acsitanro1970.netlify.com

• Aug 13, 2019 Blackjack Hand Calculator Introduction. This calculator will show you the best return for a blackjack hand. Select the rules and cards, then click the Calculate button.
• Blackjack and Probability Chongwu Ruan Math 190S-Hubert Bray July 24, 2017 1 Introduction Blackjack is an usual game in gambling house and to beat the dealer and make money, people have done lots of research on it. They come up with several basic strategy which is consist of three tables corresponding to the different rules.

The bust probability is calculated by dividing the number of Dealer's busted hands to the total possible blackjack actions. Probability Of Blackjack Hands our focus on keeping it fun. GameSenseinvolves learning how the games work and the odds of winning and losing. GameSensemeans balancing the fun part of gambling with the need to stay in Probability Of Blackjack Handscontrol and within your boundaries.

Did you know that you can play more than one hand of blackjack at a time in most casinos?

Blackjack Probability Calculator

If a table is full, this isn’t possible. But at most casinos, the blackjack tables aren’t quite full. I see a lot of my fellow gamblers playing two hands simultaneously. You’re not limited to just two hands either. You could even play three hands at the same time if you needed to.

Is this a good idea or not? A simple answer might be to think about what playing multiple hands does to your average win or loss rate.

If you’re a recreational player, even if you use basic strategy, playing multiple hands simultaneously just means you’ll lose more money faster. But if you’re an advantage blackjack player, playing multiple hands simultaneously will result in a higher average hourly win rate.

If you’re thinking about playing two hands at a time instead of just one, you should examine your reasoning for this rationally. If you think it’s just going to change your luck, you shouldn’t do it. The number of hands you’re playing doesn’t affect luck in any way because, after all, luck is just standard deviation.

The house edge will stay the same regardless of how many hands you’re playing.

What Playing Multiple Hands Does

Let’s look at a few different scenarios.

In the first scenario, you decide to play one hand at a time for $5 per hand. You’re using perfect basic strategy, and the house edge in this specific casino is only 0.4%. It’s a two-deck game with good rules. It’s also the middle of the afternoon, and the casino isn’t busy, so you’re playing heads up against the dealer. This means you’re getting in 200 hands per hour.

The amount you’re mathematically expected to lose in this scenario is easy to calculate. You multiply the number of bets you’re making per hour (200) by their size ($5) to get your total amount of hourly action.

In this case, you’re putting $1000 into action per hour. The house edge is the amount the casino expects to win in the long run, so you multiply the house edge by the action. That gives you an expected hourly loss of $4.

Now, let’s take a second scenario. It’s the same table, same rules, same amount per hand, and same perfect strategy on your part.

But because you’re playing two hands per hour, the game slows down a little bit to 160 hands per hour, but multiplied by 2, since you’re playing both of them.

Now, you’re getting in 320 hands per hour, which means your hourly action jumps to $1600. 0.4% of $1600 is $6.40 per hour in expected losses. It’s obvious that you’re going to lose more money playing two hands per hour.

Also, the more hands you get in, the closer your actual results will get to the mathematically expected results. In other words, if you’re hoping to capitalize on a short-term lucky streak, you reduce the probability of doing that by playing so many hands.

Now, let’s look at a third scenario. You’re playing the same game, but you’re counting cards, and you have a 0.4% edge over the house instead of playing against a house edge of 0.4%.

Instead of an expected loss per hour of $4, you now have an expected win per hour of $4. AND if you play two hands instead of one, you have an expected win per hour of $6.40.

Blackjack Probability Theory

Since you’re counting cards, you get more information faster by seeing more cards per hand, too. The more cards you see, the more accurate your count becomes.

One More Example of Playing Multiple Blackjack Hands at Once

I want to look at one more scenario. This time, instead of playing for $5 per hand, you have a player who’s
betting $100 per hand.

That’s 200 hands per hour at $100 per hand, or $20,000 in hourly action. 0.4% of that is $80 in expected losses per hour.

What if this player decides to start playing two hands at a time instead of just one, and he only bets $50 per hand? He’s still putting $100 “per round” into action, but the action slows down because of the extra hands.

