While craps is my game of choice at casinos, I occasionally will sit down at a blackjack table just to slow the night down a little bit. And from years of playing, I’m quite familiar with the strategy chart, which should maximize your chances to win based on your cards and the dealer’s up card. For those not familar, here is an example of chart.
But I think that the underlying assumption when using this chart is that you have no knowledge of any other cards that have been used, or are being used, from the shoe. But the fact is that you’re usually playing with several other players and are able to see their 2 cards, along with your 2 cards and the dealer’s up card. No matter how minimal, these other cards change the conditional probability of your next potential card. Of course, if you’re able to remember all of the cards from previous hands you can gain a big advantage. This is known as card counting and is very difficult to do. But my point is that even the cards that are in plain sight on any given hand should be able to help you. Clearly, having 6-8 decks in a shoe reduces this potential impact. But still…
Is there anyone who actually does this? As a simple example, let’s say you’re playing on a table with 6 other players. if your two cards total 15, and the dealer has 7 showing, the chart advises you to hit. The assumption is that the probability of your next card being a 2, 3, 4, 5 or 6 is enough to maximize your odds against an X-7 hand (X is the unknown dealer’s card). But let’s just say that all of the other players’ cards are all between 2 and 6. Thus, you have 12 fewer 2’s through 6’s available to help your hand. In a 6-deck shoe, 12 of the 30 cards that might help you are already gone. At this point, maybe the odds change and maybe you really shouldn’t hit that 17. I’m just curious if anyone accounts for these other cards when they play. If so, are there any rules of thumb that you follow?
Second question: Another underlying assumption that seems to prevail at a blackjack table is that the dealer’s hidden card is a 10. Since 5 of the 13 cards have a value of 10, it has the greatest probability of coming up at any given time. But if you assume that X is always a 10, then shouldn’t you also assume your next card is also always a 10? Thus, shouldn’t you always stand on anything higher than 11, assuming you don’t have a “soft” total or an available split?
You’re quite correct in that there is a ton of data being passed in front of you the entire game – data that you can use. Here’s the way I learned it:
You need to keep a running count in your head. Start at “zero”. Every time you see a 10-value card, subtract one. Every time you see a 2-6, add one. Once you have either a very large positive or negative number going, you have a decent idea of how you can make a play.
Large positives mean there is a greater number of 10-values in the deck – you have a better chance of getting blackjack, and you are in a better position to hang back and let the dealer bust.
Large negatives mean there is a greater number of low-values in the desk – a less desirable situation, but you can still make it work to your advantage (as long as you can deal with people who think they know all about the game berating you for hitting a 13 when the dealer is showing a four…funny thing is they never change their tune, even when you draw a six on that hit).
That’s the basic way of doing it. For a more accurate number, you should divide your running total by the number of decks remaining in the shoe (estimated, of course).
Using these methods, I’m up about 7 grand in Atlantic City.
Counting cards is very well-documented, but is very difficult to do (legally) for extended periods of time. I’m talking about just using the information available to you on a single hand with multiple players.
Your basic assumptions are correct. If you’re counting cards, you take into account all cards you’ve seen: your hands, the dealer’s hand, the other player’s hands. In practice, it’s easier to account for the other player’s hands after they turn both over (if playing face down).
Re: expecting your next card to be a 10…it’s all math. Yes, it’ll probably be a 10, but the people who put together the strategy cards have done the numbers, and (for example) determined that you’re better off hitting a 14 against a dealer 10 than standing.
The answer to your first question is “yes” people try. And because of this, casinos look for it. The “Bringing Down the House” about the MIT team explains how they did the card counting. It is technically not illegal to do this, but likewise casinos can kick out whoever they want and forbid them to play.
The kick with card counting is that the way the card-counter bets is the dead give-away. It was this aspect that the MIT team figured so clever a means around.
But as Hal Briston points out, you can also use card-counting to determine just how you play (and stick with your usual bet) to increase your odds. It isn’t as fast a method to increase your winnings, but the casinos likely won’t catch on to you either.
