinds of combos, soft combos and hard combos.

In a hard combo, all the pieces to the combo are generally useless when used outside its specific combo. That means that until you draw every piece of your hard combo, you are stuck with dead cards. Because of the tremendous risk involved, these combos must be extremely game-breaking (ideally game-WINNING).

In a soft combo, all the pieces to the combo have uses outside its specific combo. This means that if you don't draw all the pieces to your combo, there is no problem, because you still have a perfectly useable card in your hand. Because of the reduced risk involved, these combos don't have to be quite as game breaking, but should still be advantageous.

What does this mean?...

I'm sorry if you don't like this (actually, I'm not) but most hard combos are mathmatically inefficient. The basis for all other hard combos is Cyber Stein. Cyber Stein requires three cards, and provides nearly assured victory. This means that if you are running a three card hard combo that doesn't provide nearly assured victory, your deck is inefficient. If you are running more than a three card combo, even if it does provide nearly assured victory, your deck is inefficient. If your combo can still be considered efficient by those two standards, you must next look at whether or not any of the cards to your combo are restricted. Then you must check to see if any of them are reasonably searchable. Neither Cyber Stein, nor Megamorph, nor Giant Trunade are restricted. Cyber Stein is searchable by Sangan and Mystic Tomato, and Megamorph is searchable by Iron Blacksmith Kotetsu. If any of the cards to your combo are restricted, the probability of drawing the pieces is lower than the probability of drawing the pieces of the Cyber Stein combo.

Soft combos are totally different. Soft combos are somthing that good deckbuilder look to take full advantage of whenever possible. One of my current favorite soft combos is Last Will + Exiled Force. Last Will is a good card. Exiled Force is a good card. Together they produce a great effect. If I only draw one of the two, it doesn't matter, because they can both still be used in a handful of other situations. You won't get stuck with either one in your hand. Because of this, the probability of drawing your entire combo is irrelevent. If you happen to draw it, great. If you don't, you're still in good shape.


3. Card Advantage

I preach about this all the time. Either master it, or lose.

Some people get angry when someone else says something like, "that card is a -1, therefore it sucks." In nine out of ten cases, that person is correct. It's unfortunate, but it's what we are forced to work with. CARD ADVANTAGE WINS GAMES. PERIOD. It isn't a big secret as to why. It actually makes perfect sense. If I have six cards in my hand, and my opponent has three, and neither of us has any cards on the field, I am at a huge advantage. I have six options of what I want to play. My opponent only has three. Because I have a larger variety of choices as to what kind of play I want to make, I am at an advantage.

Some people will argue back something to the effect of, "well, what if you have six cards that you can't use, and your opponent has three good cards? Then THEY have the advantage." Yes, that's true, they will have virtual card advantage over you, I can't argue with that fact, but how often do you really think that will happen? Should people build their decks with the goal of letting their opponent have twice as many resources as them, and then hope that they have all unuseable cards? Of course not. If you can get six cards to your opponent's three, I promise that you will win A LOT more games than you lose. That's perfectly logical.


4. In Conclusion...

Good players know that if you are trying to draw certain cards, running 40 cards is ideal. They know to avoid hard combos to prevent bad hands, and to look for advantageous soft combos. Most importantly, they know how to get and keep card advantage during a game. These things aren't my opinion, they are facts that can be reached by understanding math.


Now I'd like to hear your opinions. If you agree with what I said, I'd like to hear it. If you don't, I'd like to hear it even more. If you think my reasoning takes the fun out of the game, I DON'T want to hear it. I'm primarily speaking to players looking to get better, not ones just looking to have fun.

Thanks for reading.

I like this Article alot and therefore i dont have much else to say about it.

All i can say is that i do agree with everything you said about Advantage. Every Deck should use 40 cards and all cards should range themselves in the 1 for 1 advantage or if posible, 1 for 2.

Great Article, I'll give it 15/10

I definitely agree with most of what you said as I have shown I am a big supporter of this kind of logic. The only thing I would disagree with is your 40 to 60 card deck in CC. As long as the minimum stays at 40 it will be best to stay around 40 all the time. This is simply because the number of the best cards in the game are limited in number and the better chance you have at drawing them early the better off you are. Your chances of having to put slightly less useful cards in your deck to reach the 60 card deck would hurt the effectiveness overall. The chance of drawing Snatch Steal, Breaker, etc would be much lower than in a 40 card deck. If your actual point of this was just on the fact some people want to raise the deck minimum to 60 I guess I would agree with your point there, CC would get the boost yet again. I did enjoy your article.

I agree with you. I was just making a comparison.

Very Good. It was rather interesting. However, there are certain things that need to be said.

