moo321 said:
Can we describe all of the potentially profitable situations? I know all tens, all evens, or 3 ranks would all help the tie.
Once we describe them, how frequently do they occur, and what are they worth? Basic frequency distribution.
And is there better than 10 card pen available? It seems like baccarat should be quite beatable if dealt to, say 6 or 4 cards.
Calculating the frequency of a given end-deck subset can be done by calculating the chance of those cards appearing from a full deck, eg for all-tens there are 128 ten-valued cards in an eight-deck pack, so 128/416*127*415...
The problem is that while favorable subsets are rare are very large numbers of permutations with all but very small card subsets, so you need a heuristic to whittle the subsets down to manageable proportions.
Additionally, and this is where it gets very complicated, you need to work out a good method of backcounting. It is frequently the case that if a lot of tens and even cards are eliminated it saves time to go and play a fresh pack since your chance of encountering a favorable subset is worse than it is off-the-top, even adjusting for the fewer hands that need to be played and/or shuffle time.
This is absolutely crucial, and something many of those who have studied this area fail to understand. It is insane to just sit there through every shoe regardless of the card distribution. You need to maximize the frequency with which you encounter favorable subsets.
I have played against packs that were dealt down to the last six cards. In some cases you can achieve similar penetration by asking to see the burn cards, because some cards are exposed during the shuffle, or one of half a dozen other tricks. The vast majority of games are not dealt down to this level deliberately.
