Calculations behind determining basic strategy plays?

[Fate]

Is there any free quality resources showing the calculations/formulas used in determining best plays in blackjack as shown on basic strategy tables?

And/or is there solid proof showing that the best plays for blackjack as shown on basic strategy tables are in fact the best plays?

How about card counting calculations/formulae/proof?

It is compelling to just ‘trust’ the basic strategy and card counting tables without question since many different sources tout relatively identical tables and the recommended plays seem logical.

However, a little voice in the back of my head keeps saying, “What if casino owners came up with the idea to have someone write a seemingly true but ultimately flawed book about how to beat blackjack?”.

And even today, maybe, just maybe, casinos continue propaganda that blackjack is beatable by paying people to continue the hoax having them write truthful sounding information and stories that are ultimately lies to entice people to believe they can have an edge over the casino by playing a certain way.

I realize my ideas really seem unlikely; however, I will not be completely satisfied until I find proof that basic strategy and card counting tables are in fact, legit.

Of course Edward Thorp’s book, Beat the Dealer, or other books may answer my questions, however I was hoping there was a cost free solution found on the internet.

[Smartpart]

The best play is going to be whichever provides the most utility. If you want in depth analysis of CC, buy Griffin's Theory of Blackjack.

[bigplayer]

The EV for every two card player hand combination versus every possible dealer up card for every possible decision is listed in Appendix E of "Professional Blackjack". In it he describes his method for calculating the various expectations for single deck, six deck, h17, and s17 games.

Perhaps your own expectations of blackjack are unrealistic. Basic strategy is called "Basic" because that is what it is...BASIC. You cannot beat blackjack by playing basic strategy, you can only reduce the house edge to it's lowest possible level, but the house edge is still there. To make Blackjack beatable you have to play an advanced strategy. You can create your own card counting strategy or double check existing strategies to your hearts content with a program like CV-Data. There is more on Basic Strategy in Peter Griffin's book "Theory of Blackjack".

[skuner]

Blackjack - A Champion's Guide by Dario De Toffoli and Margherita Bonaldi (ebook not free).
This book is from a college thesis, amslaurea.unibo.it/792/1/Bonaldi_Margherita_tesi.pdf, you need a knowledge of Italian ;-) but there are a lot of table.

[ohbehave]

I believe you might find what your looking for if you do an internet search for "combinatorial proof of blackjack basic strategy".

[ZeeBabar]

Fate, you are so lucky!!! If I had posted the same question you did, I would have been rained nasty insults because I did not read have a dozen books, the archives in a few forums, bought software and conducted simulations and on and on. I see nothing wrong with your question and if you are interested the recommendations made are very good. Once you get through those, and if you go on to become a more advanced Card counter, the best books would include BJ Attack 3rd edition by Don Schlesinger.

[mofungoo]

A really good explanation of the rationale behind the basic strategy decisions is contained in Playing Blackjack as a Business, which contains a lot of color charts that make it easy to see the gain for using basic strategy and the cost if you don't. Not free but worth it.

[Nyne]

If you insist on doing the grunt work, you can work out the infinite deck strategy by brute force. First, start by determining the possible final dealer hands for any given starting total, and the corresponding likelihood. Start with the totals where the dealer must stand, so if the dealer total is 20 for example, the dealer's final total will be 20 with probability 1. Work through the remaining hard totals. For 16, the dealer will end at 17 with probability 1/13, 18 with probability 1/13, 19 with probability 1/13, 20 with probability 1/13, 21 with probability 1/13, and will bust with probability 8/13. For 15, the probabilities will be the raw probability that you draw to exactly that total plus the probability that you draw an ace (1/13) times the probabilities you determined for a 16 total. Once you work out all of the dealer final hand probabilities for all possible hard hands, then all soft hands, you can calculate the likelihood that the dealer hits each ending total from any particular up card (taking into account all of the possible down cards the dealer may have). If you do the math correctly, you should end up with numbers similar to these: http://wizardofodds.com/games/blackjack/appendix/2a/

The numbers won't match perfectly because we aren't taking into account the depletion of each rank and the slight change in probabilities that results, but it should be close enough to convince you the Wizard's totals are reasonably accurate. Now, you'll want to follow a similar process for all player hands. Start with hard 21 and work your way down. With a hard 21 against a particular dealer up card, what is your EV for standing? With the dealer total tables, you should be able to calculate this easily. What is the EV for hitting? Obviously -1 in this case. What is the EV for doubling? -2, of course. So the correct play, unsurprisingly, is to stand, since it has the highest EV. Next you'll try 20, calculating the EV for standing, hitting, and doubling, and figure out which is best. Again, it will be stand, and you'll have an EV for standing on 20. As you work your way down the list of all hard totals, you'll be able to calculate the EV for whatever the optimal play is for each total, assuming you play optimally for the higher totals (i.e. you continue hitting or you stand based on whatever you calculated previously.) It becomes a relatively simple (but time consuming) exercise to map the possible draws to the EV of the resulting total to determine the EV for each possible play. Once you finish the hard totals, you do the same thing for the soft totals, starting at soft 21 and working your way down to soft 12 (AA). Now one more time through to evaluate the EV of the pair splits, and you will have generated a pretty accurate basic strategy table for shoe games. If you haven't made any mistakes, your EV charts for each play should match the numbers here: http://wizardofodds.com/games/blackjack/appendix/1/

This is a lot of brute force work and I don't recommend it to anyone, but if you are interested in deriving basic strategy yourself, this will get you 99% of the way there. If you want to be truly correct, you'll have to account for all of the different possible hand compositions that could get you to that total, and how that impacts the odds on your draws, but I suspect if you follow the process I've outlined above, you'll be more than happy to trust the tables produced by the experts over the years.

[Fate]

Much thanks to everyone! I really appreciate all the recommendations and advice. Cheers!

[Slacker13]

The EV for every two card player hand combination versus every possible dealer up card for every possible decision is listed in Appendix E of "Professional Blackjack". In it he describes his method for calculating the various expectations for single deck, six deck, h17, and s17 games.

Perhaps your own expectations of blackjack are unrealistic. Basic strategy is called "Basic" because that is what it is...BASIC. You cannot beat blackjack by playing basic strategy, you can only reduce the house edge to it's lowest possible level, but the house edge is still there. To make Blackjack beatable you have to play an advanced strategy. You can create your own card counting strategy or double check existing strategies to your hearts content with a program like CV-Data. There is more on Basic Strategy in Peter Griffin's book "Theory of Blackjack".

Great response. I always view your posts in high regard.