Mulligan

[Jaxly]

I'd love this..  The disadvantage should be higher though, because imo this benefits rainbows much more than mono/duo decks so it wouldn't strictly be fair to say since both players have the option to do it both are on even ground.. Id go with -1 card and you finish a turn when you use it. In addition playing any card that turn should forfeit the right to a mulligan.

[Delreich]

A kind of mulligan is being implemented in the next update (1.21). It's an automatic, one-time redraw if your first hand doesn't have any 0-cost card.
Read more here: http://elementscommunity.org/forum/index.php/topic,4066.0.html

[ScytherLoL]

Lol I was just on my way to add that but ninjad by Delriech again.

Scyther

[fl0ppy]

I badly want a mulligan of better type.

I dont know if it's just unluck but I have tried 3 different decks in the last 2 days and  I get normally 1 to 2 pillars for a max of 5 in the happy times, and keep in mind that in all  of those decks I have half of the deck that is guess what: pillars!!!

Once is a coincidence, twice unlucky, but when it's happens 95% of the times that I dont draw enough pillar to play, it's getting annoying. Now I'm playing a 60 cards deck with 25 + a nova deck and I get 1 or 2 pillars in the opening and desert for rounds, I've lost 4 match for not drawing pillars at all. So a chance to take a mulligan on the first hand for me would be more than welcome!

[PoLdeR]

HI, im a mathematician.... ive been calculating (approximately) the chance of having a bad draw with some decks:

Lava Golem rush: 11.2 % (standard build), Immogavels: 29% (standard build), gas nymph 51%, pillarless the creation of life: 24 %, supernova rush: 17 % (with 6 pillars, 6 supernova), rol/hope: 19 % (standard build)

a bad draw meaning in the golem rush that you cannot cast a golem from the first 8 cards.
in immogavels not casting a golem or gavel first 8 cards,
in gas nymph not getting a quint, nymph, wind pillar first 15 cards or starting with 2 or less pillars (23 % getting nymph).
creation of life not catching a rustler nova and firefly combo first 10 cards,
supernova rush not catching a supernova and a pillar first 9 cards, (not accounting for the automulligan, 17 % with accounting for the automulligan)
rol/hope not catching a rol, fractal and pillar combo first 10 cards.

the formulas are easy:

for instance the chance of getting a photon and an immolation in first 8 cards (in case of the immogavels) is:
(1-(22/30)^6)^2 = 0.71, that is 71 % so the chance of not getting this is 29 %

this is because the chance all immolations are in the last 22 cards is (about) (22/30)^6, so getting one or more is 1-(22/30)^6 and since you need a photon and an immo you have to do (1-(22/30)^6)*(1-(22/30)^6) QED

now i hear you saying: I can get a phoenix, pillar, immo and golem also to cast a golem....... i did add that possibility....... besides im not counting other kinds of bad draws so the percentage is probably higher than it is above

i might extend this list later.

conclusion: as long as there is no mulligan, only play monos, duos with one kind of pillar or fastdraw rainbows, any other deck has bad draws. all decks will have bad draws!
when two of these decks face eachother, theres about only a 60% chance they both do not have a bad draw.

i vote for the following system: before the game starts you get to pick upto 4 cards which get switched with random remaining cards in the deck. That way most monos also benefit from it.

NOTE: the section of pillars was wrong before... The other calculations are still right. The trick you use for calculating a one or more chance i described is easy, but when you want to calculate something like the odds of getting 1 or 2 it can get quite messy.... my apologies! The conclusion is adjusted.

[jmdt]

HI, im a mathematician.... ive been calculating (exactly) the chance of having a bad draw with some decks:

Lava Golem rush: 22 % (standard build), Immogavels: 29% (standard build), gas nymph 25%, pillarless the creation of life: 24 %, supernova rush: 23 % (with 6 pillars, 6 supernova), rol/hope: 19 % (standard build)

a bad draw meaning in the golem rush that you cannot cast a golem from the first 8 cards.
in immogavels not casting a golem or gavel first 8 cards,
creation of life not catching a rustler nova and firefly combo first 10 cards,
supernova rush not catching a supernova and a pillar first 9 cards, (not accounting for the automulligan)
rol/hope not catching a rol, fractal and pillar combo first 10 cards.

the formulas are easy:

for instance the chance of getting a photon and an immolation in first 8 cards (in case of the immogavels) is:
(1-(22/30)^6)^2 = 0.79, that is 79 % so the chance of not getting this is 21 %

this is because the chance all immolations are in the last 22 cards is (22/30)^6, so getting one or more is 1-(22/30)^6 and since you need a photon and an immo you have to do (1-(22/30)^6)*(1-(22/30)^6) QED

now i hear you saying: I can get a phoenix, pillar, immo and golem also to cast a golem....... i did add that possibility....... besides im not counting other kinds of bad draws so the percentage is probably higher than it is above

any deck with 30 cards, 14 pillars has a chance of getting 2 or 1 pillar (not counting 0 pillars) in the first 8 cards of: 0.3 %
any deck with 30 cards, 12 pillars has a chance of getting 2 or 1 pillar (not counting 0 pillars) in the first 8 cards of: 0.8 %
a 45 card timebow with 5 hourglasses has only a 86 % chance to get one or more hourglassses in the first 15 cards.

i might extend this list later.

conclusion: as long as there is no mulligan, only play monos, duos with one kind of pillar or fastdraw rainbows, any other deck has bad draws.
when two of these decks face eachother, theres about only a 60% chance they both do not have a bad draw.

i vote for the following system: before the game starts you get to pick upto 4 cards which get switched with random remaining cards in the deck. That way most monos also benefit from it.

