Fail Draw - Math people whats the percentage?

[geekz_always_win]

You taken into the chance of the first hand failing (for the mulligan), which is about 1 in 5, and you get approximately 1 in 12 million.

Would people actually be interested in a thread about how probability actually works? I'd be happy to make one if people cared.

Exactly where did this 1/5 estimate come from?

[Kamietsu]

You taken into the chance of the first hand failing (for the mulligan), which is about 1 in 5, and you get approximately 1 in 12 million.

Would people actually be interested in a thread about how probability actually works? I'd be happy to make one if people cared.

Exactly where did this 1/5 estimate come from?

I don't see the mulligan as one in five :/ so i'm curious too.

I just got my first full hand +one card starting hand without anything I could play(costing 0 quanta) in at least 100 duels.

[QuantumT]

You taken into the chance of the first hand failing (for the mulligan), which is about 1 in 5, and you get approximately 1 in 12 million.

Would people actually be interested in a thread about how probability actually works? I'd be happy to make one if people cared.

Exactly where did this 1/5 estimate come from?

That's the change of having no towers in first hand (and therefore using the mulligan), which can be calculated using hypergeometrics.

Note: The 1 in 5 is for this specific deck, so long as the towers are the only thing that cost 0 in it.

[Kamietsu]

You taken into the chance of the first hand failing (for the mulligan), which is about 1 in 5, and you get approximately 1 in 12 million.

Would people actually be interested in a thread about how probability actually works? I'd be happy to make one if people cared.

Exactly where did this 1/5 estimate come from?

That's the change of having no towers in first hand (and therefore using the mulligan), which can be calculated using hypergeometrics.

Note: The 1 in 5 is for this specific deck, so long as the towers are the only thing that cost 0 in it.

Ok, I understand what you mean now.

[Dragoon]

Would people actually be interested in a thread about how probability actually works? I'd be happy to make one if people cared.

I'd be interested.

[wizelsnarf]

what deck did you use Mr Blonde?

[teffy]

How many players fight against FGs with Nova-Rainbow decks ? How often do they do this ? And how many players would post such a "fail draw" ?

[Zubon]

This probably happens more than anyone notices because you just do not live that long against most enemies.  Getting 1 tower in the first 20 turns to be roughly a 1 in 4 event if you have 1/5 towers.  My math says that is not possible, but I see it consistently, because the RNG hates you.

[zse]

You taken into the chance of the first hand failing (for the mulligan), which is about 1 in 5, and you get approximately 1 in 12 million.

Would people actually be interested in a thread about how probability actually works? I'd be happy to make one if people cared.

Exactly where did this 1/5 estimate come from?

That's the change of having no towers in first hand (and therefore using the mulligan), which can be calculated using hypergeometrics.

Note: The 1 in 5 is for this specific deck, so long as the towers are the only thing that cost 0 in it.

That hypergeometrics is "really hardcore math" for most of people here (me included), but that probability is actually pretty easy to calculate. Basically you just calculate the probability of several events happening one after another:

First the probabilities of single events:
You draw 1st card: 48 cards, 9 pillars, 39 other -> p(1st card is not pillar) = p(1) = (48-9)/48 = 39/48
You draw 2nd card: 47 cards, 9 pillars, 38 other -> p(2) = 38/47
3rd card: 46, 9, 37 -> p(3) = 37/46
.
.
.
35th card: 14, 9, 5 -> p(35) = 5/14

Then the probability of all those things happening one after another:
p(quite bad luck) =  p(1) * p(2) * p(3) * ... * p(35) = 39/48 * 38/47 * 37/46 * ... * 5/14 =~ 0,000000426... =~ 1/2.345.604

p(mulligan) =  p(1) * p(2) * p(3) * ... * p(7) = 39/48 * 38/47 * 37/46 * ... * 33/42 =~ 0,209 =~ 1/5

[th1s1sr4nd0m]

It's 1 out of 2,500,000.

Statistics (as of 08/12/2020):

Elements have been played 3,577,011 times on Kongregate.com and 7,854,864 times on elementsthegame.com.
For a total of 11,431,875 games played so far.

So, I imagine this has happened a few times before.

And each time it's "played" (somebody connects) they play more than one game.

Maybe 8-10 times in all?

But what's the chance your'e playing a 48 card deck with 9 pillars?

[ArtCrusade]

That's like the opposite of what happened to me. My first 10 cards were Stone Pillars with a Mono- Shrieker-rush

@QuantumT: I'd be interested in such a thread, go ahead please!

[MrBlonde]

what deck did you use Mr Blonde?

It's my modded nymphbow that i use for FG farming. I prefer this out of all my other decks and percentage wise runs the same as every other top deck i've played (CCYB, Puppy's, etc). With that said this is just my personal deck that i like to play so no complaining to me if you use it and you think it sucks.

What also makes this situation interesting is how often can you actually go 36 turns, not play a pillar and actually survive. This situation hypothetically could have happened  8-10 times before but who has actually made it to this point? Also to make it sicker i would have had to play either Elidinis or Decay. The other 21 FG's undoubtedly kill me before i even come close to this point and Osiris who i could survive long enough against only has effectively 56 cards to last 28 turns (of course he can rewind but i would blow up his eternities to prevent that).

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