Hello forum, I was wondering if you could help me with a part of an article I read. The article is on using Markov Chains in the game of Blackjack/21.
It is assumed that the chance of drawing any card from the deck is 1/13, which is a fair assumption when many decks are involved. The paper is giving an example to derive a basic strategy which is a strategy of mathematically correct plays by which the player should follow to keep his expectancy favorable.
One of the assumptions used is that the strategy would only apply given neither player nor dealer have Blackjack, which again makes sense as the player will only have to make his play given that he does not hold Blackjack (which is being dealt an Ace and a card valued 10 in the first 2 cards dealt to the player, for those who are unaware of the game rules).
In the paper, a calculation is used to determine what the probability is that the face down card of the dealer is valued between 2 through 9 or an Ace given the dealers other card is an Ace. It uses Bayes theorem. They get an answer of 1/9, but I do not see how they arrived at this answer. What I have tried:
is Baye's theorem.
So P(the face down card is 2-9 or an A|the dealers face up card is an A)=P( the dealers face up card is an A|the face down card is 2-9 or an A)*P(the dealers face up card is an A)/the face down card is 2-9 or an A
I calculated an answer of 8/13 but as i stated before, the answer is 1/9. Could someone perhaps shed some light on this?