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Acceptable Risks, Part 2.Generic deckbuilding tools for sixty card decks.
Nik Smith
May 23, 2007
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Hi all.

My head hurts.

In a fit of madness at the request from a team-mate, and with the encouragement that actual feedback on the forums (and even by email!) provided, I decided that I should really expand on the theme of my last article . Thus I have attempted to calculate generic probabilities for 60 card decks, and not just 30.

Ah, but that should be easy, I hear you say. After all, if you can calculate probabilities for 30 cards, the 60 can only be the same calculations, but more of them, right?

No. No it isn’t.

You see, 60 card decks are not just a logical progression from 30 card decks. 60 card decks have these annoying little things called tutors. Now calculating the probability of simply drawing the right curve of characters in a deck with no tutors is a relatively simple process. I did that. But then I was thinking about the recent article on this site about a “pay for your tutors” VS variant, by Ian Vincent, and older discussions about how many tutors to play. Not least of which was Alex Brown’s old discussion about running 12 tutors in G’Lock variants.

And it made me realise that although I could calculate ideal curves for 60 card decks with no tutors, nobody in their right mind would actually play with a deck with no tutors. And just in case you think that doing that would be a good idea, I have some news for you. It’s bad. Really bad. Bad with capital B. Capital A and D too. And a few other capital letters just for good measure to truly express just how awfully, awfully bad it is. Maybe a capital Q (for spice).

Am I rambling? Maths’ll do that to ya.

So, I decided the only honest way forward was to calculate probabilities with tutors included as well. Now this makes things absurdly complicated. Tutors generally have a cost. Be it discarding a character of a certain type, having the right number of face-up resources, a character from the right team in play etc… Most of the time this is ok, and I will assume you can meet these conditions every time.

But some tutors need a specific combination of cards that is more difficult to meet, such as Straight To The Grave. With this one, not only must you have the tutor, but also some way of getting the character back out of the KO’d pile so it can do something useful. That requires a whole extra page of calculations, as you need to consider the probabilities of drawing both sorts of cards. In addition, the number of cards can vary. For example, if you play 4 Straight To The Grave, and say, 4 Slaughter Swamp, you have 4 tutors, and 4 ways of getting characters back. If you add 2 Soul World, then you have 6 ways of getting characters back, and the probabilities shift.

So what I have done is tried to map out some generic tools for calculating probabilities in 60 card decks. The calculations to determine exact probabilities must be done on specific decklists, and are fairly complicated, as you need to calculate the probabilities of each scenario that may crop up. For example, in one game you may draw your, 1,2 and 3 drops, and then need to tutor for you 4-drop. What are the probabilities you have drawn 1 tutor? What about if you draw you 1 and 2, and tutor for your 3? What probability do you have of drawing another tutor to go and get your 4?

Simply put, it gets messy. But I hope the Tables I have included are easy enough to understand that people can get a good feeling for the general overall probabilities they are dealing with. I will discuss each Table in turn, and then try and make some summary statements at the end, assuming anyone else gets that far.

Similar to the last article, for those who want to skip the maths, just go to the bottom of the article, and I will try and post the most relevant conclusions. If you want to get more out of it, there are a couple of maths-dense paragraphs. I’ll warn you when they pop up, and you can safely skip them.

PART 1:
The raw curve with no tutors. (or “Shuffle, present, scoop”, as I now think of it).

Ok, here is the Table for the probabilities of simply drawing the correct character at each drop in a 60-card deck with no tutors. I’ve worked out the probabilities for up to 16 characters of cost up to 8. Yeah, I know, no-on is EVER going to play sixteen 8-drops, but once you have mapped out the worksheet in Excel, it’s easy enough to simply expend it across, so I thought what the hell. In addition, for every 2 extra cards you draw in a game, you can move one column over, as each column is based on drawing the regulation 2 cards per turn. So if you could draw an extra 4 cards by turn 3, you can use the probabilities from the column for turn 5 instead. Without further ado…

Table 1: Probabilites of drawing characters by the required turn in a 60 card deck with no tutors.

