Thread: Can anyone help me with this statistics probability question ?

Can anyone help me with this problem please ?

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The question is about: Dealer’s Absorbing State Probabilities in Blackjack

I need to solve this probem in an excel file.

Hey mathlearn.

You need to show some effort by showing us your thoughts and your working out: we can't and won't just give you a full answer if you won't attempt anything on your own behalf.

Yes, I am trying to solve the problem but need guidance in a right direction.

From the problem I do understand that Suppose I am dealing with a 2 and a 2. Thus I am in state 4. I need to determine the probability of being in other
states after the next card is dealt. As am example, what is the probability I go to state 11. This means I got a 7 on the next deal. There are 4 7s. So the probability of going from 4 to 11 is 4/52. As another example, the probability I go to 14 after the next card is dealt is 16/52 since there are 4 10s, 4 jacks, 4 queens, and 4
kings (each count as 10).

How to create the transition probability matrix in dealer's hand ?
I would really appreciate if you could give me an example and show me how to do it - That would be very helpful since this case study problem is quite complex.

The first thing you should do is draw some kind of tree diagram of what states you start off in and then the possible states you end up in after you do the action you are doing.

If you have n starting states and n ending states then figure out which ones are possible (i.e. non-zero) and then just look at the probabilities of each option individually.

If it's a markov chain, the transition matrix won't change at each iteration.

So the first thing to do is to ask: How many states there are and what the states correspond to?

Hello chiro, I am trying my best to solve the problem, by using calculations like 4/52 and 16/52, I have created this matrix: Markov_Process_XLS - Copy-XLS.xlsx

Could you please take a look at it and explain me if I am wrong or right ? and what to do next in order to solve the problem ?

I would deeply appreciate if could download my xls file and edit it and show me where I am wrong or right and what to do next ?

Dude, that's a lot to go through.

I'd appreciate if you could outline your reasoning for obtaining all elements of the matrix but in the most basic manner possible if you could.

I understand that this subject is a (I took it myself a while ago), but the most important attribute is being able to understand these things intuitively and not so much by resorting to fixed mathematical models that are fudged (yes, there are lots of people who are able to get by using fudged reasoning but thankfully it doesn't last long).

This is a huge system and I hope you can empathize with my reasoning.

chiro, thank you for the reply. I know that's a lot of work, it took me a while to do the calculations. that's ok, you don't have to go through all that.
I will see what I can do to solve the problem.

Since you mentioned "You need to show some effort by showing us your thoughts and your working out" - I hope you are convinced that I am trying to solve the problem and not became a member of this forum just to get answers.

thanks for your time and guidance.

When I said what I said about effort and working out, the reason I say that is because you get a lot of people that just want everyone else to do it for them and you are clearly not in that category after seeing your work and your responses.

It's sad when people just come on forums to try and get everyone else to do all their work for them: I don't understand the benefit in that personally but it happens a lot.

thank you

Yes I know a lot time people don't wanna put effort as its easy to get hand feed because eating food requires effort.