Modern Rotisserie Draft

[Eric Chan]

Because I don't actually have a good idea for how to program that.

YO i need your help. or anyone's help! math problem:

if i have one splinter twin, one kiki-jiki, one pestermite, and one deceiver exarch in a forty card deck, what is the probability of drawing at least one of the two red cards and at least one of the blue cards by turn five?

...asking for a friend.


edit:
my back of envelope calculations (literally, i had to bust out the pen and a discarded envelope for this) says 22% while on the play, i.e. 11 cards seen by turn 5. is that anywhere near accurate?

 

[Onderzeeboot]

Yeah... I would draft a backup plan

 

[Modin]

I would be up for the 2nd Roto draft.

 

[spicewitch]

YO i need your help. or anyone's help! math problem:

if i have one splinter twin, one kiki-jiki, one pestermite, and one deceiver exarch in a forty card deck, what is the probability of drawing at least one of the two red cards and at least one of the blue cards by turn five?

...asking for a friend.


edit:
my back of envelope calculations (literally, i had to bust out the pen and a discarded envelope for this) says 22% while on the play, i.e. 11 cards seen by turn 5. is that anywhere near accurate?

Let us assume that it is turn 5. Let us assume that you are alive.
(The above is the shakiest assumption, I think.)

If your 7 card hand contains none of your 4 combo pieces, you will mulligan. (Not strictly true, but making that assumption is closer to the truth than assuming that you will never mulligan. Anything more accurate than that is too complicated for my tastes)
You are either A) on the play and have cast 3 cantrips, or B) you are on the draw and have cast 2 cantrips. In short, we're assuming you'll lay your eyes on 14ish cards by turn 5.

So far, I've gotten to a point of "your 7 card hand has a 55.2% chance to contain at least 1 combo piece. If you keep that hand, you have a 55.0% chance to either see the other half of the combo in your starting hand or find it by turn 5".

 

[Jason Waddell]

YO i need your help. or anyone's help! math problem:

if i have one splinter twin, one kiki-jiki, one pestermite, and one deceiver exarch in a forty card deck, what is the probability of drawing at least one of the two red cards and at least one of the blue cards by turn five?

...asking for a friend.


edit:
my back of envelope calculations (literally, i had to bust out the pen and a discarded envelope for this) says 22% while on the play, i.e. 11 cards seen by turn 5. is that anywhere near accurate?

I got 21.88%. So that seems accurate.

Here's my reasoning, let me know if any of this sounds wrong.

We have 4 "successes", 36 misses, and are drawing 11 cards without replacement. This puts us in Hypergeometric territory.

Our outcome of "drawing at least one of each part" can be expressed as the sum of three probabilities:
1) drawing two of the pieces (1 of each)
2) drawing 3 of the pieces (2 of one, 1 of the other)
3) drawing all four

Parts 2 and 3 are pretty straightforward. In R:

  dhyper(3, 4, 36, 11) +
      dhyper(4, 4, 36, 11)

The first part is slightly trickier. We have to account for the possibility of drawing, say, Splinter and Kiki. We are conditional on the fact that we're drawing two combo pieces, then, consider where we are after having drawn Splinter Twin. We have three combo pieces remaining, so our next combo piece drawn has a 2/3rds chance of being either Pestermite or Deceiver Exarch.

Altogether it's....

dhyper(2, 4, 36, 11) * 2 / 3 +
  dhyper(3, 4, 36, 11) +
      dhyper(4, 4, 36, 11)
[1] 0.2188606

Note that if we consider cantrips like Preordain in the like, (and fetchlands thinning the deck), things get more favorable. Seeing 15 cards bumps you to 37%. But to cross the 50% threshhold you need to get up to 19 cards seen.

Compare this with an actual deck where we have, say 14 combo pieces out of 60 and a high density of cantrips, then we pretty quickly approach the 90% mark.

 

[Onderzeeboot]

I like mathy posts

 

[spicewitch]

I got 21.88%. So that seems accurate.

Here's my reasoning, let me know if any of this sounds wrong.

We have 4 "successes", 36 misses, and are drawing 11 cards without replacement. This puts us in Hypergeometric territory.

Our outcome of "drawing at least one of each part" can be expressed as the sum of three probabilities:
1) drawing two of the pieces (1 of each)
2) drawing 3 of the pieces (2 of one, 1 of the other)
3) drawing all four

Parts 2 and 3 are pretty straightforward. In R:

  dhyper(3, 4, 36, 11) +
      dhyper(4, 4, 36, 11)

The first part is slightly trickier. We have to account for the possibility of drawing, say, Splinter and Kiki. We are conditional on the fact that we're drawing two combo pieces, then, consider where we are after having drawn Splinter Twin. We have three combo pieces remaining, so our next combo piece drawn has a 2/3rds chance of being either Pestermite or Deceiver Exarch.

Altogether it's....

dhyper(2, 4, 36, 11) * 2 / 3 +
  dhyper(3, 4, 36, 11) +
      dhyper(4, 4, 36, 11)
[1] 0.2188606

Note that if we consider cantrips like Preordain in the like, (and fetchlands thinning the deck), things get more favorable. Seeing 15 cards bumps you to 37%. But to cross the 50% threshhold you need to get up to 19 cards seen.

Compare this with an actual deck where we have, say 14 combo pieces out of 60 and a high density of cantrips, then we pretty quickly approach the 90% mark.

What if you give him a 44.8% chance to mulligan?