Similar to my older article about sealed deck, we can calculate the chance of drawing our curve by multiplying the chance of drawing each drop on the curve. You can do this for any deck you like, simply by deciding how many of each character you want to play at each resource cost, and multiplying the respective probabilities.

For now, I am going to assume a curve from of characters from cost 1 to cost 7, and I want 90% probabilities of drawing the correct character by each turn. This means that my total chance of drawing my curve from 1 through 7 is:

0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 = 47.8%

That’s a pretty horrible probability. But let’s take a look anyway, and we’ll see how many characters this takes.

OK, since we are assuming a curve of 1-7, we can safely say that our 1-drops are the mulligan condition. Thus we use the mulligan probability column for 1-drops, and the no mulligan probabilities for every following drop.

The resulting character numbers we need to run to get an approximate 90% probability are:
1-drops: 11
2-drops: 14
3-drops: 11
4-drops: 9
5-drops: 8
6-drops: 7
7-drops: 6

Yeah, that seems a lot to me too. With no tutors you need to run 66 characters in your 60 card deck to make sure you have a 90% probability of drawing each character on your curve. And that works out to a total probability of 45.8% (0.891 x 0.898 x 0.891 x 0.887 x 0.898 x 0.901 x 0.895) of drawing your full curve. Now, can anyone spot the problem here?

This alone is convincing enough that tutors are not just a nice bonus, but an absolute necessity in VS. Sure, additional card drawing can help, but not enough. The old rule about “if it hasn’t got tutors, it’s not competitive” couldn’t be more true.


PART 2: Tutor Probabilities

Ok so you get the idea that we need some tutors here. This brings up a few questions:

1. How may do we need?
2. Which ones do we need?
3. How much do they help?

Well for starters I have calculated the probabilites of two sorts of tutor. The first (Table 2) is for a generic tutor, for example Enemy of My Enemy, Mobilize, The Great Refuge, Brother I Satallite etc… By generic I mean that the additional cost isn’t hard to meet, and we can assume that generally you will be able to pay it with no real difficulty. Of course this isn’t always the case, but we can discuss the finer points a little later. Table 2 lets you see the probability of drawing at least one of the given card by the turn you want it, depending on how many tutors you have in your deck. The chance of drawing at least one by any given turn is in the TOTAL box.

You’ll notice that this Table goes up to 20 cards of a specific type in deck. Now that seems a heck of a lot really, as who would go so far as to play 20 tutors? But I have done this for a very good reason.

Now if you care about the maths, read this paragraph. If you don’t, just trust me, and go straight to the next paragraph. Still here? Well, here goes a complex bit. Imagine you have 4 characters of a certain cost , 4 Enemy, and 4 other tutors. Now it would be logical to assume that you could calculate the probability of not drawing your character, and then calculate the probability of not drawing an enemy, and then the probability of not drawing the other tutor, and multiply them all. This will give the probability you won’t draw any of the required cards. Subtract this from 1, and you get the probability of getting at least one of the cards you want. However, if you do this (you can by using the Tables in this article, but wait till later, and trust me for now), you’ll see that the resulting probability is different to that you get if you simply imagine you have 12 copies of the character in your deck. Why? Well, if you calculate it in bunches of four, you are dealing with 60 cards the first iteration, but only 56 the next one, as the first four were a negative result. For the third iteration, you are dealing with only 52 cards. So for each iteration, you would need a different Table like this one below to get the correct probability (this one is based on 60 cards). It is far, far easier to treat 4 characters and 8 tutors as being equivalent to 12 copies of the same card, and calculating the probability for that. This causes a problem with the section on Straight To The Grave later on, and I will give you additional explanation there. But for now, back to the article.

When you look at this Table, the “number in deck” column is the total number of characters of a given cost and tutors in your deck. So if you have five three drops, and nine tutors, then you look up 14 in deck (5+9). That’s why it goes to 20, so it can cater for those people with up to 20 characters and tutors at a given cost. Unfortunately I can’t account for mulligans here, it just gets too complex. But I will discuss how that affects the probability a little later.

