Programming for progressions
Years ago, I ran one program to track the incidence of the various "events" under the then-AC rules (S17, SAP, DAS, SP3, 6D, 75% pen). An "event" is any one the 13 possible outcomes of a hand, e.g., Win 12 (split a pair out to 3 hands, double each, win all three, starting bet of 2 chips), win 10....win 3 (a snapper paying 3:2 on a 2-chip bet)...win 0 (any push regardless of the number of hands -- iow, could be a triple split with one hand winning a double and the other two losing...down to lose 12. In the program, units had to be multiplied by two so 3:2 wins could be recorded using integer math, which is why it's "win 12" and "lose 12" instead of "win 6" and "lose 6."
I built those results into another program, which assigned probabilities to various double-precision buckets in 2-dimensional space; so the probability of each SEQUENCE of "events" could be recorded. This program allows the user to enter both a "trailing stop loss" figure and a win goal figure in terms of multiples of the size of the base bet of the progression.
In other words, once a sequence met or exceeded the win goal, that probability was aggregated in the win prob variable, and the amount of the win times the prob aggregated in the win amt variable. Similarly, when the trailing stop loss was hit, the results were recorded as either a win, a push or a loss. From this data, it is almost trivial to calculate average win, average loss, the amount of total action, etc., -- all the stats we love to play with.
While I found many progressions which outperformed flat betting, I had to give up on finding one which had a positive expectation.
Because of this thread, I dusted off the old software, which I hadn't run in at least 5 years (I just checked -- the final compilation was on 6/16/03), with the idea of giving fubar some stats on his 2-1-2-3-4-5-6-7... progression.
As it turns out, that isn't a bad progression, as progressions go. However, the program has no provision for the end of the shoe -- it applies the same probs to each and every hand until the unused prob (i.e., that which has not been accumulated in the win, loss and push prob variables) drops to below 0.000000001. There are no such things as "shoes" or "shuffles" in the program -- it just keeps applying remaining probabilities until all but 1 in a billion has been assigned to either win, lose or push. Thus the program is really only good for COMPARING progressions, and only partially useful in evaluating them -- i.e., identifying those deserving futher testing.
Money management is a KEY ingredient to the mix -- often much more important than changes in the steps of the various progressions.
With the right money management, fubar will likely survive quite a long time using his progression -- significantly longer than if he simply flat bet.