Probability of getting *that* one card you need - Mathematics anyone?

[rrc]

[This thread doesn't apply to SK who had 100% probability to get any cards they want. This is for other factions who suffer from much lesser consistency than SK]

Let's say I want to draw a particular card in R1 which determines my win condition. Let's say I have a tutor for that card and a tutor for that tutor. For example Royal Decree -> Avallach Sage -> That one Artifact (or) Menno -> Royal Decree -> THE card (or) Royal Decree -> Crone -> Organic Card, etc. and Prince Villam. That is 3 exact cards I want and a 4th card which *can* get one of them.

Now, what would be the probability that I will get one of the three cards in R1 after using two mulligans (and with 3 mulligans).

And if someone is crazy enough to get this to next level, what would be the chance that I get it in R2, provided I didn't draw them in R1? Answer should be like "Like 75 out of 100 games I will get it in R1 and 95 out of 100 games I will get in R2".

As Geralt says, I am too old for this sh*t.
[I know that with 3 tutors my deck is already f**ked up in provisions. But I am just curious.]

 

[4RM3D]

The same thing applies to Poker and thus you can use the same calculator: http://www.ohrt.com/odds/

For the first round you have:
Total: 25 cards
Drawn: 9 (10 + 3 mulligans - 4 outs)
Outs: 1 + 3 (the one and three tutors)
Required: 1 (of 4)
Probability: 86% chance

EDIT: Made a correction to the calculation. I am not sure if it's entirely accurate in every situation, but it should still give a decent indication.

 

[FG15-ISH7EG]

To calculate which is the chance to draw one of the 3, we should start with the opposite propability of drawing none of them.
As the mulligan means you are just drawing two more cards, we can look at the chance of drawing 12 cards out of 25 and not getting any of the 3 desired cards.
For the first card this is a propability of 22/25, because you still have 25 cards in your deck, of which 22 are undesired. For the second card both numbers decrease by 1, such that you have get 21/24 for that card. And so on until the 12th card which has a propability of 11/14 to be undesired. If we calculate the product of all those propabilities, we will get the total propability of you not drawing any of the 3 desired cards with the 12 cards that you draw, which is (13*12*11)/(25*24*23)=12%.
So the propability of drawing at least one of your desired cards is 88%.

With 13 cards (which means 3 mulligans), you get a chance of 90% to draw at least 1 desired card.

 

[rrc]

The same thing applies to Poker and thus you can use the same calculator: http://www.ohrt.com/odds/

For the first round you have:
Total: 25 cards
Drawn: 10 + 3 cards (because mulligans)
Outs: 1 + 3 (the one and three tutors)
Required: 1 (of 4)
Probability: 96% chance

This is a fantastic tool 4RM3D! I can see that if I have 2 mulligans and not counting Prince Villam, I have 87.5% chance. Thank you!

To calculate which is the chance to draw one of the 3, we should start with the opposite propability of drawing none of them.
As the mulligan means you are just drawing two more cards, we can look at the chance of drawing 12 cards out of 25 and not getting any of the 3 desired cards.
For the first card this is a propability of 22/25, because you still have 25 cards in your deck, of which 22 are undesired. For the second card both numbers decrease by 1, such that you have get 21/24 for that card. And so on until the 12th card which has a propability of 11/14 to be undesired. If we calculate the product of all those propabilities, we will get the total propability of you not drawing any of the 3 desired cards with the 12 cards that you draw, which is (13*12*11)/(25*24*23)=12%.
So the propability of drawing at least one of your desired cards is 88%.

With 13 cards (which means 3 mulligans), you get a chance of 90% to draw at least 1 desired card.

How I read it..
To calculate lakdjflkajvaijdkjfalkejfopaidjfl;kajepofijaopdijfalkdjfakdhfaiudhfkjsdhkfjhaiefuahsdkjfhakjefhaisdufhiehfskf
With 13 cards (which means 3 mulligans), you get a chance of 90% to draw at least 1 desired card.

Thanks a lot for that explanation.