Blackjack Probabilities, Card Counting – Calculation and Simulation(easylang.online)
easylang.online
Blackjack Probabilities, Card Counting – Calculation and Simulation
https://easylang.online/apps/tut_blackj.html
23 comments
Really interesting programming language. I have been looking for a easy language to include simulation examples in my course notes, and EasyLang looks almost perfect. Only missing feature for me is support for matrix algebra (multiplication, inverse, A\b, eigenvalues, etc). I don't know much about web assembly and I don't know if there is anything equivalent to blas for web assembly which you could interface to.
Thanks. I'm afraid that won't work with EasyLang. The language is kept very simple to make it easier for beginners and so that it loads quickly and so that the code can be parsed quickly in the IDE. And unfortunately it is not possible to include other libraries.
Great strategy for publicizing a language: Use it to support articles people want to read.
Very nice writeup on this calculation, thank you.
Around the turn of the century I was also interested in calculating such a thing, but I am a lousy/lazy programmer so I wound up finding C++ code by a programmer called "Eric Farmer". Is that you?
Around the turn of the century I was also interested in calculating such a thing, but I am a lousy/lazy programmer so I wound up finding C++ code by a programmer called "Eric Farmer". Is that you?
Thank you. No, that's not me. You can see that this is not so unique, what I have done there. These calculations look very complicated at first sight, but they are not. You can actually program this step by step with a few basics of probability theory without special knowledge.
wow, seems like they are still around: https://github.com/possibly-wrong/blackjack
About 10 years ago I was in Vegas at the Riviera (now demolished). At the time it was on the cheap end of the strip and tried to attract customers by offering very attractive odds on games. They had a blackjack table that was single-deck, and they would deal pretty deep before shuffling. Those are ideal conditions for an amateur card counter like myself.
But the real kicker was, they had a side game that paid out extra bonuses for blackjacks. Blackjack paid like 5-1 on the side bet, suited AK BJ paid like 20-1, etc. I'm forgetting the exact payouts.
That night I built a simple spreadsheet to analyze the game, and calculate the effect on expected value of removing a card from the deck. I discovered that if they dealt 8 cards without an ace, the side bet became profitable. If they dealt two hands without an ace, it became wildly +EV.
I cleaned up the next morning. Really surprisingly, they never cut me off, even though the dealer made some snide remarks about card counting and I didn't make much effort to hide my strategy.
But the real kicker was, they had a side game that paid out extra bonuses for blackjacks. Blackjack paid like 5-1 on the side bet, suited AK BJ paid like 20-1, etc. I'm forgetting the exact payouts.
That night I built a simple spreadsheet to analyze the game, and calculate the effect on expected value of removing a card from the deck. I discovered that if they dealt 8 cards without an ace, the side bet became profitable. If they dealt two hands without an ace, it became wildly +EV.
I cleaned up the next morning. Really surprisingly, they never cut me off, even though the dealer made some snide remarks about card counting and I didn't make much effort to hide my strategy.
I think Vegas in general profits from the awareness of card counting and that some bets can be player-advantage at times. (They’ll back off card counters who are dangerous to their profits, but small time counting is overall casino-advantage I think [people do it imperfectly, they combine their advantage play with other gambling leaks, etc.])
I sat next to a guy at the Bellagio who was obviously counting with a base bet of a couple black chips, but didn't go nuts with his betting when the count was hot. The pit boss was an older guy and clearly saw it. In fact he started counting out loud and teasing the player. They really don't care about some tourist who comes out twice a year counting. I assume they do get cross about teams though and maybe local grinders too.
Personally I don't see the appeal of counting, except maybe a simple Ace-5 count[1] since that requires basically no effort whatsoever and nudges the EV to near 1. I like to play to socialize and have that VIP experience the good casinos deliver so well. When I want to gamble for real money I trade options.
Edit: You can even ask for a courtesy shuffle on a cold count in a heads up game and I’ve never seen the pit boss deny it. Casual counters just aren’t a concern at the strip Casinos. It probably doesn’t hurt that I toke generously too.
[1] https://wizardofodds.com/games/blackjack/ace-five-count/
Personally I don't see the appeal of counting, except maybe a simple Ace-5 count[1] since that requires basically no effort whatsoever and nudges the EV to near 1. I like to play to socialize and have that VIP experience the good casinos deliver so well. When I want to gamble for real money I trade options.
Edit: You can even ask for a courtesy shuffle on a cold count in a heads up game and I’ve never seen the pit boss deny it. Casual counters just aren’t a concern at the strip Casinos. It probably doesn’t hurt that I toke generously too.
[1] https://wizardofodds.com/games/blackjack/ace-five-count/
Yeah, it took me several years, but I finally came to the conclusion that advantage gambling was the hardest way to make an easy living. Counting is boring as hell. Casinos are boring as hell. Poker can be exciting but not in a good way if your living depends on it.
What do you do when you're at 16 units and basic strategy calls for a split or double down? This is where these "simple" ones always get me.
I know that splitting and doubling have +EV which is why you do them, but if you're at $maxbet, it can really wipe you out if it goes sideways.
I know that splitting and doubling have +EV which is why you do them, but if you're at $maxbet, it can really wipe you out if it goes sideways.
You need to manage your bankroll with the Kelly criterion or something similar. Consider a hypothetical game with a 1% player edge. Even in that game naive betting will lead to certain ruin.
