I'll put it another way. There are NO stats in the game of real blackjack as played in a casino accurate to six decimals unless you are talking top of the deck or a probability of 0 or 100%.
I'll put it another way. There are NO stats in the game of real blackjack as played in a casino accurate to six decimals unless you are talking top of the deck or a probability of 0 or 100%.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
You are talking about one extreme of trillions of situations. My argument is that six decimals is an absurdity, and therefore misleading. My physics teacher taught that any number expressed to more digits than can be accurate is incorrect. When I worked with Epstein on the second edition of Gambling and Statistical Logic, I used CA for some problems and Monte Carlo for others. My philosophy has always been to use CA where appropriate and sims where not. CA results can be expressed to any number of digits when appropriate. When they actually take into account all possibilities. Sims must take into account standard error. Blackjack, other than top of the deck, simply cannot be accurately processed with CA. Albeit, it can be highly useful. One day, perhaps this will change. I've looked into using Qubits. But, even quantum computing ain't there yet.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
Not really. If you want accurate EV's for a specific shoe subset, use a CA.Originally Posted by Secretariat
If you want to look at the average EV inclusive of many shoe subsets, use a Sim.
Currently, computers are too slow to perform full CA on shoe games. There are 33^9 * 129 unique, ordered shoe subsets in an 8 deck shoe. That's around 6*10^15 unique subsets. Quite a lot!
Thanks for the info, dogman. I didn't know that today's computers were too slow. I also see Norm talking about Qubits and stating that quantum computing ain't there yet. It somewhat puts things in perspective for the rest of us.
So I guess that KCs site giving numbers that are "The difference between combinatorial analysis and simulation" should still be quite accurate for specific subsets and recommended strategy deviations. KC's site should also be close to real EV whether using basic strategy deviation or perfect strategy.
I post this with some hesitancy because I'm sure the simulation gurus will say that there are nowhere near enough rounds included to make the results at all meaningful. At the least it shows it is possible to simulate best strategy using a CA.
I simulated 2 decks, H17, DAS, SPL3 (2-10), No RSA flat betting using optimal strategy (including splits.) I ran 6 10,000 shoe simulations with a shuffle point of 80 cards. 5 out of the 6 sims showed positive results. The results, meaningful or not, show that there is a theoretical advantage of about .7% for perfect play in this game (although perfect play is not really attainable.)
A couple of things can definitely be said:
-After every reshuffle the EV for the first round is known to be ~-.38% and the full shoe composition is repeated 902030 times giving this subset more weight than any other possible shoe composition.
-Any gain in EV must come from rounds following the first round of a reshuffle since the full shoe EV is known.
My belief is that combinatorial analysis is useful in determining playing strategy (indexes, etc.) but overall results are best determined by simulation. The reason is that playing strategy can be derived from random subsets whereas computing overall EV requires the completion of a round first. The requirement of round completion causes the elimination of some random subsets completely and may change the frequency of others. Once a shoe composition is known a CA can output an overall EV but determining frequency of shoe compositions given the round completion requirement is not possible beforehand.
k_cCode:Rounds Hands Player BJ Dealer BJ Sim Total ------------------------------------------------ 150305 154037 7108 7161 +706.0 150361 154154 7264 7126 +133.5 150322 154224 7155 7302 +1030.0 150412 154188 7145 7110 -333.5 150282 154160 7196 7230 +985.0 150348 154094 7238 7223 +321.0 902030 924857 43106 43152 +2842.0 Total EV = +2842/902030 = +.32% Full Shoe EV = -.38% Player BJ % = 43106/902030 = 4.78% Dealer BJ % = 43152/902030 = 4.78% Expected BJ % Full Shoe = 4.78%
Interestin stuff KC. Questions
1) Shuffle point of 80 cards, is that 80 cards played or 80 cards left in shoe?
2) So with perfect "non-human" play, it is possible to flat bet and have a +.32 edge with all counts combined (+,0 or -). Now, during those 65% (or so) hands where we have a minimum bet out, how close to EV0 can perfect (non human) play get during those 0 and negative counts at that game (DD, H17, DAS, SPL3 (2-10), No RSA)?
Last edited by Secretariat; 12-15-2021 at 06:33 PM.
Do you know what behaviour the overall EV generates if you go to the end of some shoe? That is, as you deplete the shoe, do you notice any peculiarities with the overall EV?
Reason I ask is that, unlike a sim, the CA does not "loop around" the shoe and start with a fresh shoe (minus the already played cards) and that may bias the results a little.
Running out of cards crashes the sim program so if that happens the sim is aborted and the results up to that point are displayed before the crash occurs.
Outside of a sim my CA will not crash when a shoe composition is insufficient to complete each drawing sequence to an end result but in that case it outputs incorrect values. It's incumbent upon the user to input an acceptable composition.
My desktop version has the option to check for an out of cards condition. It will display "check for sufficient cards failed" if option is chosen and there are insufficient cards. It seemed to work pretty well although I don't know for sure if it's perfect and it has been a while since I programmed it.
k_c
SBA ignores results in the last round when cards run out -- an important event. This is an error that affects results. CVData shuffles when cards run out, finishes the round, and then reshuffles -- which is how most casinos used to handle this situation in the days when such could happen. CVData also has an option that prevents the very last card from ever being dealt as even when running out, casinos usually kept this card inverted and never dealt to keep the bottom card from being seen. It's important in a sim to sim actual casino play, not theoretical play. Simulation is supposed to completely ignore theory. Otherwise, how would it verify theory?
Last edited by Norm; 12-16-2021 at 06:14 PM.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
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