In addition, I’ve gone a step further, and included the probabilities of drawing multiples. These are the other boxes above the TOTAL boxes. For example, if you look at the box for the probability of drawing three tutors on turn 2, it looks like this:

31.0
4.3
0.2
35.4

Which means you have a 31.0% chance of drawing a single copy of that tutor by turn 2, a 4.3% chance of drawing a second copy, and a 0.2% chance of drawing a third copy. Adding these gives a 35.4% chance of at least one copy by turn 2 (yes, 35.4%, not 35.5%, because there is rounding you don’t see, and I have added the raw numbers, not the rounded ones, to be a little more accurate).

So, now that you should be able to understand the Table, here it is in all its magnificence (by the way, you can thank EXCEL for the pretty pastel colours):

Table 2: Probabilities of drawing at least one character or tutor by a given turn with up to 20 in your deck.


Let’s just take a moment to have a look at this Table for a minute, before moving on. Now personally, I kind of consider 90% my magic mark. I don’t really like going with probabilities much under 90% if I can avoid it, because if you start having several probabilities less than 90%, your whole plan starts to go haywire reasonably quickly.

Generally tutors come in packs of four, by which I mean, people will play four of each of the most effective tutor. If there are two good ones, they may play 8, and even 12 if there are three (yes I know this is a big generalisation, but this is a generic article after all). So let’s compare those.

Generally, I’m going to do examples with a 3-drop. This is because these are the probabilities that really push a lot of decks. In many decks, the 3-drops are critical for it to function, and they are at a point where you have generally seen relatively few cards. This means the probabilities are generally worse for these drops, and thus getting things right here is pretty important for most decks.

Chance of hitting a tutor by turn 3

4 in deck: 52.8%
8 in deck: 79.0%
12 in deck: 91.3%

Look those increases. A whopping 26.2% increase by going from 4 to 8 tutors. By going from 8 to 12, we get an increase of 12.3%. Still impressive, but not on the scale of that massive increase that going from 4 tutors to 8 tutors gives us.

But this is simplistic, and these aren’t the only sort of tutor. The other sort requires a combination of cards. Specifically, Straight To The Grave requires not only itself, but some mechanism for getting characters back out of the KO’d pile, be it Slaughter Swamp, Soul World, Quadromobile, etc… In a case like this, you need to calculate the probability of drawing both types of card, because the tutor doesn’t function without them. So here is Table 3. It is different to Table 2 because you have to deal with multiple probabilities, and thus I have broken it down to a turn by turn chart. To find your probability, go to the respective chart for the turn you are considering, e.g. turn 3. The find the number of Straight To The Grave you are playing on the left, and the number of return mechanisms on the top, and find the box where they intersect. That is your probability of drawing both by the requisite turn.

Table 3: Probability of drawing Straight To The Grave and a return mechanism by a given turn.

Doing the same exercise we did for Table 2, we can look at the probabilities of drawing your tutor on turn 3. We’ll begin by assuming that you have four Straight To The Grave in your deck. With four Slaughter Swamp, you only get a 27.8% probability of drawing both by turn 3. If you ran 8 return mechanisms, then you can get this up to a maximum of 41.7%. Not as good as our other tutors, by a long shot, but decks can be set up to manipulate these odds, for example by adding characters like Poison Ivy who can tutor for your location. In such a case, your probabilities increase significantly.

Now we are ready to start compiling all this information. So, as an example, what is the chance of drawing your 3-drop on turn 3? Let’s say you have four 3-drops that you ideally want to draw (e.g. Ahmed Samsarra, Dr Light etc…), 4 Straight To The Grave in your deck, 4 Slaughter Swamp, 1 Soul World, and 4 Enemy of My Enemy. What are the odds of getting your 3-drop somehow?