I think in this particular case it was because I was betting the side bet hard. Usually the side bets are sucker bets, and counters avoid them. They didn't realize that this particular side bet could be (very easily!) counted.
But also, the Riviera is out of business, so why assume they were good at their jobs?
But also, the Riviera is out of business, so why assume they were good at their jobs?
Some card counters use two counts, to separate odds from strategy. I could never imagine myself memorizing all those cutoff numbers. These two counts aren't independent; once you establish a 2-dimensional parameter space, the regions of interest aren't going to be defined by coordinate cuts. They're going to be blobs. But for some of us visual thinkers, blobs are easier to remember than a table of cutoff numbers.
I never wrote the code to compute this strategy, back in 1990. Today it would be easy. If what I said is obvious to you, have a go at it?
A card counting scheme is essentially a gradient vector, simplified to varying degrees to be memorable and practical. One takes the gradient at a full deck. Should one design the second count based on a gradient taken elsewhere, such as the typical imbalance when the whale comes over to bet?
Better, the 2-dimensional projection should be allowed to evolve in simulation. A pair of gradient vectors is a good initial seed, but only that. And a strategy based on "blob" charts will evolve differently than a strategy based on cutoff numbers, potentially realizing greater gains.
I never wrote the code to compute this strategy, back in 1990. Today it would be easy. If what I said is obvious to you, have a go at it?
A card counting scheme is essentially a gradient vector, simplified to varying degrees to be memorable and practical. One takes the gradient at a full deck. Should one design the second count based on a gradient taken elsewhere, such as the typical imbalance when the whale comes over to bet?
Better, the 2-dimensional projection should be allowed to evolve in simulation. A pair of gradient vectors is a good initial seed, but only that. And a strategy based on "blob" charts will evolve differently than a strategy based on cutoff numbers, potentially realizing greater gains.
I spent a few summers in the mid-90s card counting with a couple friends on summer vacation from college. Vegas was saturated so we focussed on Reno and Mississippi. I'm pretty sure we were about the only ones in Mississippi because the rules weren't always great (the basic rules are fixed of course but casinos can and do change the "edge cases" like the ability to double after splitting) and they played with big "shoes" of multiple decks, usually 8.
The thing is when you count you start at zero when the deck(s) are shuffled and then keep a running count. So it's just one number. Each card you see modifies the count up or down (we used the Omega II system where 10s were -2, aces and 8s were 0, 4/5/6 were +2, etc). Once you practice (a lot) it's not hard: I could count a double deck perfectly as fast as someone could push cards off the top.
The thing about playing games with a lot of decks is that they let players join at pretty much any point. In a single or double deck game you have to wait for the shuffle. So we could wander around the casino, wait for a (massive) shuffle and then start counting without playing. If the count got good, it could get really good, and once a bunch of "bad" cards were out it would stay good for a while. Long enough to jump in and play a few hands, until the count went bad and then you could pick up your winnings and move along.
Fun times. We made good money for college kids but never had enough starting cash to really make a splash and get caught.
The thing is when you count you start at zero when the deck(s) are shuffled and then keep a running count. So it's just one number. Each card you see modifies the count up or down (we used the Omega II system where 10s were -2, aces and 8s were 0, 4/5/6 were +2, etc). Once you practice (a lot) it's not hard: I could count a double deck perfectly as fast as someone could push cards off the top.
The thing about playing games with a lot of decks is that they let players join at pretty much any point. In a single or double deck game you have to wait for the shuffle. So we could wander around the casino, wait for a (massive) shuffle and then start counting without playing. If the count got good, it could get really good, and once a bunch of "bad" cards were out it would stay good for a while. Long enough to jump in and play a few hands, until the count went bad and then you could pick up your winnings and move along.
Fun times. We made good money for college kids but never had enough starting cash to really make a splash and get caught.
You discovered "Wonging in". Same strategy as the MIT card counting team. Very effective.
> So, in blackjack, you can win if the circumstances are right and you have a lot of time.
> If the "true count" is at least 6, we bet $1000, otherwise $10.
If you bet like that in a casino in Nevada, they would kick you out so quickly you wouldn't have time to count your chips. In Atlantic City they can't kick you out, but they can shuffle the deck after every play.
And nowadays almost every blackjack table uses auto shufflers that basically makes it like a new deck on every hand, which is why I don't play much blackjack these days.
> If the "true count" is at least 6, we bet $1000, otherwise $10.
If you bet like that in a casino in Nevada, they would kick you out so quickly you wouldn't have time to count your chips. In Atlantic City they can't kick you out, but they can shuffle the deck after every play.
And nowadays almost every blackjack table uses auto shufflers that basically makes it like a new deck on every hand, which is why I don't play much blackjack these days.
> And nowadays almost every blackjack table uses auto shufflers
I already thought so. That means card counting was a thing of the past.
I already thought so. That means card counting was a thing of the past.
Most casinos still hand shuffle in the high roller pit. So if you’re betting $50-$100+ per hand you can still get some good streaks going, but that’s an awfully expensive hobby.
A great website solely focused on calculation and simulation. That in-depth explanation left me wondering about the nature of the game itself. I'll probably try to play blackjack if I have the chance.
Now many years later comes the next attempt to publish it. In the meantime I have made the beginner programming language Easylang, which is also quite well suited to show mathematical concepts and programs on the Internet.
And, I haven't been to the casino in years and have never counted cards there.