Conditional Probability

After reading Theory of Blackjack, I’d really like to be able to understand how to use the equations for my own personal satisfaction. I’m basically illiterate when it comes to math and all of the above YouTube videos on the subject use exactly the same brief examples with the assumption that their brief examples should suffice for an understanding. I’ve looked and looked but haven’t found a dummies guide to learning this. Perhaps some of you might have a constructive recommendation for me, perhaps a resource or two for the laymen.

I'm curious on the cimbinational analysis initially used to determine hit, stand, split, double down, surrender for a hand versus dealer uo card.  My understanding the initial derivation on basic strategy determined these values for all dealer, player hand combinations.  Thr Roger Baldwin statistical paper.

Cconditional Probility.  Chapter one of "Probability and Random Processes and Estimation Theory for Engineers"  by Henry Stark and John Woods.

Here is some material that I found very useful:

If you want a grounding in the fundamentals of Probability, conditional probability , combinatorial analyis,  statistics, etc., I recommend "Introduction to Probabiliyt, Statistics and Random Processes, by Hossien Pishro-Nik.  It's a very readable textbook, with example Problems/Solutions. and the author makes an effort ot give you an intuitive grasp for the concepts. The book's content is also available on the web. 

If you want to see how all this is applied specifically to gambling games (BJ, Craps, Roulette, Poker, Keno,  Lottery, Slots. Ruin, House Advantage, etc.) get "The Doctrine of Chances - Probabable Aspects of Gambling" by Stewar N. Ethier.  It helps if you have some working knowledge of Probability and Combinatorial analysis first, as well as first year calculus.

Also, look up the videos from the Khan Academy - that's the best I've found for people looking for material for  "dummies".  Lot of simple examples to get across the fundamentals.

Actually, I learned probabilities partly from wikipedia and partly from communicating to several posters on this forum. 

Wikipedia definition for conditional probability.  Take note of statistical independence and mutual exclusivity.

https://en.m.wikipedia.org/wiki/Conditional_probability

This is the forum of Blackjack 21, so naturally it’s the conditional probability of a natural (blackjack hand) that really helps the understanding of this particular terminology. The probability of a natural in all blackjack hands is about 4.7%, while that of a player winning hand is about 42.5%. With these two probability numbers, what is the probability of a natural in all player winning hands? 
 

Is this a good example of conditional probability? 

Conditional probability is not in my thinking relating to Blackjack derivation. Blackjack optimal play was derived from the discovery of a fixed set of optimal equations available due ro dealers required actions. Then using combinational analysis to determine expectations for each hand led to basic strategy.  Same procedure followed when cards removed.

What do you mean by Blackjack derivation? In the example I just posted above, if we consider an infinite deck blackjack game, this is a good math question. Is it a conditional probability problem? 

You're example does not indicate to me it's a conditional probability.  In this thread I previously asked for an example of the math behind combinational analysis.  To solve the problem of determining the expectations of A,6 versus a dealer 6 as an example.  When I spoke of optimal derivation I was speaking of Roger Baldwins derivation of basic strategy.  The statistics you speak of is not what I'm looking for.

You need to read Peter Griffin's The Theory of Blackjack.

Don

Sadly, I answered you, but the post didn't seem to go through. Short version: 4.7/42.5 = 11% = probability that a winning hand is a natural.

Don

I have the book.  I'll do in index check for what I'm looking for.  Thanks.

I’ve got a good example of conditional probability. What is the probability of a winning two-card 20 hand in Blackjack? 

In other words, if a blackjack table offers a Lucky Ladies side bet, what is the probability of winning both the main bet and the side bet simultaneously? 

CV Data for my count system says at +8 Lucky Ladies has positive expectation.  Don't know what you imply by good example of conditional probability.  Blackjack counting methods and Lucky Ladies side bets have good correlation due to reliance on 10 value cards.

Your point of correlation is valid, I guess, but I am thinking of a probability problem in Blackjack to understand conditional probability in general.

Try: Given that you have a blackjack, what's the probability that it's suited?

There are dozens of other possibilities. Be creative!

Don

Thank you for the feed back. I'll read some of the suggested material you all have referenced. I have read Theory of Blackjack and understood about 1% of it. Some of the tables do make sense but the rest is all non-sense to me. I'll give these references a try and then re-read Theory of Blackjack, and with any luck I might understand at least 10% of it.

Spend a little extra education $$ on Don Schlesenger's publications:

Blackjack Attack and

Latest Hi/Lo in depth publication

OP,  given you’re interested in diving into the math behind Blackjack, or any other gambling game, you would benefit from a basic course in probability, and that would cover combinatorial analysis, probability, conditional probability, expected value, distributions, variance, etc.  you should be able to work through all that  with some of the good textbooks available on  Amazon.  

Personally,  I  think the books are so much better at building up In a structured way your knowledge and understanding of the concepts as opposed to  searching on individual topics online. Those  posts and Wikipedia articles assume you have the basics down already. Maybe I’m just old school.