It’s no good simply finding the probabilities for each and adding them. That doesn’t work, because any number of combinations could be correct. Instead, we have to find the probability of NOT drawing ANY of them, and subtract that from 100%. So we need to work out the probability of not drawing a 3-drop, or Enemy Of My Enemy, and the probability of not drawing the Straight To The Grave/Slaughter Swamp/Soul World combo. Once we have those, we need to multiply them together, to find our total chance of whiffing.

Now I could make you find all those out for yourselves, but as I am a nice guy, I have made a bunch of Bizarro Tables™ for you. These may look similar to Tables 1,2 and 3 but are actually the inverse; that is, the probability of NOT drawing the required cards by the relevant turn. (I toyed with the idea or reversing everything because it’s Bizarro, after all, but it was confusing even me when I tried to work stuff out).

So all you need to do is look up the correct boxes, multiply the results, and subtract from 1. This is your probability of hitting one of either your character, your tutor, or some combination of both.

Here are the Bizarro Tables:


Bizarro Table 1: The probability of not drawing a character by the requisite turn (including mulligans).

Bizarro Table 2: Probabilities of not drawing at least one character or tutor by a given turn with up to 20 in your deck

Bizarro Table 3

: Probability of not drawing Straight To The Grave and a return mechanism by a given turn.



A note on the Bizarro Tables: The astute among you will have noticed that the total boxes in Bizarro Table 2 bear little relationship to what’s in the boxes above them. But if you were to subtract each of the numbers in the boxes from 100, and then sum them, then subtract that from 100, you would end up with the number in the total box. I could have removed these, but I thought it may come in useful to know your percentage chances of not drawing multiples of a tutor at a given turn, so I left them in. For most calculations, simply use the total box, which is the probability of not drawing any of the given card by the given turn, with the given number in your deck.

So back to our example:

We need to work out the probability of not drawing a 3-drop, not drawing the Straight To The Grave/Slaughter Swamp/Soul World combo, and not drawing an Enemy Of My Enemy. Once we have those, we need to multiply all three together, to find our total chance of whiffing.

Another maths bit. Non maths people skip to the next paragraph. Now I mentioned earlier that we consider tutors as extra copies of characters, since we get our probabilities a little off if we do it all as bunches of 4. What do we do with Straight To The Grave then? We can’t simply count it as another tutor, as the probabilities are completely different. So we simply have to estimate as best we can. It is possible to work out the exact probability, but it requires a lot more Tables than I want to put in here. It changes for every deck, depending on a lot of different factors (number of characters, number of regular tutors, number of Straight To The Grave, number of returners, and mulligans). Basically though, it works out to about a 1% difference. Back to the non-maths explanation…

Due to complications, it is inevitable that the calculation you get will be about 1% out from the actual probability. For every Table you use, add 1% to your total probability, and you will be very close (within 1%). For example, say you use Bizarro Table 2 and Bizarro Table 3, you will add 1%. If you need to work out the chance or drawing a character with a mulligan, then use Bizarro Table 1 (for characters), Bizarro Table 2 (for tutors), and Bizarro Table 3 (for Straight To The Grave), and then add 2% to your final probability.

Ok.

Probability of not drawing our 3-drop (4 in deck) or Enemy Of My Enemy (4 in deck, so look up Bizarro Table 2, turn 3, 8 in deck) is: 21.0%
Probability of not drawing Straight To The Grave /Slaughter Swamp/Soul World (4 Straight To The Grave /5 returners in deck) is: 67.7% (0.677)

Multipled that gives us: 0.142

So our total chance of missing is: 14.2%

Subtract that from 100 and we get: 84.9% plus our 1% bonus for the inaccuracy in the Straight To The Grave numbers gives us approximately 86%.

Which is our total chance of getting our 3-drop, one way or another.


What about if we ran 8 generic tutors instead of the Straight To The Grave engine? Since we are only looking for a positive probability here, we can use either the Bizarro Table 2 or simply use Table 2.

