Making Your Own Luck: Your Opening Buys and How Not to Bottom-Deck Them

by Scott Heise aka HomerJr

It is generally acknowledged that cards with strong trade and scrappers are some of the strongest opening buys in the game.  (Freighter, Supply Bot, Patrol Mech, Cutter, Trade Pod, just to name a few.)  However, as has been discussed in The Pace of the Game Part 1, economic cards and scrappers are “time-sensitive” in that they require an shuffle to amortize their value. For example, for a Freighter bought on Deck 1 (opening buy), the earliest it can be played is Deck 2 which means the earliest a card that bought using the Freighter’s trade can be drawn is Deck 3.

This time-sensitivity of economic cards and scrappers means that they are very sensitive to the bad luck of “bottom decking”, which is where a shuffle is triggered before you get a chance to play the card because it was near the bottom of your deck.  If your opening buys revolved around buying economic cards and/or scrappers (which they often will), then it can be a complete disaster if these cards are bottom decked at the end of Deck 2. Such bad luck can literally ruin your game by delaying disrupting the timing of your deck and delaying the benefit of trade and/or scrap until Deck 4.  In a game where you only get 4-5 decks on average, this bad luck can often be irrecoverable.

Bottom-decking is mostly just bad luck of the shuffle… but is it really that simple?  Is there something that can be done to shift the odds in your favor and avoid your opening buys from being bottom-decked?  Yes, there is.

Bottom decking occurs when you have fewer than 5 cards in your draw deck at the end of your turn;  as you draw your next hand, a shuffle will be triggered and the cards that were at the bottom of your deck (up to 4) have essentially skipped a shuffle and will not be included in your next deck not only will you play the card one fewer time over the course of the game. Bottom-decking of the strong cards in your deck always hurts, but if it was a trade or scrap card that was bottom decked, not only do you play the card one fewer time, but the benefits of the card bought with that trade or the velocity gained by scrapping a starter will be delayed as well.  In the Freighter example above, if instead the Freighter is bottom-decked at the end of Deck 2, then the card that you buy with it will also miss the shuffle and not be available to be drawn until Deck 4.  DISASTER!!!

(NOTE:  Bottom-decking is not just a phenomenon that affects your opening buys… it can have a major impact throughout the game.  For more on this, check out FlyingArrow’s recent article Deck Size for Spiked and Flat Decks)

Enough Talk, Let’s Look at the Numbers

So, what can be done about this?  Although bottom-decking is primarily just luck of the shuffle, it is not beyond your control.  When it comes to avoiding bottom-decking of your crucial starting buys, there is one major factor that affects the probability of them being bottom-decked… the number of cards that you buy with your first two hands directly affects the probability of one or more of these opening buys being bottom-decked for the critical second shuffle (deck 2 -> 3).  To be specific, whether you are 1st player or 2nd player, the number of cards that will you buy with your first two hands (opening buys) will be equal to the number of cards that will be bottom-decked at the bottom of Deck 2.

Let’s take a look at the numbers…

(Side note:  Opening buys that draw a card, such as Survey Ship or Corvette, aren’t considered as a Buy for the purposes of these probabilities since they don’t increase your effective deck size.  This isn’t quite true, as the Survey Ship could still be bottom decked itself and thus would still count toward deck size for the purposes of bottom-decking probabilities, but we’ll ignore that case for now for the sake of simplicity.)

Probability of Opening Buys Bottom-decked in Deck 2
0 Exactly 1 Exactly 2 Exactly 3 Exactly 4
# of Opening Buys
1 Buy 90.9% 9.1% 0.0% 0.0% 0.0%
2 Buys 68.2% 30.3% 1.5% 0.0% 0.0%
3 Buys 42.0% 47.2% 10.5% 0.3% 0.0%
4 Buys 21.0% 48.0% 27.0% 4.0% 0.1%
5 Buys 100.0% 0.0% 0.0% 0.0% 0.0%

 

Cumulative Probability of Opening Buys Bottom-decked in Deck 2
0 1 or more 2 or more 3 or more 4 or more
# of Opening Buys
1 Buy 90.9% 9.1% 0.0% 0.0% 0.0%
2 Buys 68.2% 31.8% 1.5% 0.0% 0.0%
3 Buys 42.0% 58.0% 10.8% 0.3% 0.0%
4 Buys 21.0% 79.0% 31.1% 4.1% 0.1%
5 Buys 100.0% 0.0% 0.0% 0.0% 0.0%

In other words, if you want to minimize the risk of one of your opening buys being bottom-decked at the end of Deck 2, then BUY FEWER CARDS as your opening buys.   If you buy just 2 cards with your opening hands, such as Freighter and Patrol Mech with a $4/4 split, then there is a very favorable chance (68.2%) that neither of them will be bottom-decked.  Not bad!  However, if you buy 3 cards with your opening buys, such as Freighter + Missile Bot + Trade Pod with a $4/4 split, the chance that none of them will be bottom-decked falls to just 42.0%, meaning it is now more likely that one or more of them will be bottom-decked!  Is the card you just bought worth the added risk of bottom-decking?  That’s a tough question and highly dependent on the situation, so I guess the best answer I can give is…

https://i0.wp.com/top5lists.net/wp-content/uploads/2011/04/do-you-feel-lucky-punk.png