Instead of 200 bets per hour at $100, he’s getting in 320 bets per hour in at $50 per hand, or $16,000 in hourly action. His hourly expected loss goes down to $64 instead of $80.

If this player were counting cards with an edge of 0.4%, his hourly win rate would drop correspondingly. This seems counterintuitive, but if you think about it, this is the case.

Some Conclusions to Draw From All this Math

The first conclusion is that if you’re not changing the size of your bets, but you’re making almost twice as many bets per hour, you’ll lose (or win) more money based on your mathematical expectation. Average players will lose more per hour, and advantage players will win more per hour.

But if you reduce the size of your bets AND reduce the number of hands you’re getting per hour, you’ll lose (or win) more money, again based on your mathematical expectation.

Most of my readers are basic blackjack strategy players. This means that, over time, they’re going to see a net loss. But that net loss is lower than you’d see at almost any game in the casino.

My hope for that player would be that they’d realize the importance of getting in fewer hands per hour. The fewer hands you play per hour, the less money you’ll lose on average over time.

Playing two hands at once is one way to get in fewer hands per hour, but it’s not the only way. You could also limit your play to tables with a minimum number of players.

If you stick with games where there were at least four other players at the table, you’d only play 70 hands per hour instead of 200 or 160. You could afford to bet more per hand and still lose less money per hour at such a table.

And if you stick with your other betting amounts, you’d save a lot of money and have a lot of fun socializing while you’re at it.

Conclusion

The pros of playing multiple hands of blackjack at the same time are simple enough.

• If you have an edge over the casino, you can make more money per hour doing this.
• If you don’t, you can put the same amount of money into play per round by playing two hands instead of one and betting half the amount. This will reduce your hourly expected loss rate.

The cons of playing multiple hands of blackjack are simple enough, too.

• You’re less likely to see a lucky winning streak based on short term variance.
• You’re going to lose more money per hour if you don’t reduce your bet size, because you’ll be getting in more hands per hour for the same amount per hand.

Should you play multiple hands of blackjack simultaneously? That depends on all the factors discussed above.

Are you a card counter? Do you think you’ll try to earn more by playing two hands at a time after reading this? Are you a basic strategy player? Do you think you’ll try to get in less action per hour to try to reduce your hourly loss rate?

Let me know in the comments.

Please enable JavaScript to view the comments powered by Disqus.

By Hon. Ion Saliu, Founder of Blackjack Justice

First capture by the WayBack Machine (web.archive.org) May 21, 2020.

Your Honor, I hereby accuse the Order of Casino Sycophants of damaging public deception. They make-believe that the glamorous game of blackjack has a frivolous house edge. Said game with its odds is so attractive to the masses that we can treat it equally to tossing a golden coin.
Our complaint shall prove that the real conditions of the game are far worse than the fake-news promoted, indeed imposed, by the Order of Casinos and their Sycophants.

Let me just say that benign ignorance has been at the heart of the matter. Nobody really knew what the real odds (probability) of blackjack were. Analysts lacked the fundamental elements required by the fundamental formula of probability: favorable cases (over) total possible cases.

Calculating the odds is the sine qua non condition of calculating the house advantage or the edge the casinos have in the game of blackjack. No casino offers a game where they don't have an edge or advantage. It's their bloodline — a legal requirement, as a matter of fact.

The first attempt at calculating the house advantage in blackjack is granted to John Scarne, a non-mathematical man who had the ambition of being the greatest gambling writer in history. Personally, I grant such honor to Blaise Pascal who analyzed a backgammon game. The historical event is known as de Méré Case and it founded a branch of mathematics hence known as theory of probability.

John Scarne rightly figured out that the casino gains an edge in blackjack because of the simultaneous bust — the dealer and the player bust at the same time. However, when the player busts, he/she loses the bet immediately as he/she always plays first. It is possible that the dealer can bust his/her hand (in the same round), but it is too late for the player; they already lost their bet.

John Scarne calculated the odds of dealer's bust to be 28%. If the player played by the same rules as the dealer, the simultaneous bust would be: 0.28 * 0.28 = 7.8%. But since the player is allowed to stand on 16 or less under certain circumstances, our 'mafia' man calculated that the final odds would be around 5.9%. That's the 'physical probability' of casino winning at blackjack.

