Probabilities of a Risk battle - Part 2

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In this video we go over the probabilities of winning one round. Since a battle is made up of many rounds we need to know the probability of how each scenario plays out.
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Do you know how the probabilities of each round was calculated?

unclesam
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so basically as long as you have more dice than the defender always go for it?

mrnoneofurbusiness
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I'd be interested to know the probability of the cards delivering the right combination for turning in reserves, after just 3 cards, then 4 then five..

constructioneerful
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How does someone calculate 7776 possibilities?

brunogebara
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Curious as to how you determined how many rolls each defender wins vs. the attacker. I understand how you got the total amount of rolls (6 to the power of the number of dice). How did you figure out winners/losers totals? Surely not by counting?

colinwarn
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How does someone calculate the number of combinations that player 1 wins?

brunogebara
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Hey, your video is really helpful, but i wanted to know if there is a way to find the probabilities (second 20) through Excel, and if so how can we do it, i am a bit confused...
Thank you in advance!

mouniachafik