### MMDOC Probabilities and Combinations Guide

MMDOC Probabilities and Combinations Guide by Infernal_Wisdom

Here I will make some calculations in order to avoid people always complaining about luck, just want to let everyone know you can direct your luck

First Rule

Its best to have your deck minimum to keep your chances optimal and higher and that is 1 hero+8 event cards+50 in board cards(might magic and fortune)

So it is just a simple formula used to calculate combinations

1- What is the all combinations of cards, which are given to us in start?

it is that you will have 7 cards in your hand when your first turn has come

so it is

C(50,7)= 50!/7!*(50-7)!= 99 884 400

so as you see your first 7 cards can come to your hand in almost 100 million different combination, its a huge probability pool

2- What is the chance of getting at least one certain card at start hand? (its like what is my chance to start at least one firebolt when Im playing inferno)

Lets assume we have 4 copies of firebolt in our deck

We can calculate this by thinking opposite, what is the chance of not getting even one firebolt card at starting hand?

For example we think there will be no firebolts coming to our hand, so in 50 cards deck we assume our “7 starting card” can contain every card except firebolt

so except firebolt we have 46 cards in our deck

so without firebolt there can be C(46,7) different combination

C(46,7)= 46!/7!*(46-7)!= 53 524 680

So as you see there is about 53 millions of combination that not contains even a single firebolt

so we can find the combinations that contains 1 or more firebolts in our starting hands if we extract this combinations from all combinations

and thus we can calculate the probability of starting 1 or more firebolts

(99 884 400 – 53 524 680)/99 884 400=%46,41

3 – Also we can unaccept our starting hand and shuffle our deck again and can gain another hand, what is the effect of that chance?

so when we start we see there is no firebolts and we want that card right?

than we shuffle again and there is a %46,41 chance to get at least one fire bolt again

and that chance is calculated by

%46,41 + (1-%46,41) * %46,41 = %71,28

So if we use all of our chances we can start %71,28 probable with one desired card, so this is not luck as you see. better think when placing dark assassins against inferno or don’t curse player who placed dark assassin in his first turn.

I feel kinda sleepy now. I will add the effects of dropping a cards copy number in our deck from 4 to 3 and what will happen if we do? we will see
also I will calculate exact probability of having only 1-2-3-4 cards probabilities separately

COMING SOON

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