Probability of not drawing our 3-drop (4 in deck) or tutor (8 in deck) means we use Bizarro Table 2, turn 3, 12 in deck, which gives us:

A total chance of missing of: 8.7%

Subtract that from 100 and we get: 91.3%

If you look at Table 2, Turn 3, 12 in deck you will see that our probability is also 91.3%

Which is our total chance of getting our 3-drop (note we only used one Table here, so no 1% bonus this time)

Let’s do something else. What about comparing running 0,4,8, and 12 tutors in a deck? How much does that help us get our 3 drop (assuming 4 in deck)? Similar to the example above, we can do this with the Bizarro Table 2, but it’s easier to use Table 2.

Probability of not drawing our 3-drop (4 in deck) and add the number of tutors (0, 4, 8 or 12). Look up Table 2, and look at turn 3, and then 4, 8, 12, and 16 in deck respectively.

That gives:
0 tutors in deck: 52.8%
4 tutors in deck: 79.0%
8 tutors in deck: 91.3%
12 tutors in deck: 96.7%

Which is our total chance of getting our 3-drop for the respective number of tutors we run.

Of course, all probabilities improve if you make a certain cost your mulligan condition. For example, if your 3-drop is your mulligan condition, these probabilities improve markedly. As with the Straight To The Grave calculations, you get an approximately 1% bonus probability if you work out the character and tutor probabilities separately. We need to go back to Bizarro Tables 1 and 2 here:

0 tutors: Caracter with mulligan: 33.5% . Subtract from 100. Gives a total of : 66.5%
4 tutors: Caracter with mulligan: 33.5%. 4 Tutors: 47.2%. Multiply and subtract from 100. Add 1% gives a total of approximately: 85%
8 tutors: Caracter with mulligan: 33.5%. Tutor: 21.0%. Multiply and subtract from 100. Add 1% gives a total of approximately: 94%
12 tutors: Caracter with mulligan: 33.5%. Tutor: 8.7%. Multiply and subtract from 100. Add 1% gives a total of approximately: 98%

Now that’s pretty decent. Anything that can get you to around 95% or more is a very big bonus.

Unfortunately, it’s not possible for me to build an ideal curve for a 60 card deck. There are simply too many variables for me to do this and have it applicable for more than a single deck. But I can at least do a single deck as an example.

There are a few things to keep in mind, however:

• There is no guarantee that you will be able to meet the conditions of your tutor, eg having the correct character to discard to Enemy Of My Enemy. Every now and again, this will happen. The odds are small, but it will happen.
• Each time you use a tutor, you are thinning your deck by one card, and this has a small positive effect on the probabilities. It is very small, but it is there.
• I can’t calculate the effect of drawing multiple tutors. If you use one for your 3-drop, then your odds of getting a second decrease for your 4-drop. This is inevitable, and while you could do the calculation as you go during a game, this would be time consuming.
• I cannot account for other tutor effects, card drawing, milling your deck or other deck manipulation effects. All of these will improve your odds. The more of your deck you see, the better things get.

The bottom line is that these numbers are a ROUGH GUIDE. They will give you a feel for overall probabilities, and when used correctly can help a lot in determining the correct number of characters and tutors for your deck to run reliably. But they are not the complete solution.

OK, for analysis, I figured I would take a look at a deck most people will now be familiar with, the Skrulls deck played by Michael Lou to a second place finish at 10k Sydney.

Here’s the deck:

THE Skrull Deck
Michael Lou
$10K Sydney, December 2006

Characters
4 Lockjaw, Inhuman's Best Friend
4 Nenora
4 Franklin Richards, Creator of Counter-Earth
1 Black Bolt, Illuminati
4 Warskrull
3 Wolverine, Skrunucklehead
3 Captain America, Skrull Impostor
1 Crystal, Elementelle
4 Ethan Edwards
1 Triton
4 Paibok
Plot Twists
4 Act of Defiance
4 Mutopia
3 Extended Family
4 Interstellar Offensive
4 Call to Arms
4 Blinding Rage
Locations
4 The Great Refuge

For the purposes of this, I’m going to consider Lockjaw as being a tutor for your 2-drop Franklin Richards. I’m also going to try for the basic curve of
Lockjaw (4)
Franklin (4)
Captain America/Wolverine (6)
Ethan Edwards (4)
Paibok (4)

I assume this is ideal, and while you have backup drops at some of your curve, these generally seem like your best options. You have 4 tutors (though I will consider a turn 1 Lockjaw a tutor for turn 2). Franklin Richards/Lockjaw/Great Refuge are your mulligan conditions. I consider Lockjaw a bonus character, and so I won’t work out the full curve from Lockjaw to Paibok. Your chance of hitting lockjaw is 35.1%, and if you were to mulligan for it, 52.8%, so I wouldn’t recommend it.