Another common example is being 1st player with a $2/4 split.  You buy a Cutter with your $2 hand.  You have three choices for your $4 hand… Blob Wheel ($3), Survey Ship ($3), or 2 Explorers ($4).  It’s better to use all of your trade to buy those Explorers to avoid wasting $1, right?  Not necessarily!   Both the Cutter plus Blob Wheel or Survey Ship buys put you at much less risk of bottom decking your buys, making you a favorite to draw both opening buys and having a stronger economy in Deck 2,  whereas in the Cutter + 2 Explorer case it’s more likely that one or more of the buys will be bottomed and you’re at risk to get stuck with a string of $5 hands.  Obviously, the former case is a much better scenario if you’re chasing a strong $6+ card like a Port of Call.

The 5 opening buy scenario is obviously a special case.  Buy buying 5 cards, your deck size will be 15, which is a multiple of 5, meaning that no cards at all will be bottom-decked.  This scenario is discussed at length in FlyingArrow’s article Deck Size for Spiked and Flat Decks so I won’t go into it here.

It’s Not All Doom and Gloom

Where there is risk, there is also opportunity.  The inverse of your opening buys being bottom-decked is that those annoying starting cards (scouts and vipers) can be bottom-decked as well.  So, while the more cards you buy increases the risk that they will be bottom-decked, it also increases the chances that you’ll get lucky and bottom-deck more starters instead.  If this happens, get ready for some good times in Deck 3, as you get to take full advantage of the trade/scrap from your opening buys in Deck 2 AND from all your good cards being concentrated in Deck 3 without those starters in the shuffle.

The odds of bottom-decking 3 or more starters aren’t aren’t overwhelming (42% for 3 bottomed starters with 3 buys, 21% chance of 4 bottomed starters with 4 buys), but they are significant enough to occur a noticeable number of games and thus worth considering.   For example, if your opening buys revolve around several cheap cards or combat-oriented cards (4 explorers, for example), then bottom-decking is not as likely to hurt you and the chance of getting lucky and bottoming 3-4 starters  is a reasonable gamble to take.   I personally like making this gamble when I’m going for an early green or yellow rush, where you’re opening buys consist of 3-4 cheap attack cards like Blob Fighters, Battle Pods, and Blob Destroyers, and Imperial Fighters and Frigates.

https://i2.wp.com/i.imgur.com/5ec7n0a.jpg

So, let’s take a look at how all these probabilities average out over the long run:

# of Opening Buys # Cards Bottomed  TOTAL # Buys Bottomed AVERAGE # Starters Bottomed AVERAGE Starters/Buys Bottomed RATIO
1 1 0.09 0.91 10.00
2 2 0.33 1.67 5.00
3 3 0.69 2.31 3.34
4 4 1.14 2.86 2.50
5 0 0.00 0.00

It’s no surprise that the average number of your opening buys that are bottom-decked increases significantly with each additional buy.  But the average number of starters (scouts, vipers) that are bottom-decked increases as well.  Isn’t bottoming your starters a good thing?  Yes, it is… the problem though is that the ratio of bottomed starters to bottomed buys goes down as you buy more cards.  This means that over the long run, you’re going to bottom-deck  more of your opening buys relative to your starters if you always buy 4 cards.  But it also means that you’ll be injecting a lot of chaos because of the 1-in-5 chance that you’ll bottom-deck 4 starters and turbocharge your Deck 3, and injecting chaos might be your best chance of stealing a win when your opponent gets off to a much stronger start.

In summary:

  • 1-2 opening buys is “safer”.  Less risk of opening buys being bottomed, but less opportunity for beneficial chaos as well.  Better for “spiked” or trade/scrap-focused opening buys.
  • 3-4 opening buys are more”chaotic”.  Higher risk that your opening buys will be bottomed, but more starters are bottomed on average.  Better for “flat” opens or combat-oriented opens, or where your opponent gets the better cards first and you want to try and create some luck.
  • Think carefully about whether buying another card is worth increasing the risk of your opening buys being bottom decked.
  • If my opening buys revolve around one or two strong economic/scrap cards, then I like to play it safe and buy as few cards as possible if I can.   For example, if I have a $4/4 opening shuffle and buy a Freighter ($4) with my first hand and a Supply Bot ($3) with my second hand, it’s probably a good idea to  leave that extra $1 unspent rather than buy a Imperial Fighter /Fed Shuttle/Blob Fighter, especially if I’m chasing a valuable $6+ card.

FINAL THOUGHT:  It’s generally still best to buy the best cards available even if it increases the risk of bottom-decking, but don’t buy extra cards if you don’t need them.   This is the main reason I’ll almost never buy an Imperial Fighter with my opening buys.  🙂

Thanks for reading!

 

BONUS EDIT – 2 Explorers vs 1 Blob Wheel

In the comments, creynolds31 asked a GREAT question about the difference between buying 2 Explorers and 1 Blob Wheel, when both seem to add the same amount of trade on average after bottom-decking probabilities are taken into account.

