Question about basic strategy in Blackjack I was watching Beating Blackjack with Andy Bloch where he runs through the basic strategy charts that outline the best strategy with playing the game. Later he also talks about the methodologies to count, but that is not relevant to my question. 
He states in that video that the basic strategy is an outcome of computer simulations, and that suggests to me that its a rather weak method to go about doing it. I have a two-fold question, one is when is a computer solution considered good enough to be "true", and the second, surely, this is a much easier problem that does not need computer simulations to solve, are there any known methods to derive the basic strategy. 
 A: I'm not sure I understand your first question. You don't have a "computer model" for blackjack. The rules of the game are given. You can model the dealing of the cards as if they were uniformly random draws from a collection of objects (distinct objects if you are using a single deck of cards) without replacement.
Since it is a game with randomness built in, it is a good candidate for Monte Carlo simulation. To my knowledge, it is not very simple to derive basic strategy using just pen and paper because you would have to deal with a number of different cases and keeping track of them all can be tedious. I'm not aware of any elegant solutions to this problem.
If you go further and look at card counting strategies, things become even more complicated and the methods and strategies appear to be more and more heuristic.
A: The sort of question you would do with Monte Carlo is to decide "If the dealer shows a 6, what value should I draw to?"  You would do this by simulating many deals with the dealer showing a 6, try out various strategies, and see which has the highest expectation.  Under certain statistical assumptions, you can state that a particular strategy wins a% of the money at stake with a standard deviation of b%.  Raising the number of trials will decrease b%, roughly by the square root of the number of trials.  So if one strategy is clearly better than another, it won't take too many tries to know that.  If they are close, it will take a lot.  If they are really close, you will never know, but then it doesn't matter much.
As svenkatr states, the details of Blackjack make it difficult to do an analytic solution, but you could in particular cases.  Going back to dealer shows a 6, you could say suppose I draw to 15.  After tedious counting, you could exactly calculate your winning percentage.  After more counting, you could compare that with the winning percentage of draw to 14, and you would have a rigorous answer. 
Added:  counting just changes the frequency distribution of cards that are dealt.  The same approach works-you just ask questions like "If the proportion of cards that count 10 drops from 4/13 to 2/13, how does that change the results?" and adjust your strategy accordingly. Generally if the high count cards are depleted you draw more because you bust less.  More high count cards are good for the player, because s/he can stop and let the dealer bust.