It is important to note that you cannot tutor for your ideal 3,4 or 5-drops naturally with the tutor you have in this deck (The Great Refuge). You must team-up first, which means drawing a three-drop, or Nenora and a tutor, as you have no way of teaming up until Nenora is in play. I will assume you draw a team-up (since you run so many), and thus if you get Nenora or your 3-drop, you can then tutor for your 4-drop. This adds a complication though, as it makes the calculation for your three drop a little more complicated. If you need to draw Nenora and a tutor, then that’s a two card combo, and we can use the same table as we used for Straight To The Grave. We have 4 Nenora, and 4 tutors, so we simply say that Nenora is the equivalent of your returners, and the tutor is the equivalent of Straight To The Grave. This means we look up turn 3, 4 Straight To The Grave, 4 returners, on Bizarro Table 3, which gives a probability of 72.2% of not drawing
the combo. Then we look at the probability of not drawing Captain America is 57.3% (Bizarro Table 1). Se we multiply that and we get 0.722 x 0.573 = 0.414. Subtract from 1 = 0.586 = 58.6%, add 1% (two tables) and we get approximately 60%.

Chance of drawing Franklin/Lockjaw/Great Refuge by turn 2 with a mulligan: 95.0% (Table 1, turn 2, mulligan, 12 in deck)
Chance of drawing Captain America/Nenora and tutor on turn 3: 60% (Table 1, turn 3, 3 in deck)
Chance of drawing Ethan Edwards on turn 4 (4 tutors): 85.3% (Table 2, turn 4, 8 in deck)
Chance of drawing Paibok on turn 5 (4 tutors): 89.8% (Table 2, turn 5, 8 in deck)

Multiply and we get 0.95 x 0.6 x 0.853 x 0.898 =0.437

So your probability of drawing an ideal curve with this deck is approximately: 43.7%

If you consider any 3-drop acceptable, then your probabilities go up quite a lot, with seven 3-drops, and the possibility that The Great Refuge can get you Crystal. This makes in effect eleven 3-drops plus Nenora and a tutor, which gives you a chance of missing of .722 x .109 = 0.079. Subtract from 1, add 1% gives a 93% chance of getting a 3-drop somehow, and an overall probability of 67.7% chance of getting a full curve from 2 to 5. Still not great, by any means.

To shore up these numbers, it would make sense to play several other tutors that can find your ideal 3-drops. Looking at this list, with the banning of Nenora, it might be an idea to add some other 1-drops, which would give access to other tutors. This deck seems like a prime candidate for the old Wild Ride/Midnight Sons/Dagger Engine, as it can search for your ideal 3-drop, and even gives you a way to find extra team-ups. But that’s just off the top of my head. (aside: I wrote a draft of this article before PC Sydney. From what I saw at the PC, a number of Skrulls decks made a similar judgement, and were running Wild Ride as well as Marvel Knights characters in order to shore up the decks poor draws. In particular, I know Dave Spears was running a build with Wild Ride).

