TITLE: Question about basic strategy in Blackjack
QUESTION [5 upvotes]: 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.

REPLY [2 votes]: The scenario that you described is a single deck game where the dealer must
stand on Soft 17, which is a disadvantage to the casino. Every casino table has its own specific rules. On some tables, the dealer will hit Soft 17, others will stand.
In a single deck game, there are also other factors which can have an effect
on the overall game odds. One of these is deck penetration, another is the number of "rounds" played, which is just the number of times a new hand is played from the same deck before it is shuffled.
I noticed that there is no consideration of the cases where the dealer ties the player (but this is only applicable when the player is hitting). Also, the dealer can bust on 4 or more card. Example: dealer has 6-2 and then draws 4,10 to 
form 6-2-4-10 = 22. 
I have a blackjack Monte Carlo simulation program which runs 
on my Apple notebook. I checked the data for the scenario described above.
In my simulation, I have used deck penetration of 65% and limited the number of rounds to 6. The results show that in the case where the player draws 10-5 and dealer draws 6, and the player stands, the player will win 42.1858%, lose  57.8142% and push 0%. The average loss by standing is 15.6283%. If the player hits however, the player will win 28.5349%, lose 67.1360% and push 4.3291%. 
The average loss by hitting is 38.6011%.
This data was extracted from the following table for the case 
that Dealer Stands of Soft 17:
The columns represent the following in this order:
(1)  Player Card
(2)  Player Card
(3)  Dealer Card
(4)  Strategy (Stand or Hit)
(5)  Frequency (Trial size during simulation)
(6)  Wins
(7)  Losses
(8)  Pushes (player tied dealer)
(9)  Net Gain/Loss
(10) Win probability
(11) Loss probability
(12) Push probability

10 5 6 S 2985424 1259426 1725998      0 -0.156283 0.421858  0.578142 0 
10 5 6 H 2983974  851474 2003320 129180 -0.386011 0.285349  0.671360 0.043291
9 6 6 S  562585  230554  332031      0 -0.180376 0.409812  0.590188 0
9 6 6 H  562917  157084  380592  25241 -0.397053 0.279054  0.676107 0.044840 
8 7 6 S  748253  305639  442614      0 -0.183060 0.408470  0.591530 0
8 7 6 H  748480  222004  492233  34243 -0.361037 0.296606  0.657643 0.045750 

Notice that the trial size in both of the 10-5-6-x cases is higher than the other four cases. This is simply due to the higher number of 10 valued cards in the deck, i.e. each value is the set {10,J,Q,K} is equal to 10. Also note that the sample sizes the two 10-5-6-x cases are not identical to each other. This is due to the random selection of the players strategy during simulation where 
the probability of the player standing is assumed to be 1/2 and probability of the player hitting is also assumed to be 1/2.
The calculated 63.26 percent chance of busting by hitting (which was posted earlier), is pretty close to the simulation loss result of 67.1360%.