The casino offers bonuses to the player, however. They pay 3 to 2 for a natural 21 (Ace+Ten in the first 2 hands of the player). They also allow double-down and splitting pairs. At the end of the day, the bj house advantage goes all the way down to that glamorous figure of 0.5%.

Right now, we focus our attention on the raw figure of 5.9%. Based on that figure (and so-called simulations), everybody agreed that the results of blackjack were:

• 48% winning hands for the dealer
• 44% winning hands for the player
• 8% hands end up as pushes (ties).
• 44/92 = 47.8% winning probability for the player

In order to calculate the probability precisely, we must generate all the elements (blackjack hands) in lexicographical order. Nobody even knows how many hands are possible, as their size varies widely: From two cards to 10 cards (for one deck)! When two or more decks are employed, the blackjack hands can go from two cards to 11 cards.

Of course, there is a lot of blackjack software out there! But all that software belongs to the simulation category. That is, the blackjack hands are dealt randomly. Based on the well-known-by-now Ion Saliu's Paradox, random generation does not generate all possible combinations, as some elements repeat. So, we can never calculate the probability precisely based on random generation. If there are 334,490,044 total possible complete hands in blackjack, only 63% will be unique and 37% will be repeats — if we randomly generate 334,490,044 hands.

I had started years ago a blackjack project to generate all possible hands. It was very difficult. I found the project in the year of grace 2009 and also the code to generate sets from a list (last update: 2014). In this case, the list is a 52-line text file with the values of the blackjack cards, from the four 2's to the 16 Tens, to the four Aces. That's a stringent mathematical requirement. The deck of cards must be also ordered lexicographically, if we want to correctly generate all qualified sets in lexicographical order.

I generated blackjack hands as both combinations and arrangements. Then, I opened the output files (text format) and checked as many hands as possible. Yes, computing things are so much better today than just a decade ago. The generating process is significantly faster.

I wrote a special Web page dedicated to the topic of calculating precisely mathematically the bust-odds at blackjack following the Dealer's rules. There are lots of details, plus screenshots of the probability programs:

• Blackjack Dealer Bust: Software to Calculate Probability, Odds, House Edge, Advantage HA.

Keep this new figure in mind: The odds for a blackjack Dealer's bust are at least 33%. The bust probability is calculated by dividing the number of Dealer's busted hands to the total possible blackjack actions.Blackjack actions is a parameter that counts everything: Busted hands, pat hands (17 to 21), blackjack hands, and draws or hits to the first 2-card hands (incomplete hands). The software does NOT print the incomplete bj hands.

How can we apply the new programming to determine the bust odds for the blackjack Player? After heated debates in forums in 2014, I simply modified my software. The hit-stand limits can be set by the user. Initially, it was fixed — the ubiquitous hit all 16 and under, stand on all 17 or greater.

The software user can set the hit-limit to any value. The choices are, obviously, from 12 to 16. I tried, for example, the hit limit to 11 — that is, hit anything 11 or under, stand on anything 12 or higher. Evidently, there is no bust in such situations. That's another proof that my programming is 100% correct.

I believe that setting the hit limit to 14 or 13 reflects pretty closely the bust odds for the Player. That is, stand on 15 or greater (as arrangements):

Or, stand on 14 or greater (as arrangements):

• Now, the house edge goes between something like .3355 * .2248 = 8.3% and something like .3355 * .1978 = 6.6%. It averages out to 7.5%. It is a far cry from the intentionally false house advantage (HA) of .5%, or even .17% (promoted by several crooks)!
• The overwhelming majority of blackjack players lose their bankrolls quickly, because this is NOT a 50-50 game or so much close to that margin.
• And always be mindful that blackjack is strongly sequential: The Dealer always plays the last hand. Otherwise, the casinos would go bankrupt.

Recalculating the raw figures for winning/losing hands, my theory shows:

• 50% winning hands for the dealer
• 41% winning hands for the player
• 9% hands end up as pushes (ties).
• 41/91 = 45% winning probability for the player

Axiomatic ones, who's right and who's wrong? If you have been a frequent visitor of my website, you already know how many hits I've been taken from casino executives, agents, moles, other gambling authors, system developers, vendors, gurus, bishops, saints, etc. Granted, the attacks against yours truly were far more intense earlier (beginning 1998 and ending early 2000's). They realized I wouldn't get intimidated, so they have given up, by and large.

