Coldsnap Draft: The Effectiveness of Surging Dementias

[jro]

By now anyone following the Coldsnap draft format must be aware of the potential brokenness of Surging Dementia.  While unplayable in small numbers, triple Coldsnap draft offers the potential to receive as many as 8 or 9 of the same common.  With so many in a deck, Mind Twisting your opponent for their full hand on turn 2 or 3 (and for a measly 2 mana and 1 card!) becomes possible.  There are two questions that I think need to be answered regarding the potential strength of Surging Dementia decks.  First, how many Surging Dementias do you need to make the card effective?  And second, how many Surging Dementias are you likely to see in a draft?  I'm going to try to answer the first question here.

One of the problems in determining the effectiveness of Surging Dementias is that it's hard to agree on criteria to establish "success" with the card.  Making your opponent discard his whole hand on turn 2 is obviously a success, but what about making them discard 5 cards on turn 3?  Or 2 cards on turn 3 and then 4 cards on turn 4?  To remove this qualitative assessment, I decided to determine the average number of discards (D) a deck with N Surging Dementias would cause by turn T, if the player was playing every Surging Dementia in hand as soon as possible.  I also determined the average amount of mana spent over this time per discarded card.  Qualitative judgments about what was successful could then be made afterwards.

If it is even possible to solve this problem analytically, the skills to do so are well beyond my capability.  A conceptually simpler approach would just be to play a very large number of games with each number of Surging Dementias, and see what happens.  The patience to do this is also beyond my capability, so I instead wrote a computer script to do it for me.  Being many years removed from any serious programming efforts, I used the tool most readily available to me: Microsoft Excel's Visual Basic for Applications.  Excel's macro language made easy what other programming approaches might have required sophistication to do.  For example, generating a randomized deck required just following few lines:

Code:

Range("B1:B40").Formula = "=RAND()"
    Range("A1:A5").Value = "sd"
    Range("A6:A40").Value = "a"
    Range("A1:B40").Sort Key1:=Range("B1"), Order1:=xlAscending, Header:=xlGuess, _
        OrderCustom:=1, MatchCase:=False, Orientation:=xlTopToBottom

This code yields the values "sd" (for surging dementia) and "a" (any other card) randomly distributed in cells A1 to A40.

All runs were performed with the assumption of drawing first, although the program could easily be changed to intead consider playing first.  Additionally, mana was assumed to develop at 1 additional available mana per turn.  These choices were made for ease of coding, although drawing first may be desirable in this kind of deck anyway.  The code is undoubtedly sloppy, but I believe it to be sound.  To conduct a run, the number of Surging Dementias was adjusted by changing how many fields were populated with the tag "sd" in the "generatedeck" procedure.  Then, the number of turns was adjusted by changing the block of cells tallied in the "TestSomeGames" procedure.  Currently, it counts from turn 2 to turn 5 (the cell ranges are B2:B5 and D2:D5).  This would be adjusted to turn 3 by changing these cell ranges to B2:B3 and D2:D3.

Here is the output I received from running the program considering having between 5 and 9 Surging Dementias in the deck, and considering total discards produced from turn 2 up until turn 3, 4, or 5.  Each combination of SDs and turns was run 100 times, except for 8 SDs and turn 4, which was run 300 times.

Code:

With N Surging Dementia, casting them ASAP, how many cards will you hit from opponent's hand by turn 3, and how much mana will you spend to do it?

With 9 Surging Dementias in deck:
 332      mana spent for     569 cards.
Average of   0.583479789103691       per card.
Average of   5.69        per game.

With 8 Surging Dementias in deck:
 300      mana spent for     430 cards.
Average of   0.697674418604651       per card.
Average of   4.3         per game.

With 7 Surging Dementias in deck:
 268      mana spent for     281 cards.
Average of   0.953736654804271       per card.
Average of   2.81        per game.

With 6 Surging Dementias in deck:
 266      mana spent for     256 cards.
Average of   1.0390625     per card.
Average of   2.56        per game.

