This one time to this poster only
...to be a very straight forward question about a hard number you present as fact. Why would you not be willing to provide the calculations or proof of your number, or point out the error in other's calculations of their 13% number in contrast to your number?
I can't point out any errors in the calculations of others, should they in fact exist, till the work is released into the public domain. I am not a member of Don's Domain, nor am I likely to apply, nor indeed would any such application be accepted.
The only published text quoting the 13% figure. Grosjean himself is extremely tenative about the figure, since it contradicts Thorp and Braun (read it). If the source is unsure of his figure I am obviously not going to use it.
Note: I am not under any obligations to recalculate every figure in blackjack literature. How many theorists do you think recalculate ordinary basic strategy, or test the effectiveness of the hi-lo system? Numerous studies already exist confirming these strategies effectiveness. Reinventing the wheel is not on my agenda. Plenty of original research exists in my books if that is what you are after.
Either you can prove your number or you can't, and there is no need to hide the calculations.
Do you know how difficult it is to "explain" how to calculate basic strategy? It is a chicken and the egg process whereby you calculate the frequencies of initial hands based on an optimal strategy whose creation depends on those frequencies. This ignores legitimate questions such as the cc effect, rule changes and different procedures, none of which are standardized (though studies by others may use a specific model). It is not even easy to define what basic hole-card strategy is (try it). Schlesinger, Jacobs and myself had a major disagreement on this topic only a few months back.
For the record, I did some preliminary research on basic strategy calculation and decided that, because I disagreed with some of the underlying principles used in its calculation, that this was not a profitable avenue of research. Even though when replicating Thorp and Braun's methodology I didn't get the same results (not the same as Grosjean's incidentally) I just wasn't interested in presenting an alternative figure because that muck up the accepted heuristic on which the rest of blackjack strategy is based.
Barring you presenting proof of your number, I believe it would be a very hard sell to most here that your number is correct and the 13% number agreed to by well known BJ mathematicians like Don & Cacarulo is incorrect.
Well known as those mathematicians may be, they are not as well known as Thorp and Braun. In addition, as skilled mathematically as Don may be, he cannot program a computer, as he has admitted on a number of occassions, and this requires a computer, unless Don has spent ten man years on the subject with a calculator. That leaves Cacarulo, who is very intelligent, but I can't accept that he has "proved" the 13% figure without some idea of the underlying assumptions, in the absence of any actual data. You don't expect me to change my opinion on this matter in the absence of the actual source material do you, surely? That would just be going on blind faith.
Anyway, with absolute certainty this thread will end up with a bunch of cheap jibes from SOTSOG & LVCHM and his various schizoprenic personality offshoots, with no productive content whatsoever.