In your blackjack appendix 6, concerning late surrender you advised surrendering a 10+5 and 9+6 against dealer’s 10. In the basic strategy of Unified Gaming, you advised hitting 15 against dealer’s 10. I don’t understand why hit instead of surrender in this case because the 9+6 and 10+5 are much more probable way to have 15 than 8+7.

Moisan from Paris, France

This is an interesting situation. Although you should surrender 5/6 of the time with 15 against a 10 in single deck it is still better to always hit than always surrender. Following is the expected return by hitting each way to compose a 15.

10+5
-.501091
9+6
-.509827
8+7
-.474794

There are 4 ways to make a 10+5 and only 1 each of the other two. So the overall expected return by hitting is 15 against a 10 in single deck is (4/6)*-.501091 + (1/6)*-.509827 + (1/6)*-.474794 = -.498164. In other words the odds just barely favor surrendering a 10,5 and 9,6 but the odds favoring hitting 8,7 by a much wider margin. The reason the 8,7 has the better expected return is all the 5’s and 6’s are still in the deck, resulting in a greater probability of attaining a total of 20 or 21.

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