art: Computing Basic Strategy

[art]

Is there any source of information that shows how the decision in a single cell on a basic strategy card is calculated?

For example H16 against dealer 8, how the percentages are calculated and compared to determine the proper play.

I am trying to learn more about the math behind the decisions.

[ES]

There are two ways to calculate basic strategy: direct calculation and computer simulation. Consider the insurance bet (single deck). Direct calculation works as follows:

Gain if insurance is taken and the dealer has blackjack is 2 X 1/2 unit, or 1 unit. Probability that dealer has blackjack is 16/51. This ignores the player's hand, which may have 0, 1 or 2 tens.

Loss if insurance is taken and the dealer does not have blackjack is 1/2 unit. Probability that dealer does not have blackjack is 35/51. Again, this ignores the player's hand, which may have 0, 1 or 2 tens.

The expected value of insurance is 1 X 16/51 - 1/2 X 35/51 = -.0294... per half-unit bet or -.0588... = -5.88...% per unit bet.

Obviously the expected value of not taking insurance is 0.

Therefore, basic strategy is not to take insurance.

The calculations are extremely complicated for other decisions. Consider 7,7 v 10. The player has 3 or 4 possible plays: surrender if available, split, hit or stand.

The expected value of surrendering is ovbiously -.5.

To calculate the expected value of splitting, you must consider all possible sequences of additional cards received on each 7 and all possible dealer hole cards and then all possible sequences of additional cards received by the dealer until he gets 17, 18, 19, 20, 21 or breaks if he does not have a pat hand.

To calculate the expected value of hitting, you must consider all possible sequences of additional cards received on the hand of 14 and all possible dealer hole cards and then all possible sequences of additional cards received by the dealer until he gets 17, 18, 19, 20, 21 or breaks if he does not have a pat hand.

To calculate the expected value of standing, you must consider all possible dealer hole cards and then all possible sequences of additional cards received by the dealer until he gets 17, 18, 19, 20, 21 or breaks if he does not have a pat hand.

Computer simulation involves programming a computer to Play the hand by splitting, hitting and standing, each about 1,000,000,000 times and comparing total expected values with each other and with -.5 for surrendering and choosing the play with the highest positive or least negative expected value.

[Art]

ES, thanks for the detailed explanation.

One final question. Do the basic strategy cards take the peek into account?

For example, if the dealer is showing an Ace and play continues after the peek, we know for a fact that the card is not a 10-K. Is there added value in this information for 2, 4, or 6 deck games where the dealer stands on soft 17?

[Don Schlesinger]

> ES, thanks for the detailed explanation.

> One final question. Do the basic strategy cards take
> the peek into account?

Yes.

> For example, if the dealer is showing an Ace and play
> continues after the peek, we know for a fact that the
> card is not a 10-K. Is there added value in this
> information for 2, 4, or 6 deck games where the dealer
> stands on soft 17?

No. All BS is based on the fact that the dealer has a playable (non-natural) hand.

Don