I meant to specify ignoring the issues of card counting (i.e assuming that current cards are independent of previous cards but it somehow must have been dropped in one of my edits.
People go to Vegas for the gambling and the shows and the party and the experience. I think that the strip and downtown is fucking disgusting but I will go there once a year or so for concerts if a band that I love is going to be there and aren’t also coming near me. I tend to just chill in my room until the show starts.
As for legal cannabis, why in the world would you go to Nevada for that? I would be that most people are closer to a place they can get weed than they are to a casino and nearly certainly closer to a place where they can get weed than to Vegas.
Perfect basic strategy for Blackjack was unknown until Thorp’s ‘Beat the Dealer’ was published, and he figured it out by running Monte Carlo simulations on a computer. That proved that the blackjack ‘experts’ of the day like John Scarne (“Scarne on Cards”) were wrong. No one could figure out basic strategy from first principles.
Unless you’re counting, “the exact composition of your hand” is a single integer number. And if you are counting, then you should be including all of the known cards in your count, not just those in your own personal hand in this one specific round.
I wonder if with computing power if we could now derive best play at least at a basic level. Knowing nothing about the cards in the shoe (or assuming infinite deck shoe) if I have a 13 with a dealer 7 showing, what is my probability of winning if I hit? What if I stand? It would be a probability of me getting a bust card vs staying 21 or under combined with the probability the dealer would draw out (including no draws when they are hard 17 or higher) to beat me / push me / bust themselves
This is not correct. See my previous post.
Specific example a situation in Single Deck blackjack.
Initial two cards.
If you have 9/3 against a dealer’s 3, best strategy is to hit.
If you have 8/4 against a dealer’s 3, best strategy is to stand
Three cards:
If you have 8-5-3 against a dealer’s 9, best strategy is to stand
If you have 7-6-3 against a dealer’s 9, best strategy is to hit.
And this was found out by searching every possibility in the tree.
I’m not sure I understand what you are asking. Are you asking if this could be done in real time at a table? If so, the answer is yes, but it would be a felony.
If you are just asking if a computer can derive the best play for every combination of hands, the answer is yes. That’s exactly how we do it. Set up 13 against a 7, then try hitting it a million times. Record the expected value. Nos set up the simulation the same, except this time for standing. A good simulator will allow you to set ip any scenario you want, including the exact cards that have already been played, jow far into the shoe the simulated dealer deals, etc.
The first exposure I had to blackjack, or any gambling for that matter, was as an editor for a software company. I had sold them a computer game I wrote in high school and they subsequently hired me to review other software submissions. One of them was called “Blackjack Trainer” and was all about teaching card counting by running simulations. I learned to count cards because I decided I couldn’t in all conscience recommend the program unless I knew if card counting even worked. So I learned it, and it did. That was in… around 1982.
Here’s a site where you can download a simulator:
It’s in Python and you can get it from github. I haven’t used it and can’t vouch for its accuracy, but it shows that these things are pretty simple and straightforward these days.
Did you miss where I said “unless you’re counting”, there? The difference between a 9/3 and an 8/4 is in the counting. But it’s a very crude count that looks only at your own cards, not at all the other cards you can see.
Well… I would argue that this falls under the definition of ‘counting’. You are making strategy variations based on inspection of the specific cards and adjusting your play accordingly.
For everyone interested:
There are two ways to gain an advantage when card counting in blackjack. One is through bet variation when the count is high or low. The maximum-expected value approach is to never play a hand unless the count goes higher than +2 or so, then bet the max. So counters will sometimes just wander around the blackjack pit, stopping to count cards when a new shoe is dealt. If the count goes positive they’ll sit down and play, and if the count goes negative they leave for the next table.
The problem with this strategy is that A) the casino will notice, and B) they will counter by not allowing you to join a game in mid-shoe. So, the alternate strategy is to play all hands, but to bet the minimum when the shoe is negative or neutral, then start increasing bets as the count goes more positive. To win this way in a shoe game you generally have to bet 8-10 times the minimum when you have the advantage. It also helps if you take as many breaks as possible when the count goes negative. The casino will eventually spot this behavior as well, but unless you are betting ‘green to black’ ($25 to $100 per hand), they’ll generally not care.
For betting variation, all you need is to keep one integer number in your head - the ‘running count’. This is enough to make you a winning player in a shoe game. But the last wrinkle is before you make your bet decision you have to estimate how many decks are left and divide the running count by that to get the ‘true count’ which is the actual ratio of high cards to low cards per deck. So if I’m playing a four deck shoe and roughly a deck has been dealt out, my running count of say, +4 has to be divided by three. It’s close enough to just say the true count is just over +1.
