[Article] The Peril of Playing a Coinflip Deck.

[the Luke]

This article is in response to the new Meandeck Tendrils deck.  To make things clear, my position is that Dark Ritual should be restricted and that player interaction should be encouraged in this two player game.  However, I don't intend to let my bias influence this analysis.  When I assume figures, I'm going to try to assume them in the combo deck's favour.  This is simply because it makes my logic more solid.

What is a coinflip deck?  I define a coinflip deck as an ultrafast combo deck that aims to have no interaction with the opponent at all.  While the deck may require a lot of skill to play, essentially any matchup turns into a biased coinflip, either the deck goes off, or it crumples in a heap.  I think it is safe to call Meandeck Tendrils and the Goblin Charbelcher deck coinflip decks.

Why is playing a coinflip deck bad?  I think they are bad because while the deck requires playskill, it doesn't really reward playskill.  I think you're only really rewarded for playskill when you are playing a deck that interacts with an opponent.  Here's why:

Meandeck claim that their Tendrils deck has a 70% first turn goldfish rate.  Now, pretend that this directly corresponds to a probability of 0.7 of winning any matchup.  0.7 is probably too high an estimate, but this is okay, because I contend that 0.7 is not high enough.  I also assume that this matchup probability is when the deck is played optimally ALL the time.

Now, why is 0.7 too low a match win probability for a coinflip deck?  Well take Waterbury.  To get into the top 16, you had to achieve 6-2 or better (it is a little harder than this to get into top 16, but again, this overestimates the chances of top 16, which is good).  By the binomial theorem, the probability of this coinflip deck getting to the top 16 (by going 6-2 or 7-1 or 8-0) is:

p = C(8,6)x0.7^6x0.3^2 + C(8,7)x0.7^7x0.3 + C(8,8)x0.7^8
p = 0.2965 + 0.1977 + 0.0576
p = 0.5518

So your probability of getting into the top 16 is 0.5518, IF you play perfectly and IF your chance of winning any match is 0.7 (which, of course, is likely an overestimate).

Now if you have (say) 11 players playing the same deck, and assume that they all have an independent chance of top 16 (which in a big event is fairly likely... I recall hearing about only one mirror match for Meandeck Tendrils), then the chance of the coinflip deck having at least one member in the top 16 is:
1 - (1 - p) ^ 11
= 0.9999
So the coinflip deck is virtually guaranteed a top 16 participant, although individually, the chance isn't that great (though better than average).

To summarise, coinflip decks force the outcome of any game they play into an exercise in statistics.  As there is no (or minimal) player interaction, there is no real way to outplay the opponent.  You play optimally, and either win or lose, at random.  There is no possibility to take advantage of opponent mistakes, or outplay them in anyway.  Although the (high) coinflip value I chose did make the chance of top 16 more likely than not, if that rate dips to just 0.65, then the chance of top 16 falls to only 0.4278.

-Luke

[Elric]

Let me say that while I love the way you do the analysis, I would take a 70% win coin flip deck any day of the week.  If you can beat everything (but the mirror) 70%, regardless of your skill (once you learn to play the coin flip deck other skill is irrelevant), you have to be an extremely skilled player to do any better with a non-coin flip deck.  

In fact, if you have a constant chance to win each game (not actually true, because sideboarded games are different, and the difference in sideboarded games where you go first and second causes extra problems), then you need a 63.7% chance to win each game to have a 70% win percentage in the (2 out of 3 games) tournament matchup.  As a player who does not expect to outplay his opponents enough to win 1.75 games for every one I lose, I would take this deck in heartbeat.  

In fact, if you were the only person who knew about the deck, most all of us (no, not you, The Atog Lord) should take this deck over our existing one.  Otherwise, we’re pretending to have more skill than we actually do.  If I were playing Rich, you bet I’d want the coinflip deck.  Carrying this to its logical conclusion, imagine if this deck were available to everyone.  Then most of us should all take the coinflip deck.  But for each person who takes the coinflip deck, the effects of true skill get lower and lower.  You can see that what will happen in equilibrium is that everyone should be playing the coin flip deck.  

Now, this isn’t quite true because this model isn’t accurate.  If I were playing Rich with a coin flip deck, I wouldn’t have a 70% chance to win (no deck removes skill to that extent, so his playskill would change things somewhat).  As long as he could beat me over half the time (and could beat everything else over 70% of the time) he should continue to play Control Slaver.  The best players should play a deck that enables them to take more advantage of skill.  If an objectively 70% deck came along, though, everyone should end up playing it.

A 55% chance to get into the top 16 at Waterbury is incredibly good.  If you let me bet on the chance a given player would make it to the top 16 at Waterbury, there are very, very few players I'd guess to have a higher than 50% chance to make top 16 (this is out of 200 people!)

I wrote this on consistency in a post last summer (funny, I used 70% as well):

"Here is a note on consistency: I don't think that inconsistency means that much for a deck except that this deck often loses to itself.  Having to mulligan to 4 with Belcher is annoying and getting unlucky with Belcher means that you can lose to any random deck.

Consider this: what if you could play a deck that won 70% against absolutely anything, from a top T1 deck to your recent draft deck. Of course you'd play it. If everyone else was actually playing draft decks it would be a bad choice, but you would still win the vast majority of your matches. The problem with the 70% deck when you are much better than most of your opponents is that your superior playskill most likely won't improve your matchups beyond 70%. If you really are that good, pick a deck that lets you completely outplay your opponents to a 90% win percentage.

Spoils of the Vault causes your deck to lose to itself, but that isn't a good reason to not play it. A good reason to not play it is if it lowers your win percentage. In his article on Charbelcher vs. Tog, Smennen said that inconsistency may keep people from playing Belcher. If all matchups are similar and Belcher really does have the highest win percentage after taking every factor into account, then you should be playing Belcher, mulligans to 4 and all."