These are pretty awesome stats.

[teffy]

But probably most of them are wrong (without mulligan, as PoLDeR did)

this is because the chance all immolations are in the last 22 cards is (22/30)^6

No. You need the hypergeometric distribution  you can calculate here:
http://stattrek.com/Tables/Hypergeometric.aspx

Also see the topic "Hypergeometric Probability and You (http://elementscommunity.org/forum/index.php/topic,7893.msg96239#msg96239)"

Pop Size = 30
Sample Size=8
Number of success in pop=6
Number of success in sample = 0
P(X=0)=12,6 % that´s not (22/30)^6=15,6%

You made an estimation( binomial distribution), which you can only make, if your sample size is much smaller than the pop size (and some other assumptions).

And the rest:

any deck with 30 cards, 14 pillars has a chance of getting 2 or 1 pillar (not counting 0 pillars) in the first 8 cards of: 43 %

No. Hypergeometric probability says:
Pop Size=30
Sample Size=8
Number of Succes in pop=14
Number of success (X) in Sample =2
P(X<=2)-P(X=0)=15,4%-0,2%=15,2%

Edit: I probably know your mistake here. You calculated (P(X<=3)- P(X=0) instead of (P(X<=2)-P(X=0).

any deck with 30 cards, 12 pillars has a chance of getting 2 or 1 pillar (not counting 0 pillars) in the first 8 cards of: 28 %

ca 28 %. correct.

a 45 card timebow with 5 hourglasses has only a 86 % chance to get one or more hourglassses in the first 15 cards.

No. ca.88%
P.S.
The same things are written in Troubleshooting (http://elementscommunity.org/forum/index.php/topic,12755.msg172047#msg172047).
Same problems there.

[PoLdeR]

You made an estimation( binomial distribution), which you can only make, if your sample size is much smaller than the pop size (and some other assumptions).

And the rest:

any deck with 30 cards, 14 pillars has a chance of getting 2 or 1 pillar (not counting 0 pillars) in the first 8 cards of: 43 %

No. Hypergeometric probability says:
Pop Size=30
Sample Size=8
Number of Succes in pop=14
Number of success in Sample =2
P(X<=2)-P(X=0)=15,4%-0,2%=15,2%

You are right about that i approximate... i got caught ^^, you are right and i am wrong :S.... i only had a basic course in stochastics 6 years ago and its not my specialization. I actually sux at stochastics ^^, but i know this approximation gets close enough. What went wrong for the pillars section I dont know, I will remove this section then before ppl will sue me ^^

[PoLdeR]

so if you DO want to this exactly for the immogavels chance of getting an immo and a photon, you actually need to calculate

P(X > 0 & Y > 0 ) where X is the number of immos in the first 8 cards and Y the number of photons. This can be rewritten to P(X > 0 ) + P(Y > 0 ) - P(X > 0 or Y > 0 ) , which are probabilities you can calculate more easily using the hypergeometric calculator or on paper:

P(X > 0 or Y > 0 ) = 1 - P(X = 0 & Y = 0 ) = 1 - (12 over 0 )*(18 over 8 )/(30 over 8 ) = 1 - 1*(18*17*16*15*14*13*12*11/(8!))/(30*29*28*27*26*25*24*23/(8!)) = 1 - 0.00747626186906546727 = 99.26 %

P(X > 0 ) = P(Y > 0 ) = 1- P(X = 0 ) = 1 - (6 over 0 )*(24 over 8 )/(30 over 8 ) = 1 - 1*(24*23*22*21*20*19*18*17/(8!))/(30*29*28*27*26*25*24*23/(8!)) = 1 - 0.12565870910698496905 = 87.5 %

so  P(X > 0 & Y > 0 ) = 2*87.5 % - 99.26 % = 75.74 %
which means you have 24.26 % bad draws.

You see why i dont wanna do this all the time for all these decks cuz its a lot of work. It seems that if you take the percentages in my above post and take like 5/6 of them you get a bit closer to reality. Anyway i still think these numbers are interesting, easy to calculate and it was a good effort. DEMA i think was made better by math.

Thanks, btw

PoLdeR

[craawzy]

You can mulligan down to 1 card (no-one is stupid enough to do that ? )