Determine the right amount of copies; Draw Chance

[CuCN]

The draw chance of any card depends not only on the number of copies of the card and the size of the deck, but also the number of zero-cost cards in the deck.
Because the mulligan is a bit weird in EtG (it leaves the original hand on top of the deck), I don't see an easy way to calculate the correct probabilities. Populating the tables using a simulator may be the only real solution.

[andretimpa]

The draw chance of any card depends not only on the number of copies of the card and the size of the deck, but also the number of zero-cost cards in the deck.
Because the mulligan is a bit weird in EtG (it leaves the original hand on top of the deck), I don't see an easy way to calculate the correct probabilities. Populating the tables using a simulator may be the only real solution.

If my calculations are in the right direction you can write the result as a sum over 3 variables of a bunch of things involving factorials. Not doable by hand, but feasible to calculate in a computer.

The game reshuffles the deck after the mulligan, doesn't it?

[Chapuz]

The game reshuffles the deck after the mulligan, doesn't it?

We don't know if it shuffles again or if the cards are sent to the bottom of the deck. Take the option you like most, the result won't change considerably

[andretimpa]

[15:39:38] Chapuz: 1) the deck is shuffled. 2) You draw 7 cards. 3) if you didn't get any 0-cost cards, the deck is reshuffled and you draw another 7 cards
[15:39:45] Chapuz: am I right?
[15:39:53] ColorlessGreen: yeah, 4 year old outdated thing in tutorials != current thing in stats forum
[15:39:55] ColorlessGreen: no
[15:40:16] Chapuz: no?
[15:40:19] ColorlessGreen: (3) if you didn't get any 0-cost cards, a new hand is drawn out of the cards you don't currently have in your opening hand and your opening hand is put back on top of the deck
[15:40:30] ColorlessGreen: meaning the top seven cards are guaranteed non-zero-cost
[15:40:41] ColorlessGreen: and the second opening hand has a higher than normal chance of zero cost cards

I'll try to do it like this. I foresee some nasty correlations appearing though ...

First conclusion: The mulligan has no relevance for n>14, that is after the first 7 cards have been drawn.

[andretimpa]

I think I got an answer. It is not pretty but should be easy to use it to build a tool like the one Xeno got, but without doing simulations.

https://dl.dropboxusercontent.com/u/7229007/mulligan.pdf