With 5 Surging Dementias in deck:
 248      mana spent for     201 cards.
Average of   1.23383084577114        per card.
Average of   2.01        per game.

How about by turn 4?

With 9 Surging Dementias in deck:
 404      mana spent for     670 cards.
Average of   0.602985074626866       per card.
Average of   6.7         per game.

With 8 Surging Dementias in deck:
 1300      mana spent for     1696        cards.
Average of   0.766509433962264       per card.
Average of   5.653333     per game.

With 7 Surging Dementia in deck:
 386      mana spent for     424 cards.
Average of   0.910377358490566       per card.
Average of   4.24        per game.

With 6 Surging Dementia in deck:
 338      mana spent for     309 cards.
Average of   1.09385113268608        per card.
Average of   3.09        per game.

With 5 Surging Dementia in deck:
 260      mana spent for     214 cards.
Average of   1.21495327102804        per card.
Average of   2.14        per game.

How about by turn 5?

With 9 Surging Dementias in deck:
 426      mana spent for     727 cards.
Average of   0.585969738651995       per card.
Average of   7.27        per game.

With 8 Surging Dementias in deck:
 490      mana spent for     573 cards.
Average of   0.855148342059337       per card.
Average of   5.73        per game.

With 7 Surging Dementias in deck:
 400      mana spent for     423 cards.
Average of   0.945626477541371       per card.
Average of   4.23        per game.

With 6 Surging Dementias in deck:
 358      mana spent for     323 cards.
Average of   1.10835913312693        per card.
Average of   3.23        per game.

With 5 Surging Dementias in deck:
 306      mana spent for     247 cards.
Average of   1.23886639676113        per card.
Average of   2.47        per game.

Based on these results, I'd say that 7 Surging Dementia is the point at which this deck strategy will cause reliable enough disruption to warrant playing this approach.

The full Excel macros I used to make these calculations are available below.  I release all the code I wrote in it to the public domain.  I will field questions about how the code works, although you must promise not to make fun of my non-1337-h4X0r coding skills.  Anyone wishing to reproduce a substantial portion of the actual text I've written in this post should give credit to "a post on themanadrain.com".

A useful followup to this analysis would be to determine the percentage of drafts which are likely to contain N Surging Dementias.  I believe that the expected number in an 8 man draft is 4.06 (8*3*11/65), so getting the 7 that I think is desirable seems improbable.  Unsanctioned drafts containing more than 8 players represent a better chance of seeing enough Surging Dementias to make the strategy worthwhile.

Appendix: Microsoft Excel Visual Basic for Applications macro code for analyzing Surging Dementia

Code:

Sub Shuffle()
    Range("B1").Select
    ActiveCell.FormulaR1C1 = "=RAND()"
    Range("A1:B40").Select
    Selection.Sort Key1:=Range("B1"), Order1:=xlAscending, Header:=xlGuess, _
        OrderCustom:=1, MatchCase:=False, Orientation:=xlTopToBottom
End Sub

Sub draw()
    If Range("A1").Value = "sd" Then
        Range("C1").Value = Range("C1").Value + 1
    End If
    Range("A1").Delete Shift:=xlUp
End Sub

Sub generatedeck()
    Range("B1:B40").Formula = "=RAND()"
    Range("A1:A5").Value = "sd"
    Range("A6:A40").Value = "a"
    Range("A1:B40").Sort Key1:=Range("B1"), Order1:=xlAscending, Header:=xlGuess, _
        OrderCustom:=1, MatchCase:=False, Orientation:=xlTopToBottom
    Range("B1:B40").Clear
End Sub

Sub playsd()
    Dim n, hits, turnb As Integer
    hits = 0
    turnb = Range("C2").Value
   For n = 1 To 4
        If Not IsEmpty(Range("A1")) Then
            If Range("A1") = "sd" Then
                hits = hits + 1
                Worksheets(1).Cells(turnb, 2).Value = Worksheets(1).Cells(turnb, 2).Value + 1
                Worksheets(1).Cells(turnb, 4).Value = Worksheets(1).Cells(turnb, 4).Value + 1
            End If
            Range("A1").Delete Shift:=xlUp
        End If
    Next n
    For n = 1 To hits
        Call playsd
    Next n
    