 

[spicewitch]

one splinter twin, one kiki-jiki, one pestermite, and one deceiver exarch

I thought you were asking this question to try to bait someone into wasting a pick on hate-drafting you, only for you to end up doing a RW version of the combo with Village bell-ringer and such.

I think in general my experience with player counts of 2-4 really works against me here. I may have overvalued staying "open" (there are 3 decks that I know of which I can go into with these picks) and overestimated the likelihood of others to hate draft at all.

Edit: I'm looking for a few volunteers who aren't already in this draft to help me pick which direction to go. We'll have a team name and a logo and maybe snack-prizes!

 

[Jason Waddell]

What if you give him a 44.8% chance to mulligan?

Uh, this gets into other weird assumptions that I'm not entirely comfortable with. I don't think mulligan rules for such are so clear cut, nor do I think tossing any 7 without a combo piece is advisable.

Technically you can do the math telescopically, giving him 10 cards seen with a mulligan to 6, etc., but I don't think it tells us a ton about the deck. As is, I think you can't expect it to be your win condition a majority of the game, and whether you want to dedicate picks to it being part of your gameplan is a calculated risk for somebody else to have to consider.

 

[Eric Chan]

I thought you were asking this question to try to bait someone into wasting a pick on hate-drafting you, only for you to end up doing a RW version of the combo with Village bell-ringer and such.

maybe i am! but then again, maybe i'm not. THE MIND GAMES

 

[Jason Waddell]

Also, I am moderately surprised that Eric and I ended up on the same number. Are you secretly a statistician, Eric?

 

[Eric Chan]

hah! i'm no more a statistician than apparently everyone on this board is secretly a programmer...

uh, i googled around until i figured out that this was the urn problem (e.g. in this case we have an urn with 2 red balls, 2 blue balls, and 36 purple balls), and that apparently the term for this is multivariate hypergeometric distribution. i then watched a youtube video where a guy shows how to calculate this type of problem using pencil and paper. if i had known there were functions for this in R...!

actually, is there a function in R for multivariate hypergeometric distribution? in case i wanted to play around with those numbers some more.

...you know, that friend still wants to know.

 

[spicewitch]

hah! i'm no more a statistician than apparently everyone on this board is secretly a programmer...

uh, i googled around until i figured out that this was the urn problem (e.g. in this case we have an urn with 2 red balls, 2 blue balls, and 36 purple balls), and that apparently the term for this is multivariate hypergeometric distribution. i then watched a youtube video where a guy shows how to calculate this type of problem using pencil and paper. if i had known there were functions for this in R...!

actually, is there a function in R for multivariate hypergeometric distribution? in case i wanted to play around with those numbers some more.

...you know, that friend still wants to know.

Preliminary work is on the Math Games tab. It's not a formula though, it's a link to some page I found and some dicking around with the results from it.

 

[Jason Waddell]

hah! i'm no more a statistician than apparently everyone on this board is secretly a programmer...

uh, i googled around until i figured out that this was the urn problem (e.g. in this case we have an urn with 2 red balls, 2 blue balls, and 36 purple balls), and that apparently the term for this is multivariate hypergeometric distribution. i then watched a youtube video where a guy shows how to calculate this type of problem using pencil and paper. if i had known there were functions for this in R...!

actually, is there a function in R for multivariate hypergeometric distribution? in case i wanted to play around with those numbers some more.

...you know, that friend still wants to know.

I believe there's a package 'biasedUrn' that deals with this: http://cran.r-project.org/web/packages/BiasedUrn/BiasedUrn.pdf

I've never used it, but I think that stuff is out there.

Can't wait til you guys start drafting hate cards.

 

[vennythekid]

All goes accroding to plan, Tezzerett makes my Torpor Orb into a 5/5 Twin Hoser! Ccccombo

 

[Jason Waddell]

All goes accroding to plan, Tezzerett makes my Torpor Orb into a 5/5 Twin Hoser! Ccccombo

In your Mono deck?

 

[Onderzeeboot]

I have a feeling I can predict Jeff's next two picks...

Spoiler

Stoneforge Mystic
Umezawa's Jitte

 

[Eric Chan]

Preliminary work is on the Math Games tab. It's not a formula though, it's a link to some page I found and some dicking around with the results from it.

uh, i think your mull math is a little sketchy. consider constructed. if my opening hand was 3 Island 4 Serum Visions, i probably would not mull that. it's not a great keep, but it lets me dig for a lot of cards.

i'd rather take the simplistic approach and ignore mulligans altogether and get some baseline statistics. anything else requires you to first know the exact deck composition.

 

[Jason Waddell]

Eric, when you going to give me them sweet, sweet edit rights?

 

[vennythekid]

Movin' right along to a sweeeet deck

 

[Eric Chan]

Eric, when you going to give me them sweet, sweet edit rights?

whoops, i missed the skype chat! check your email now

 

[MCMcEmcee]

I was strongly considering picking pestermite + restoration angel instead

 

[vennythekid]

In your Mono deck?

Before I picked up the Finks, I was considering going for Artifacts/Tezz. I think there's too much fighting for blue to do that at the moment though

 

[James Stevenson]

I'm not too sure where this is going, but I like that it's going there:

 

[Eric Chan]

I was strongly considering picking pestermite + restoration angel instead

i honestly can't tell if you're being serious or if you're just trying to get me to waste early picks on the other half of my combo

MIND GAMES!