How are Blackjack Basic Strategy tables calculated (What is the maths behind them) Lets assume a very basic set of rules and table for them, these rules are unlikely to be seen in any casino and the reason is clear, there is only a 0.04% edge in favour of the casino, this could be beaten without ever counting cards simply by applying basic strategy and not even knowing the exceptions to it. Here are the rules.
1). We always start with a full deck of cards.
a). Assume this for 2 reasons, first the count (for card counters) is irrelevant as there is not enough cards out to establish a pattern (such patterns can affect the way you play using basic strategy and therefore the stats of the game).
b). Second it means we are always working from the same base numbers outlined below
2). We have 1 full deck of 52 cards
3). 4 of these cards are gone out of the deck leaving 48 (these 4 cards are the first 4 used in play above)
4). One of the 4 cards above in point 3 are unknown (because it is the dealers face down card)
5). This leaves only 3 cards whose value are known to us (from which we make all our decisions)
6). After the game is finished, all the cards are replaced in the deck and the deck is reshuffled to begin again (this brings us back to point 1 to repeat the process for every game).
I cannot include screenshots because I am new to this forum. But I wanted to post one of a basic strategy table with the rules specified.
If the dealer up card is 6, and your two cards show a total of 14 (perhaps 8 and 6, or 9 and 4, it does not matter the combination), you should stand (take no more cards).
However if your hand was an A3 (soft 14), you should double down.
Finally if your hand was a 77, (double 7), you should split.
The questions I have are, what are these decisions based on.
The reasons for questioning these tables are because almost every website or book quotes such tables without explaining the maths behind them. And when the maths is outlined, it’s usually done in either a convoluted and inefficient way, or over simplified to the point that it does not explain properly the other decisions in the table.
Essentially what I am asking is how do you calculate your next move given a set of rules and a specific hand. Meaning how exactly are the three examples above worked out. Is there a specific formula that can be used so that I may program it and build my own tables.
 A: Taking your example:  If the dealer up card is 6, and your two cards show a total of 14 (perhaps 8 and 6, or 9 and 4, it does not matter the combination), you should stand (take no more cards).
The basic idea is to see if your probability of winning the hand is increased by drawing over standing.  If you stand, you only win if the dealer busts.  You can calculate this either exactly or by simulation.  If you hit, you lose if you go over 21.  If you don't go over 21, you might get a higher total than the dealer.  Again, you can calculate this either exactly or by simulation.  The easier way is to simulate lots of hands.  Note that it does matter what your 14 is-if it is two 7's, you have a higher chance of busting than if it is 8+6, 9+5, or 10+4, as there is one less card left that you can draw without busting.
I would not say the basic strategy is useless, as playing that way reduces your losing percentage substantially from two alternatives:  either never bust (stop when you are at 12) or play like the dealer.  It is not sufficient to get above even, but one part of a long term winning strategy will include losing as little as possible when you can't win.
A: Ed Thorp was the first to devise a system for beating casino blackjack, by simulating millions of deals on an IBM computer and turning the results into a card counting system. But if you always start with a full deck the casino has the edge. Basic strategy just gives the player (almost) an even chance.