The next level of counting involves advanced counts that assign more than a simple +1, -1 to the cards. These get harder to track, and you gain very little in multi-deck games.
The other way of winning at blackjack is through strategy variation. This is more important the fewer decks there are. In single deck with good rules, you can actually beat the game with strategy variations only. There are hundreds of potential strategy variations for each count, but there are diminishing returns. It’s generally accepted that with the simple hi-lo count there are 18 variations to basic strategy that will get you 80% of the advantage without memorizing a zillion plays.
For example, you should stand on two tens against a dealer’s 6 for any count below +5, and split them for any count above that. For a 6 against a 5, the count for doing that is +6. You should stand on 12 against a dealer’s 2 any time the count is greater than +3, but hit it if it’s lower.
The highest skill level in counting comes from using a multi-level count, coupled with side counts of critical cards like Aces. I never bother with that - I’d rather use my extra clock cycles to hide my counting, chat with the dealer as camouflage, etc.
Strategy variation is critical in single deck blackjack, but as the number of decks in the shoe goes up, bet variation predominates and you can ignore most of the strategy variations.
Finally, one factor no one seems to talk about outside of blackjack pros is penetration. That is, how far the dealer deals into the shoe. Most large advantage situations come near the end of the shoe. Remember the true count? If I’m playing an 8 deck shoe, even if the first hand was all 2-6 I might have a running count of +16, but the true count is still around 1, which isn’t enough to have an advantage on the next hand.
On the other hand, if there’s only half a deck left and I have a running count of 4, the true count is 8 and the remaining cards are wildly in my favor.
Knowing this, many casinos will only deal halfway through a shoe before reshuffling. but that annoys the players and slows the game down, so some places will deal deeper. Some dealers who tire of constantly changing decks may also deal deeper.
An 8 deck shoe dealt down to 4 decks before shuffling is unbeatable unless you do massive bet swings or walk away from the table when the count goes negative. The same game dealing down to a half deck would be wildly profitable. Our local casinos had for a while a 4 deck game dealt down to half a deck. I made a lot o money from them.
I once such a book, but I can’t remember the name. It had many charts. One of them showed the common grid of every possible player hard versus every possible dealer up card. Each square showed every possible play and the percentage of times you would win. The charts of the Basic System show only that best (or sometimes least bad) option.
Does that answer your question? If not, I hope you find a book that does.
I’m not counting, so it doesn’t apply.
I’m talking without using Monte Carlo. For example: with a 13 and hitting I have a 4/13 probability of getting a 18/19/20/21. With a dealer showing a 7 they have a 4/13 probability of a hard 17 and a 1/13 probability of a 18 so standing I have a p=5/13 of losing right then and there but by hitting one card I have p=19/169 of winning right then and there and a p=1/169 of pushing.
Extend that out over all possibilities like p=1/13 dealer has a 16 and if I stand they have p=8/13 of busting so that scenario gives me a 8/169 chance of winning. Now what if I hit what is the p of me busting vs p of the dealer drawing out to beat my hand. 16 is easy since the dealer can only take one card. It would be more difficult if a dealer has a 9 because then there are many scenarios to drawing out.
That’s incomplete. Your odds change if your 13 is made up of a 7 and 6 rather than a 10 and a 3. Remember, blackjack is a game of card removal without replacement, which means the odds change with every single card shown.
The permutations of possibilities would be enormous. you would have to calculate not just for every hand value, but for every hand that can make the same value. And you would have to do this for every combination of card values that have gone by, and for each place in the shoe the hand could take place.
Here’s a paper which simply attempts to calculate the odds of various starting hands and the results of hitting:
Nope. And I’ve noticed that within these casinos the best table games like poker and blackjack are slowly being replaced by slot machines, pai-gow, etc.. I suspect poker is only there to draw in players who might play the slots or other sucker games while they wait for a seat. And low limit poker players are being raked into oblivion.
Yes. I’ve done it. Discussed above.
That’s single deck. No one plays that because who is willing to win 6-5 on a blackjack instead of 3-2?
Is there something similar for, let’s say, a 6 deck shoe?
Yes, the program I wrote calculates the odds for any variation. See how I said my program calculates the chance of me, or the dealer, getting several aces in a row. Which should indicate that it’s more than one deck. My program takes account of the number of aces dealt, and the number remaining in the shoe, which changes according to the number of decks used.
And single deck blackjack has a very slight positive EV, even with 6-5. I’ve played it.