My response:

You are thinking about this correctly, however there’s another important aspect that needs to be considered. Although as you say, the average trade of 2 Explorers vs 1 Blob Wheel opening buy vis-a-vis bottom-decking are the same, but the way in which this trade is distributed between the 2 hands of Deck 2 are very different. This can make a huge difference, especially if you’re hoping to buy a strong $6+ card in Deck 2 (which is often a good strategy).

Specifically, in the 2 Explorer case, you either need to draw both Explorers in one hand or draw 1 Explorer and 4 scouts in order to get a hand with $6. There is also a small chance of drawing a $7 hand with both Explorers and 3 scouts. In the Blob Wheel case, a $6 is easier to get because the Wheel just needs to avoid being paired in a hand with both Vipers, and a $7 only needs the Wheel and 4 scouts.

I worked out the actual numbers of the trade distribution for these scenarios in Deck 2 really quickly, so hopefully I got this right:

  • 2 Explorers
    • Chance of drawing hands of $5 or less: 58%
    • Chance of drawing a $6 hand: 35%
    • Chance of drawing a $7 hand: 7%
  • 1 Blob Wheel
    • Chance of drawing hands of $5 or less: 13%
    • Chance of drawing a $6 hand: 53%
    • Chance of drawing a $7 hand: 33%

So as you can see, although both scenarios add roughly the same amount of trade to your Deck 2 hands, the Blob Wheel is clearly more advantageous if you’re going after a big card in Deck 2. This advantage in “big trade” is generally going to be more profitable than the extra 3 combat the Explorers give you.

 

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6 thoughts on “Making Your Own Luck: Your Opening Buys and How Not to Bottom-Deck Them

  1. creynolds31

    Great article! Question: If I buy two explorers to acquire incremental economy of $4 at a 68.2% chance of not bottom decking them, or a blob wheel alone for only three incremental economy with a 90.9% chance of receiving full value, these two buys yield the same expected value of 2.728 and 2.727 respectively. Doesn’t that mean that the explorers have the clear advantage over the blob wheel opening buy, since in all cases we assume scrap in deck two of all cards in question and the explorers yield an additional 3 damage over the blob wheel? You could be trying to combo with green, sure, but either way you scrap the blob wheel ASAP so the benefit of even a possible green deck 2 combo has to run through another probability calculation further diluting the expected value, the outcome of which is probably less than the guaranteed incremental 3 combat in the two explorer scenario. Am I thinking about that correctly?

    Liked by 1 person

    Reply
    1. HomerJr Post author

      Thanks! This is a GREAT question.

      You are thinking about this correctly, however there’s another important aspect that needs to be considered. Although as you say, the average trade of 2 Explorers vs 1 Blob Wheel opening buy vis-a-vis bottom-decking are the same, but the way in which this trade is distributed between the 2 hands of Deck 2 are very different. This can make a huge difference, especially if you’re hoping to buy a strong $6+ card in Deck 2 (which is often a good strategy).

      Specifically, in the 2 Explorer case, you either need to draw both Explorers in one hand or draw 1 Explorer and 4 scouts in order to get a hand with $6. There is also a small chance of drawing a $7 hand with both Explorers and 3 scouts. In the Blob Wheel case, a $6 is easier to get because the Wheel just needs to avoid being paired in a hand with both Vipers, and a $7 only needs the Wheel and 4 scouts.

      I worked out the actual numbers of the trade distribution for these scenarios in Deck 2 really quickly, so hopefully I got this right:

      2 Explorers
      – Chance of drawing hands of $5 or less: 58%
      – Chance of drawing a $6 hand: 35%
      – Chance of drawing a $7 hand: 7%

      1 Blob Wheel
      – Chance of drawing hands of $5 or less: 13%
      – Chance of drawing a $6 hand: 53%
      – Chance of drawing a $7 hand: 33%

      So as you can see, although both scenarios add roughly the same amount of trade to your Deck 2 hands, the Blob Wheel is clearly more advantageous if you’re going after a big card in Deck 2. This advantage in “big trade” is generally going to be more profitable than the extra 3 combat the Explorers give you.

      I hope that answers your question!

      Liked by 1 person

      Reply
  2. Chester Baker

    I’m loving it. I’m very very tired, so if I missed this in the article, let me know. But I’d think that the Wheel also has a couple of other advantages that are worth considering.

    It throws your opponent off… They often will either assume you are going all blob, or try to figure out the purchase. I have heard a lot of beginning players talk about the Blob Wheel as if it’s useless, and they don’t understand it sometimes. Also, they have to make the choice of whether or not to destroy it… It might soak up some damage for you, but it’s almost certainly going to last a round or two.

    Also, I like that you can leave it sitting there until you have the $ to buy the big cards, you can still buy another Explorer or the like, then grab the larger buys with the Wheel on another hand!

    Keep up the great work guys!

    ~NoisyCricket

    Like

    Reply
  3. Pingback: And Now for Something Completely Empirical: Opening Hands and Buys | Star Realms Strategy!

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