Originally Posted by Brock Windsor
Ok. I follow the theory, but don't plunk your bankroll behind your expected EV. In the real world you will get false keys (except in single deck), the ace will be stripped (especially in single deck), and you will see multiple riffles. All you're showing is the expectation a dealer will interweve a single card in one riffle. Im not sure why you square that number (77%). It means 77% of the time a key card will have a single card following it, and then the target card. (other factors being ignored of course).
I square .776 becuase it is both the probability that the A and the K will be in different clumps and the probability that the shuffler will only release one other card from the other grab.
And what does stripped mean? I also have to factor in the probability that the key card and the ace will get separated when the deck is cut to get my numbers as accurate as possible. And account for whatever this stripping is.
I should be able to use this data to make it into a formula for any number of rifles so that I can get more realistic data for a casino. That might take me a bit though.
Edit: Your right. .776 is not the probability that A&K will not be in the same clump. It's actually (1-0.224).
Edit2: I should be checked for retardation. 1-.224 is .776