Getting out of 2/2/2 hands

You’re staring down a 2/2/2 hand, wondering what you’ve done to anger the RNG gods. you play two cards from one house. It feels bad, but surely you’re going to draw into a 3/2/1 or a 3/3, right?
Wrong, you manage to draw into another 2/2/2 hand. Situation looks as grim as ever. You’re playing two card a turn and your opponent is churning out three-four cards in rapid succession.
You pick another two cards to play, take a deep breath, and draw into yet another 2/2/2 hand. Sure enough, you lose the game. You just didn’t have the resources.

The first step is to recognize the problem

Realize you’re holding a 2/2/2 hand and that you’re at risk, which is why you almost always mulligan a 2/2/2 hand going second. Because the chance of going back into a 2/2/2 hand is roughly 10% (10/30 * 9/29). I am not good enough at math to figure out the chances of going back into 2/2/2 hand from a 2/2/1 if you play a 2, but my gut says they’re smaller because you’re drawing 3 cards.

EDIT: According to Penguin in the comments, the chances are actually higher, at 11%. I’m not sure yet how I feel about this information, I still think it is best to mulligan away a 2/2/2 hand.

 

10% is not insignificant, if you’re at a vault tour, you don’t want to throw away your best of 1 on a 10% chance, that’s a lot.

Plan ahead

You’ve realized that you’re in a risky position and you’ve decided to do something about it, now what?

Consider a mostly empty board and this hand.

029_039_067_075_338_358

In the wild, Mind Barb + Lash of Broken Dreams can be a very strong play here. You’re disrupting your opponent’s hand, and you’re developing your Lash to be used later. However, our objective is to get out of 2/2/2 hands, so what we’re looking for, is which of those plays will make us least worried about drawing back into 2/2/2.

For me, the answer is clearly Valdr and Krump. If you draw two more Brobnar cards, you’re still going to have a solid hand + board of four. If you manage to hold those two, you might even survive drawing into a third 2/2/2 hand, especially if one of those 2 additional Brobnar cards help you develop your board further.

Not only does playing Brobnar again give you a solid four cards to use, it will also greatly reduce your chance of running into that third 2/2/2 hand split, as you’re cutting down the size of the Brobnar in your deck.

Know your odds

I’ve already gave a fairly deep look into counting discard piles in a previous article, but I did not mention 2/2/2 hands specifically. It is important to know what the effects of different house distributions have on your chances to run back into a 2/2/2 hand.

Because of the way it is calculated, the house split doesn’t really matter, what matters is only the total number of cards, and the number of cards in the house you’re choosing.

Cards in house (H) divided by total number of cards in draw pile (D). Then again with Cards in house minus one, and total cards minus 1.
H/D * (H-1)/(D-1).
That’s a bit hard to calculate on the fly, so I suggest you just do H/D*H/D and get a good estimation.

Since distributing larger numbers is easier on the brain, you can even do H*H/D/D. For example 5 cards of a house in a draw pile of 20.
5*5 = 25
25/20 = 1.25
1.25/20
This is a good enough result to give you a feeling of your chances but if you remember some of those school-taught math skills, you can also multiply both 1.25 and 20 by 4, resulting in 5/80, then divide by 5 to get 1/16.

Weighing the risks

Lastly, you might be facing two risk factors at the same time. You might be staring down a Duskwitch along with that 2/2/2 hand split, and you’re going to have to ask yourself if you need to deal with the threat on the board, or increase your chances of getting out of 2/2/2.

435_320_36h3p8vpwc2_en-1

This is naturally harder to do by the numbers, since it’s impossible to quantify the damage of a Duskwitch in percentages. But as we know, Keyforge has two rules:
1. Reaping is better than fighting.
2. Witches must die.

So most likely, you’re going to risk another 2/2/2 hand to kill that Duskwitch, and if you do get that 2/2/2 hand again, I really feel for you, it’s a terrible situation to be in.

 

Afterword

I’ll be heading to Vault Tour Krakow and I’m looking forward to meeting you all there. I’m likely going to post about some preparations I’m doing for the Vault Tour, namely picking a deck for my first Archon Vault Tour. If you’re interested in keeping up to date, follow me on Twitter.

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6 thoughts on “Getting out of 2/2/2 hands

  1. > I am not good enough at math to figure out the chances of going back into 2/2/2 hand from a 2/2/1 if you play a 2, but my gut says they’re smaller because you’re drawing 3 cards.

    The probability is 11%. You need to draw two cards from the house you played, and one card from the house you had one card from. There are (10 choose 2)*11 ways to do this, out of the (31 choose 3) possible sets of three cards you could draw. This gives 99 / 899, which is about 11%.

    Liked by 1 person

  2. You’re looking at it wrong.

    So if you want to count the split hands, you typically want to look at failure rates of the desired outcome. In this scenario the desired outcome is a split hand, to prove why they’re bad.

    So it a split hand is 10%, a GOOD hand is 90%.

    Now if playing a 2/2/1 gives you 11% to draw into 2/2/2 and playing a 2/2/2 gives you %10 to draw a second 2/2/2 I’m gonna call both 10%.

    To simplify, this is like rolling a d10 and hitting 1 twice in a row, which is significantly less likely than hitting 1 once.

    Had to Google. You actually just multiple. So a split hand twice in a row is 1% ish regardless of milligan it not.

    Which means if you start with a 2/2/2 or a 2/2/1 and all things close enough to estimate, you’re 99% to have a better hand next turn.

    And if you mulligan then you already hit the 1%, so a THIRD split hand is 1/10 x 1/10 x 1/10. So the failure rate of a GOOD HAND (remember split is desired outcome for this) is .1%.

    Do almost 100% guaranteed to have a better hand after a mulligan. Even if the individual split-draw goes from 10% to 11%.

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    1. That’s the chance before you’ve drawn anything. After you’ve already drawn the 2/2/2, the chance is 10%. You can’t retroactively apply the chance of initially drawing into the 2/2/2 onto the next draw.

      Unless I misunderstood your meaning.

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      1. Then take the original odds and multiply. The idea is still the same.
        It’s still better to Mulligan.

        Like

      2. Ah, I see what you mean. When you’re holding the first 2/2/2 hand, it’s always best to Mulligan because at that point the chance of drawing into two junk hands is very slim. Good call.

        Like

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