Wahrscheinlichkeit bei Magic the Gathering?
Its a "just 4 fun question":
i have a 60 card deck with 24 lands in it. i played 5 games MTG arena and had 5 games in a row no lands after 4 or 5 mulligans (i think i had to start with 3 cards).
how high is the probabilty for that? xD i think i have to be incredibly unlucky ?!
someone knows how to calculate the probability for that?^^
im just curious.
Übersetzung:
Ich habe ein Deck mit 60 Karten und 24 Ländern darin. Ich habe 5 Spiele in MTG Arena gespielt und hatte 5 Spiele in Folge keine Länder nach 4 oder 5 Mulligans (ich glaube, ich musste mit 3 Karten beginnen). Wie hoch ist die Wahrscheinlichkeit dafür? xD ich glaub da muss ich wahnsinnig pech haben?! Weiß jemand, wie man die Wahrscheinlichkeit dafür berechnet?^^ Ich bin nur Neugierig.
1 Antwort
You need hypergeometric distribution for this. I don't know enough to explain it, though. Luckily, in the age of internet I don't have to know how it works as I can just use a tool → https://aetherhub.com/Apps/HyperGeometric
I did enter the numbers as follows:
- Population size 60 (Number of cards in deck)
- Sample size 7 (Number of cards drawn)
- Successes in population 24 (Number of lands in deck)
- Successes in sample 0 (Number of lands drawn)
The calculator says that the probability for not having a land in the starting hand is 2,16 %. To account for four mulligans you have to raise the result, written as 0,0216, to the fourth power, which gets you the rather low probability of around 0,000000218. For this to happen five games in a row you have to raise that result to the fifth power. This gets you the incredibly low probabilty of around 0,000000000000000000000000000000000492. Note that I'm not absolutely sure that my thinking here is correct. Anyways. I feel safe to say that you should have played the lottery with your luck!
Saffron Olive here does a good job at explaining hypergeometric distribution:
Brewer's Minute: Hypergeometric Distribution in Deck Buildinghttps://www.youtube.com/watch?v=NPH17prodgM
Ergänzung: Das Tool für die hypergeometrische Verteilung gibt es auch auf deutsch. Sieht im Grunde genau so aus → https://magic.freizeitspieler.de/wahrscheinlichkeiten.php
You're welcome! It's about randomness but not a random question. I find it quite interesting.
just wow! thank you....i didnt expected such a thought through answer considering it was a kinda of random question! thx!