As a maths major myself, I found some of the stuff on http://www.beyondcounting.com/articles.html quite entertaining. I also plan to read the books Tthree recommended, which are often mentioned on these forums as being thorough and rigorous examinations of the game.Originally Posted by Preferrd
Those books are incredibly valuable, and they should be in every AP's library, but for the math major poster, they don't compare to The Science of Casino Blackjack, a book that nearly does require a degree in mathematics.
"There is no passion to be found playing small, in settling for a life that is less than the one you are capable of living."
Sorry, can't agree on The Science of Casino Blackjack. Werthamer is one very sharp guy. But, some of his conclusions are way off, as pointed out by Mike Canjar in Optimal Play Mathematical Studies of Games and Gambling. Also pointed out by Schlesinger.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
Others may disagree but I don't think a game theoretic approach is the most useful for analysing simple table games. A better approach is just the application of probability and computation. This is hard enough already! Some games can be reduced to exact combinatorics if they have enough symmetries and are "small" enough. When there are too many combinations, you can resort to sampling methods. For other simple game, you can even just calculate the distribution exactly. A good start (and good unit tests) would be to replicate results from wizard of odds, modern blackjack, CAA etc.
As for game theory, there is an interesting introductory book on poker which uses game theory to analyse and solve toy poker games. I found it interesting but it didn't really help my Hold 'Em!!
http://www.amazon.com/The-Mathematic...e+theory+poker
Right now I'm trying to find out how to calculate a risk of ruin for small stakes with a small bankroll on a single trip. I've been reading up on it a bit online but I can't seem to find much on how they come to their conclusions except via simulations under specified conditions.
What I would like to know is, if I go up to a casino with $40, $100, $200, or $500 and play on a 6D, H17, DAS, RAS then what is the risk of losing it all vs time assuming I am using Hi-low counting strategy with a 1-8 spread on a $5-100 table? What if I don't know all the indices and I only use the Ill18? What if I know Ill18 + 15 more?
Also, how does one calculate my average bet and my EV out of that? Standard deviation I can expect?
I see many benchmark charts but they aren't suited to my needs.
Well first of all, one mistake typically won't erase all gains instantly. You have to remember that when you're playing, you're playing for EV (Expected Value), not necessarily true-results. So if you play a game with $10/hour EV (ie: Your expected value of playing for 1 hour is $10 gain), then for every hour of play, you're expected to make $10. I guess that's fairly straight forward....not sure if you understand how EV and all that works, so no offense meant if you did. You are building up EV by playing. Your actual results are likely to not be the same as your EV, at least in the short run.
You gauge everything by EV, not what actually happened. For example, if you bet $100 when you have a 2.5% edge, you are expected to make $2.50 on that hand. If you bet $100 when the house has a 1.5% edge, you are expected to lose $1.50. Again, this is over the long run....(it's not possible to win $2.50 on a single hand or lose $1.50 on a single hand at $100 bet).
So, every bet you make is either +EV or -EV, right? Every playing decision is either +EV or -EV, right? You add up all your -EV situations with all your +EV situations, and you have your overall EV for that session. Hopefully this makes sense.
So, when you say "the cost of 1 mistake can erase all gains instantly", that is not necessarily true. I don't know the true numbers, but I'm just going to make some up for an example. Let's say that splitting 6's against a 6 is +2% EV and hitting 6,6 versus a 6 is -3% EV. With a $100 bet, you would expect to win $2 if you split, and lose $3 if you hit. Hopefully this makes sense.
You are EXPECTED to win $2 or lose $3, depending on if you split or hit, right? Even if you hit that 6,6 and lose $100, you only give up $3 in EV. If you split, you'd gain $2 in EV. As I said before, it's not possible to win $2 or lose $3 on a single hand of $100 bet. Your actual result of this hand is going to either be -200, -100, 0, +100, or +200 (unless you end up re-splitting or doubling down...).
Let's say you hit the 6,6 -- you lose $3 in EV, regardless if you win or lose the hand. If you split the 6's, you gain $2 in EV, regardless if you win or lose the hand. If you hit and lose, your actual result is -$100, but your EV is -$2.
It's kind of a confusing concept, and I probably didn't explain it the best way, but hopefully that helps you understand how a single mistake doesn't/can't erase all gains. You have to look at the game in terms of EV and not in terms of your actual result.
"Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]
Exactly the way to look at it. Everyone makes mistakes. It just depends how bad they are. Standing on 15 v 10 because you overestimated the discard tray isn't going to cost you much...freaking out and doubling hard 16 against 4 with a max bet out will wipe out your session EV!But you're very unlikely to make a mistake that will turn your game -ve.
If you're worried about mistakes, slow down when you have larger bets out and make sure you play them right. Pay particular attention to multiple card hands in case you've added them wrong. With practice and experience, all this will fall into place!
Good luck!
Most casinos in my area all hit Soft 17. However, they also let you re-split aces, double down on any two cards, and double after splitting. However, when splitting aces, you are only given a single card. Can the H17 be beaten and is the single card draw on split aces normal?
Most games are H17. One card on split aces is normal -- it would be abnormal to see a game that allows hitting or doubling down on split aces.
"Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]
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