Surrender Calculations

The following graph shows expectation as a function of count for various hard hands versus a dealer 10 with different decisions. The intersections of the hit curves with the stand and surrender lines are circled and indicate a change in decision should be made. I did the calculations through an indirect manner. Basically, I found the card PDFs as a function of count, then I monte carlo'd based on the PDF for various counts. Might not be perfectly accurate, but I think it gives good results and allows for doing what would take an enormous amount of time through a direct MC approach for high counts.

I matched the book for standing 16 vs 10 at a count of 14. My surrender values are slightly higher than the books (for 15 v 10 I have 9 vs 13, but for 14 v 10 I have 26 vs 23). My stand values are also higher (for 15 vs 10 I have 32 vs 27, and 14 vs 10 I have 44 vs 35). My guess is that the KO book took into account variance instead of just expectation. For example at an expectation at exactly -50%, it's better to surrender instead of hitting/standing, since the latter adds unneeded trip variance. There might be slightly higher expectations where you still might want to surrender, since the overall expectation/std is higher with a lower std even though the expectation is slightly less.

Anyway, since my values are more liberal than KOs, I think it's safe to say that for 13 vs 10, and for counts >= 40, surrendering is the best option. If the KO book had derived it, they would've probably had a value somewhere in the 30s.