Blackjack by Dario De Toffoli

Author:Dario De Toffoli [Toffoli, Dario De]
Language: eng
Format: epub
ISBN: 978-1-78099-610-3
Publisher: John Hunt Publishing
Published: 2013-07-25T16:00:00+00:00

Finally we will examine a more complicated case, analysing all the possible options:

player 18 - dealer 8

The choice is not always between standing and hitting only, in some specific cases we will have to decide whether to split (with an initial 9+9) and whether to double down (with an initial A+7).

From the table we can see that the choice to stand leads to an average gain of 11 hundredths per hand, while hitting leads to a worse outcome. If the player hits with a hard hand, the mathematical expectation becomes decidedly negative (-0.59), this decision leads to an average cost of 70 hundredths per hand (0.11+0.59).

If the player stands with a soft hand, he remains in positive territory (+0.04), but the average gain decreases by 7 hundredths per hand.

In both cases the player must stand.

If the player’s 18 is made up of 9+9, the possibility of splitting comes into play. If this option is chosen, the average gain increases in comparison to the decision to stand, from 0.11 to 0.20. In this case the player should split the pair, why give up those 9 hundredths per hand?

With an initial Ace and 7 on the other hand, we can consider doubling down, but doubling down would be an error because this decision leads to a decrease in mathematical expectation to -0.03, at a cost of 14 hundredths a hand in comparison with the decision to stand.

In conclusion, with 18 against 9, the player should always stand, unless he started with 9+9, in which case he should split.

This data can be seen more clearly in a block diagram.

We will continue this chapter by considering all the possible totals of the player

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