If we do this though, and give access to 4 more tutors, and add the 4th Captain America, we can even cut characters from the top end. Now doing this makes the maths very complicated, so I won’t show all the calculations, but here are the basic results. Your mulligan hand goes up to close to 98%, your chance of drawing your optimal three goes to 84.8%, your 4 and 5 drops go to 95% and 97.2% respectively. Even if you cut a 4-drop and 5-drop to make room for the additional tutors, your 4 and 5-drop probabilities go to 93.4% and 96.1%. If we now work out our probability we get a 74.6% chance of hitting your ideal curve. That’s a huge improvement, from 43.7% to 74.6%. Originally we would statistically miss our ideal curve nearly one game in three, but by adding 4 more tutors, we make it so we get our ideal curve three games out of every four. Keep in mind that our worst probability is still for getting that 3-drop. If we consider any 3-drop good enough, and add a Marvel Knights 4-drop, then the probabilities go up to around the 90% mark for hitting our curve, so we will very rarely miss some sort of curve from 2 though 5.

The take home message is that by going from 4 to 8 tutors, and adding a couple of affiliated characters to use those tutors to maximum effect, we can essentially minimise the number of bad draws for this deck. The change in probability is enormous, going from less than less than 50% to almost 75% of getting an ideal curve, and from 67.7% to better than 90% of drawing a curve of some kind from 2-drop through to 5-drop.

Like I have said a couple of times, these are not exact probabilities. There are a lot of variables in calculating all of this and I am by necessity making a lot of assumptions (eg you have 4 Paibok and 4 tutors by turn 5 assumes you have not used a tutor yet). But the assumptions are made to determine the maximum probability, so I feel they are somewhat justified.


My basic summary:

Tutors have an absolutely enormous effect on the probability of drawing your ideal curve. I know everyone realises this, but I am not sure that everyone realises just how much effect they have. Without tutors, your probability of drawing an ideal curve, given that you are limited to four copies of any card, is absolutely abysmal.

For myself, I don’t think I could ever run a deck with less than 8 tutors. 12 may be overkill, as the gains in probability diminish exponentially, especially in the mid-late game. In the early turns, multiple tutors are fine, as you dramatically increase the odds of drawing your ideal characters. In the later turns, however, excess tutors run the risk of clogging your hand, and they take up additional space which could be used for other plot twists and locations. There is a balance to be struck, and it will vary from deck to deck as to where the balance between number of tutors, number of characters, and the number of other plot twists/locations/equipment lies.

Keep in mind, though, that tutors are not the only way to improve draws. For example, Secret Society has milling effects, and ways to return characters to hand from the KO’d pile, acting as a pseudo-tutor. This can be quite effective, and may allow decks like that to get away with running less direct character tutors, without harming their probability overmuch. Similarly, cards like Willworld, while not enough in and of themselves, can act in conjunction with tutors to really add to your chances of drawing the correct cards. An active Willworld from turn 1 lets you see an additional 8 cards by turn 4. In effect, if you look at probability Table 1, and consider that you have four 4-drops in your deck, you are now working on the same effective probability as if you would normally draw an 8-drop. That is, your probability of drawing your 4-drop goes from 60.1% to 81.3%. An increase of 20.2% is nothing to sneeze at, and the increases are even greater for turns 5 and up.

Unfortunately for those who skipped to the end and missed out on the maths, there is no magic answer here. I can’t build your deck for you and get the probabilities right. Suffice to say that I would consider about 8 tutors about right for any curve deck. More if your early drops are key to the deck’s success. I assure you the maths isn’t that complicated if you want to try working things out for yourself. There are a bunch of worked examples above which should explain the principles, so it may be worth scrolling back up and taking a bit of a look ?

So there you have it. This should provide you with enough information to calculate (or at least make an educated guess) at the probabilities of drawing your ideal curve for any deck you build. It can be quite daunting at first, but is really quite simple, if you take the time to sit down and play with the numbers for a while.

I hope this is useful to people out there. Feel free to email me specific questions, and I’ll do my best to answer promptly. However my work does take me out of email contact for up to a month at a time, so if I don’t reply, I’m not a jerk, I’m just away.

Finally, I’d like to put in a huge thank-you to Ian “DTee” Vincent. Ian read the article, offered advice, and pointed out some important maths details I had missed. I hope this is all correct now. Thanks again Ian.

Until next time,
Nik Smith
Replicant on the forums
replicant.nexus7@gmail.com



 

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