End Sub

Sub PlayGame()
    Range("A1:D40").Clear
    Call generatedeck
    Range("C1").Value = "0"
    Dim counter As Integer
    For counter = 1 To 7
        Call draw
    Next counter
    Dim turn As Integer
    turn = 0
    Dim num_playable_sd, n As Integer
        Do While Not IsEmpty(Range("A1"))
        turn = turn + 1
        Range("C2").Value = turn
        Call draw
        num_playable_sd = turn \ 2
        For n = 1 To num_playable_sd
            If Range("C1").Value > 0 Then
                Range("C1").Value = Range("C1").Value - 1
                Worksheets(1).Cells(turn, 2).Value = Worksheets(1).Cells(turn, 2).Value + 1
                Call playsd
            End If
         Next n
    Loop

End Sub

Sub TestSomeGames()
    Dim n, numgames, hits, successes, totaldiscarded, manaspent As Integer
    Dim avgmana, avgcards As Single
    numgames = 100
    successes = 0
    totaldiscarded = 0
    manaspent = 0
    For n = 1 To numgames
        Call PlayGame
        hits = 0
        For Each mycell In Range("B2:B5").Cells
            If Not IsEmpty(mycell) Then
                hits = hits + mycell.Value
            End If
        Next mycell
        totaldiscarded = hits + totaldiscarded
        For Each mycell In Range("D2:D5").Cells
            If Not IsEmpty(mycell) Then
                hits = hits - mycell.Value
            End If
        Next mycell
        manaspent = manaspent + hits * 2
    Next n
    avgmana = manaspent / totaldiscarded
    avgcards = totaldiscarded / numgames
    Debug.Print manaspent, "mana spent for", totaldiscarded, "cards."
    Debug.Print "Average of", avgmana, "per card."
    Debug.Print "Average of", avgcards, "per game."
End Sub

[Harlequin]

I did an anaylisis of this useing Probabilities rather than deck randomizaion, and did a test over 10,000 trials.  Here is what I did.

First use Combinitorics to deturmin the Probability of being able to cast at least 1 SD on turn 2 (assuming you run 16 lands and N SDs).  The results of that are:
N -- Prob(Turn 2 SD|N=n & Lands = 16)
9   86.76%
8   84.50%
7   81.05%
6   76.24%
5   69.86%

Now I'll explaine my logic tree.
First I set up 10 rows and labled them 0 through 9.  This represents the number of times I was able to Discard that many cards.  So if I was able to cast it turn 2, and then it rippled twice, I would add 1 to the "3" Row (becuase the resulting discard was 3).  The code was essetially this logic Tree:
For T = 1 to 10000

Output row = "0"

If Rand < Prob(Turn 2 SD|N=n & Lands = 16)
  A = 1
    --- A is the number of times we need to preform a ripple
  Out Put Row = "1"
  Do Until A = 0

    Q = Number of SD in the deck / Size of the shuffled deck
       -- therefore: Q = Prob of the top card of the deck being a SD.

    For B from 1 to 4
      If Rand < Q Then
         A = A + 1
         # of SDs = # of SDs - 1
         OutputRow = OutputRow + 1
      End If
      Deck = Deck - 1
    Next B
   
    A = A - 1

  Loop 'Until A = 0
End If
Output_Row.Value = Output_Row.Value + 1

So essentially we are counting the number of times a spesfic trial comes up for a spesific number of discards.  And running 10,000 Trials  for each # of SDs from 9 to 5


Outcome   -- # of trial -- Dirrect % -- Cummulative
If you draft 9 SD...
0   1318   13.18%   
1   2382   23.82%   86.82%
2   1110   11.10%   63.00%
3   672   6.72%   51.90%
4   479   4.79%   45.18%
5   365   3.65%   40.39%
6   258   2.58%   36.74%
7   166   1.66%   34.16%
8   0   0.00%   32.50%
9   3250   32.50%   32.50%

What this says is that... 13% of the time, you will not have cast SD on turn 2.  It also says that 23% of the time, you will have your opponent Discard exactly 1 card.  the Cummulative Col is really what we care about.  This is how many times will they discard "At least" N cards.  So for example rougly half the time, 51.9% of the time, they will discard 3 OR MORE cards from there hand on turn 2.  and assumeing they played a land on turn 1, then 36% of the time you have them discard thier entire hand.

