Quote Originally Posted by Gronbog View Post
it might be reasonable to run this experiment.

Rather than removing an ace, I think the equivalent adjustment for my software would be to discard and count an ace at the start of each shoe (after the burn card). This would place all instances of A,A vs ? into a context where at least three aces have been observed and counted just they would be when playing A,A after splitting.

Does this sound reasonable?
Quote Originally Posted by Cacarulo View Post
Perfectly reasonable. That is what I suggested in a previous post. I think there's a semantic issue about removing an ace, but it's exactly what you're proposing. That's why we're counting it.
In my program I don't burn any cards although I don't think that affects the results.
I didn't forget about this experiment. It just took some time for me to get to it.

Under the conditions suggested above, for doubling over hitting A,A vs 3 I now get +8 as the index S17 (was +9). This matches Cac's simulation result. However, I'm still getting +8 for H17 where Cac's simulation result is +7.

Some suggestions regarding the H17 difference:

  1. Encountering this hand with at least three aces and a 3 removed at +7 and +8 is a rare event occurring only 122,878 and 98,232 times respectively over the course of 100 billion rounds I simulated. As such, the EVs that were computed are separated by only 0.5 standard deviations (the standard deviation of the difference in the EVs) giving a probability of about 30.85% that doubling might be correct at +7.
  2. My software never computes indices in isolation. It always includes the effects of other related index plays. It does this automatically and I've never found a practical reason to prevent it. In the case of A,A vs 3 at +8, the only relevant index play which can also be triggered downstream would be 12 vs 3 (stand) at +2 (there are others but their indices are too negative for them to be relevant in this situation). I would be interested to see what index Cac and others get for this situation (A,A vs 3, at least 3 aces removed, H17) when 12 vs 3 is also enabled. This would tend to increase the value of hitting and therefore tend to make the index for doubling higher.