zengrifter said:
That almost sounds contradictory. And I thought that it was Thorp's computer-power that revealed SOME of of the errors in the Los Alamos BS... and then it was Braun's even faster computer in '66 that revealed the final mistakes.
Are you saying that I can't simply run a simulation to figure out BS?
Like say 20m hands 88v10 SPLIT, 20m hands 88vs10 STAND, etc.?? zg
Ps - If not, then I'm really showing my ignorance!
Simulation needs a lot of rounds to find very fine differences and the only sim I know of that can do that is Cacarulo's. He can get an accuracy of around 5 decimal places.
I mentioned that sims are used to confirm. CA's for very complicated situations are prone to bugs just like any other program. Sims are easier to program since you just need to make sure hands are played and paid off correctly. Brute-force computer CA is actually the most accurate but obviously very time consuming. T Hopper's program is the fastest in that regard but Ken has one that works too.
Sims however obviously take much longer than CA so once a CA is found to be functioning properly for a few key hands, it can be assumed that it's accurate for the rest.
For example, CA in rare situations isn't exact e.g. with Australian rules for splits (BBO and OBBO). In this case simulation was very useful because it confrimed a few different split hands and so the remaining split hands/different deck numbers in question could be assumed to be very close.
Sim is also better for counting because the number of possible subsets and variations in betting/game play would cause a CA in these cases to be very slow - much slower than a sim.
One of the main problems for CA's and counting is that even the determination of the possible subsets that result in a particular counts can take a very long time as it's a form of "Subset Sum" problem.
Anyways, that's a longer answer than you were anticipating I'm sure...