Here are the rest of the results:

With 8...
0   1529   15.29%   
1   2828   28.28%   84.71%
2   1317   13.17%   56.43%
3   805   8.05%   43.26%
4   637   6.37%   35.21%
5   514   5.14%   28.84%
6   466   4.66%   23.70%
7   534   5.34%   19.04%
8   1370   13.70%   13.70%

With 7...
0   1914   19.14%   
1   3301   33.01%   80.86%
2   1497   14.97%   47.85%
3   867   8.67%   32.88%
4   710   7.10%   24.21%
5   596   5.96%   17.11%
6   532   5.32%   11.15%
7   583   5.83%   5.83%


With 6...
0   2332   23.32%   
1   3593   35.93%   76.68%
2   1628   16.28%   40.75%
3   988   9.88%   24.47%
4   656   6.56%   14.59%
5   491   4.91%   8.03%
6   312   3.12%   3.12%

With 5...
0   3005   30.05%   
1   3896   38.96%   69.95%
2   1582   15.82%   30.99%
3   819   8.19%   15.17%
4   468   4.68%   6.98%
5   230   2.30%   2.30%


=======================
What this doesn't Say.  This assumes you only play 1 SD.  The numbers are not 100% accruate but that assumuption actually both over estimates and underestimates the number of times you can discard.  It over estimates it because if you have 2 in hand then you actually have 1 less in your library.  however it underestimates it on turn 4 because essentially you can attempt to ripple agian.  so I think by turn 4 the numbers will even out.  So essentially if you have 2 in hand, then your turn 2 expectation of ripple is dropped down 1 table (because you have less SDs in your remaining library).  And on turn 4 you can try it again.

[jro]

For what it's worth, I played a 9-man Coldsnap draft on Tuesday, and got 8 Surging Dementia.  I picked them very highly, including first in pack 1 over Rimewind Owl, second in pack 2 over Deepfire Elemental (I was B/R), and many times over Zombie Musher, which they seem to be in the same common run with.  I obviously don't advocate this strategy in general, but I wanted to see if I could make the deck happen.

In the six games I played, I managed a full discard on turn 2 twice, left 1 card on turn 2 twice, a full discard on turn 3, and all but 1 on turn 3.  I unfortunately lost my first two games, even after that, to good white weenies with rippled Surging Sentinels.  (I was playing lots of 2 toughness red dudes, and couldn't get my 3x Martyr of Ashes on line either game.)  One key thing I learned is that you want to play land based on your post-rippling deck size.  In my case, 14 land was the way to go.  Next, you need beaters that will win in combat, not a weenie rush.  You especially need to be able to get by a 2/2+ (the white toughness pumping bear) or a 3/3 (Boreal Centaur), since they can come out before you've made them lose their hand.  In black, only Balduvian Fallen is really good in this capacity.

[Mindstab_Thrull]

jro: Sounds about right. A deck running that many Suging Dementias is, when all is said and done, a control deck of sorts, and control decks usually have to rely on big beaters for the win. Not being a draft expert of any sort, I probably would have taken the Elemental over the Dementia (and I'm guessing you would too - it's the biggest reason I splashed for black at the CS prerelease), as that card is so good at filling two roles: removal AND beats (much like the Rimescale Dragon - why isn't that a blue or white card?). If you're going to take Dementias high for a reason, then if you don't find any you should look for beaters next. That being said.. if a deck is properly designed for it, is it feasible to consider SD a nonrandom Hymn? Should we be calling it that way in Limited only?

[Hi-Val]

In a similar vein, I've heard of downright stupid things done with Surging Aether. I don't know how highly picked they are these days, but rippling into 8 of those is such a huge tempo swing.