While most people will say "Card Advantage is better than life points" (And they are usuall right) thats not always the case. Take, for example, a burn deck. Not many Burn decks play mathematically (Card Advantage-wise i mean), simple burn cards such as Just Desserts, or Ojama trios are all -1, with the possibility of a 1 for 1. Now burn decks arent very successful, so most player automatically blame it on the Card Advantage issue. If you cant keep good resources, you cant keep a board, aka you lose. But is keeping a good board necessesary? If you are staring at a Jinzo, D.D Warrior Lady, Dark Ruler Ha-des, and Horus the Black Flame Dragon Lv 8 because your opponent wasted his life points all the way down to a measly 100 points and you topdeck Cannon Soldier. You win. The card advantage, field advantage, all becomes irrelevant. This allows me to make the two following statements.

1. Card Advantage DOES NOT equal Victory. It equals a passage to victory.
2. Lifepoints > Card Advantage is a possibility if enough damage is dealt.

Lets deal with the first statement. If we go back to the Cannon Soldier example, we can see that the player with Jinzo and all the othe rmonster has the upper advantage. If you have that, chance are you have good, and option full, hand too( if the other player has managed to stall out some how). However, Cannon Soldier finished you off. What happened? I thought Card Advantage meant Victory. The fact is that no. What Card advantage does is give you a usually safe passage way towards victory. It is mathematically the best option. THe more options you have, the more answers you have to problems. However, we cannot forget the cards themselves. For example, when some people heard about Graceful Charity + Dark World(Goldd) they thought "Wow its a +2. Pot of Greed was a +1 and it was BANNED!" however, probabality wont lead to that happeninng often ( excluding in Dark World of course). However what we can say is that while Card Advantage is great, we cannot delve ourself into it. We have to use it as a way to Victory. Not as Victory itself.

Now for my second statement. Using the same Cannon Soldier example, what happen to the almighty Jinzo, Horus, D.D Warrior Lady, and Ha-des? A game mechanic( sorta) threw them away. Thats because while most player trade blindly their Lifepoints for Card Advantage they miss out on certain things. It doesnt matter how many cards you have if you left your Spirit Repear in attack mode and I summon a monster with a high attack that can take down all of your life points. The thing is this: Lifepoints,in theory, are worth more than Card Advantage. However, in reality, you can not damage lifepoints, if you are Card Advantage is low(You cant damage them if you have nothing to damage them with). So how do we fix this? Inflicting the most damage possible using the least amount of cards. While you still recieve several -1's( such as from Reflect Bounder, Magic Cylinders, Ceasefire), at the end of the game what matters? The winner. It doesnt matter the Card Advantage, the Mass Number of +1's or Mass Number of -1's, it matters who won.(Or had fun, i am tallking in a tournament point of view)

Thats my 2 cent. Take em, or leave em.

I knew I had to read this as soon as I saw the word "math", because math is fun!

Anyway, to the point. I'd like to breakdown my reply so it's organized.

I hope you understand that your statistics on the cookie cutter deck is biased. Sure, I understand why you'd say that that each topdeck is 100% guaranteed to be a good draw, but I can't whole heartedly agree because of my conflicting views on the cookie cutter deck and on the numerous other possible draws. I'd like to use Mobius as my first example. It's your standard tribute monster that finds its way into most decks. However, I would not consider that a 100% good topdeck, according to your calculations. All cards in the cookier cutter deck, though they are in the deck because they have probably one of the greatest individual effects in the game, are still a part of a larger "cast", where each "character" has a specific role to play. Mobius's role is primarily spell/trap destruction. Most probably don't even care if it gets Bottomless-ed when summoned. As long as it took out the opponent's (or yours if you want it to) spells and traps, it did it's job. But to get it to do it's job, another card needed to be on the field for Mobius to do its job (thus not always making cookie cutter cards +1 or 0). My second example is Chaos Sorcerer. Sure, it's unrestricted and it's a great card, but it depends on other cards in order for it to do its job. If you so happen to draw all three, though the chances are small, then that automatically removes Chaos Sorcerer as one good, possible, future topdeck. Then what would take it's place? A Nobleman of Crossout I suppose, which is not always guaranteed to be good topdeck.
Basically, my main point is that cookie cutter decks can't always be believed to contain good topdecks all the time.

My second point under #1 is in regards to the imaginary Dark World deck. Yes, the topdecking probabilities of drawing that one card are very small, but don't forget that they increase after every draw. From a purely mathematical standpoint alone (not factoring luck, skull, or any of that junk), that puts you in a greater position every turn that passes to draw the card, so it is not as low as it seems, only initially. In addition, another thing to keep in mind that the probabilty of topdecking that one card in a 40 card deck grows much faster than in a 60 card deck.