As to your second question, the reasoning that the dealer’s downcard is a 10 is used to determine whether you should take a hit or stand. If the dealer is showing 6 or less, then you know they have to take a hit and therefore increase their chances of busting. So (unless you are counting as Hal B does), you would opt to stay on your 12 or whatever.
But if the dealer is showing a 7 or better, and you have 12 to 16, then you’re correct that there is a good chance that you will hit a 10 and therefore bust. But if you stay, sticking to the same “downcard is a 10” reasoning, then you are conceding defeat - the dealer already has you beat. So though the odds may be against you, it is a worthwhile risk to take the hit - you can lose by busting, but you may also get lucky and pull a card that helps you.
The other way to look at it is this: the dealer must take a hit on 16 or lower, and look how many times they win having to do this. Since the dealer has no say in this, it must be a reasonable way to play.
I am always surprized to see how many people stay on 15 or 16 when the dealer is showing a 10 card. It is as though it is better to lose by not busting, than to bust (less humilation in having to have your chips pulled away in front of your co-players ?).
That really chaps my ass, too. It’s all fine with the casinos if mathematically-challenged people want to make bad bets, but let someone with a brain show up, let the brainiacs outwit the casino, and suddenly they’re kicked out. Bullshit, IMO. “We don’t want to play anybody who’s smarter than we are…we might lose money!”
One of MIT’s strategies, if memory serves, was to wait to make larger bets till the end of the shoe so that they had an excellent idea which cards were left. Most games, e.g. craps or roulette, have unchanging odds so to speak—he odds of rolling a seven is the same with each independent trial. Not so with blackjack, and that’s the edge they wanted to exploit.
But wern’t the MIT dudes using computers to help? I mean if I had a laptop helping me I’d feel a lot more comfortable than using my Vodka Tonic analysis.
To have a different person counting than is making the big bets - it was team card counting. If you wait until the shoe is in your favor to start upping your bet, this is how the casinos spot a counter. So the MIT guys would set counters at the tables, and they would (secretly) signal the big bettors when the shoe became favorable. The big bettors would then join the table and start raking it in. Not only did they “hand off” the shoe, but they would also communicate the relative state of the shoe (it’s complicated), and the big bettors could then “pick up”. What is most amazing is that they learned how to “predict” the state of the shoe beyond the next shuffle !
The MIT guys did NOT use computers. A few people have come up with pretty ingenious ways to utilize computers (especially considering the technology at the time - WAY before PDA’s and laptops). But again, the change in betting gives them away.
As I posted earlier, they were a team. Couldn’t remember all the details but that’s why I said one person couldn’t do it.
BTW these guys also flew all over the world to casinos b/c when ppl win big, they come on the casino’s radar. If they do that week after week in one place, they’d be asked to leave. But by going to Monte Carlo one week, Vegas another week, etc. they avoided detection longer.
Hitting a 15 or 16 against a dealer’s 10 is always a long shot, but a better play than standing…unless you’re counting cards, and know that the deck is rich in 10’s. If the odds have increased that the next card is a 10, then standing on 16 is the right play. (basically, you’re crossing your fingers and hoping that the dealer’s down card is a 6 or lower).
And a movie about the MIT team (loosely based, probably) is about to hit the theaters.
Yeah, I’ve written a computer program that does this, which I’ve used while playing online casinos. You couldn’t possibly do it in a real casino.
[Arghh, computer crash a few days ago, lost it, backup corrupted, don’t have it currently. Trying to recover it.]
It rarely makes a difference anyway. Most of the time the option on the strategy card is the best option, anyway. My program hardly ever advised me to play differently to the strategy card. When it did, the difference was only a couple of pence in the pound. It gave me, maybe a half of a percent advantage, which would only matter if I was playing for high stakes.
Never heard of that one, and it’s not a valid assumption.
No.
No. You’ll lose a lot that way. Yes, there’s a high chance of busting if you draw to a twelve, but it’s still often the best option.
For instance, if you have 8+4, and the dealer shows a 7, you will lose about 21% of the time if you hit, but you will lose about 47% of the time if you stand.