Actually, I think the basis for hard combos should always be relative to the Magical Scientist FTK rather than Cyber-Stein. Cyber-Stein requires alot more preparation on your part and passiveness on the opponent's part, and it is only the next best thing to what is probably the best combo card in the game (Magical Scientist) because Cyber-Stein is nearly as quick, that's all.
And I'm trying to find out where the math is involved in this point. Sure, I understand it to be a great point, but what are you trying to explain? Resource accumulation and management? If that were the case, then I'd have to say the hard combo is better than the soft combo since resource management involving the hard-combo leads to the ultimate goal, victory. Sure, hard combos are harder pull-off, so you can say it's a give-and-take situation where they ultimately balance out. Soft combos, on the other hand, are basically less efficient means to the end, assuming you even get the ending you want, since you don't get to the end after pulling off the combo.

Don't forget, card advantage isn't limited to how much more one has over the other in regards to hand count. When a person with three cards says they have the advantage over the person who has six cards because the six card person has nothing but useless cards in hand, then they have the advantage. You stated that already, I know, but it seems as if you totally disgarded that situation after considering it based only on the numbers of cards in the hand. I see it as this, there is always a way to generate a counter measure to the opponent's card advantage with field advantage. Then it's not so clear cut. The best example I can think of is the stall-burn deck. In my experiences, I've grown to learn that stall-burn decks don't wait for anything. They put all the stall and burn they can and let it go to work. By the end of turn 2, you may be down by three cards in the hand, but so what? If the deck you designed is providing more advantage on the field, which is where most of the action takes place, then you are good to go.

I liked reading it, but it seems to me as more of a reminder about what principles you think are important in this game.

Xav, you make some excellent points. I'm glad to see discussion coming out of my article.

I didn't address deck with alternate win conditions, but since you brought it up, I will. To an extent, you are correct. Burn decks don't rely on advantage the same way regular Aggro/Control deck do. However, that doesn't mean you can dismiss it entirely. Late game, burn decks can easily topdeck into a game winning card, but if they get down on cards early on, there is a good chance they won't be able to recover enough to protect themselves while dealing enough burn damage for the win. If you're using a burn deck, you can easily get away with running -1's like the ones you mentioned, but that still doesn't mean you can play recklessly.


Yes, to every rule, there is an exception. You acknowledged that my logic has merit, then provided a "what if" situation that contradicts it. That's good enough for me.


You are correct. I've actually said this before regarding an Aggro/Burn deck. If you can build a deck that can burn fast enough, it may be possible to disregard advantage. However, if you don't win fast enough, your lack of advantage will eventually catch up to you. Like you said, you can't deal damage if you have nothing to deal damage with. You have to make sure you win before this situation occurs.

Like I said, I agree. I was just making a comparison.


You right. I should have mentioned that because it further proves me point.

First of all, we can't compare our decks to a deck that is illegal. Cyber Stein is debately the most efficient PLAYABLE deck.

The point of this section was that it is mathmatically illogical to sit and wait for pieces of a combo. It is better to run cards that work independently, but also combo together for an even better effect.

Card advantage and virtual advantage are two totally different things. I acknowledged that both are important.

Again, card advantage is different from both hand advantage and field advantage. The cards you have on the field are still resources you have, therefore they still count toward your overall card advantage.

wow this is the stupidest article i have ever read in my life. If you think math is what governs yugioh, i feel very bad for you. Everyone knows yugioh is all about the heart of the cards. I could have a 231 card exodia deck and still pwn everyone, and do you know why? Because the heart of the cards are with me.






hehe im messin buddy great article. :p

Good point about the card advantage statement. From reading your initial article, it seemed as if you were specifically concerned with only hand advantage. That's why I mentioned field advantage.

And why can't we compare our legal decks to something like a Magical Scientist? We all already know how quick and effective Magical Scientist decks are, but because it's illegal, what other decks can be as fast? This is what makes Cyber-Stein so playable. It can be nearly as quick as Magical Scientist. If any other deck can be nearly as quick and effective, then I don't see the problem in the comparison to determine overall effectiveness, as long as you understand where the deck may be lacking because it's an advanced deck.

I consider it irrelevent to differentiate between hand and field advantage most of the time. As long as you don't overextend to the field, it makes little difference as to where your resouces are.

My response to any combo just I deem inefficient is, "Why don't you just play Cyber Stein? It is more efficient." I can't say this to any Advanced Format player. If we were talking about Traditional, you would obviously be correct.

But still-do math and chance mix?

You could have a Confiscation(1/40) and 3 Spirit Reapers(3/40) and still possibly get a opening hand with Confiscation and no Reapers.

But this is a pretty good article. Good job.

Chance IS math. It isn't guaranteed, but wouldn't you agree that you have a better chance of drawing a Reaper than a Confiscation? The purpose of this isn't to make guarantees, but rather to put the odds as much in your favor as possible.

Viewtiful article ZaQ, I look forward to the next one ^_^

nice article. good to see so many concepts consolidated together into a comprehensive description of card advantage...just messing around with the big words :)