In this year of grace 2019, I came up with a new idea: Let's set at the same table mathematics and reality. The first attacks aginst me went along the lines: 'Mathematics, specifically formulae, have no place in gambling — as it is totally random.' And I've always counterattacked: 'But what is not random, crooked idiots? The entire Universe is ruled by Almighty Randomness, as voided of consciousness as it might be!'

Standard deviation is the watchdog of randomness. Let's see what figures of blackjack odds are right by employing the binomial standard deviation. Then, compare the results to casino gambling reality.

It is time now to apply the most important bonuses the casinos grant to the blackjack players:

• natural 21 pays 3-to-2
• double down pays 2-to-1 (if successful)
• splitting pairs pays 2-to-1 (if successful).

We ignore the current tendency in the gambling industry to pay a natural bj 6-to-5.

The double down success is closely around 60%. The same success rate of 60% occurs in the pair splitting situations.

Next, it is very important to know the probability/odds of appearance for the 3 bonuses above.

• natural 21 occurs in 4.8% of cases, but only when dealing 2 cards to oneself at the beginning of a 52-card deck. We average the odds to 4% for multiple players (4 players and a bj dealer is an average situation in my book). Refresh your memory by reading this popular resource:
  • Calculate Blackjack Probability, Odds: Natural 21, Insurance, Double-Down Hands, Pairs.
• double down hands have an appearance rate of 8%, as first calculated by yours truly. Please read this very popular resource:
  • Calculate Probability of Double-Down Hands.
• splitting pairs hands have an appearance rate of 3%, as first calculated by yours truly. Please read this very popular resource:
  • Calculate Probability of Split Pair Hands.

Axiomatics, we run my probability software widely known as SuperFormula.exe, the function D: Standard Deviation. We run the function twice: First, for the traditional black jack parameters (5.9% odds, 48% winning probability for the player); secondly, for what I consider closer-to-reality blackjack parameters.

We take a common case of playing 100 hands. That is, the blackjack player must cash in the amount needed to play 100 hands at the minimum bet. For example, in the rare case of $10 minimum bet, the player must chip in at least $1000. I can't stress enough the stupidity of players who start with $100... they lose quickly... then leave the table... go to another table and cash in $100... etc. Vae victis! Poor victims!

WHOA! ON AVERAGE, THE PLAYER WINS 52 BET UNITS AFTER PLAYING 100 HANDS!!! That's a flagrant impossibility in 99.7% to all blackjack players, in all casino situations. You and I will never, ever, see a basic strategy player be ahead $52 after playing 100 hands, at $10 table minimum!

We come back to earth by going with my fundamental blackjack parameter: 45% winning odds for the player.

Blackjack Probability Math

You, the player, do lose. Still, this is the happiest case calculated by my blackjack-odds software: One deck of cards. Today's PCs are still incapable (at least in the case of this programmer) to calculate for two or more decks of cards. But I experimented with calculable amounts of cards. The rule is very clear: The more cards, the worst the odds get for the player. In other words, the more decks, the worse conditions for the blackjack hopeful! And even worse with multiple players at the table (the common reality)!

Haven't you witnessed this in any casino, at any blackjack table? The overwhelmingly vast majority of players lose their bankroll quickly. They leave the venues almost on their knees. 'How the hell is this possible,' they ask themselves (sometimes loudly). 'Blackjack is supposed to be a 50-50 game... damn it!'

It ain't such a golden coin game, kokodrilo (royalty-name for big-time gambler)! I'm afraid you were misguided big-time... you still are. You are mostly cheated by the card-counting crooks, the bedfellows of the casinos in that gambling bedlam! You go by their insane odds and you are guaranteed to win as a matter of fact. Play 100 hands and win $52 at $10 minimum bet. Well, then, ask for a $100 table minimum and make a $500 net. This is the average, but it will be confirmed in any reasonable long run. Not the billions of hands long-run prophesized by the crooks!

Blackjack: Software, Content, Resources, Systems, Basic Strategy, Card Counting

See above: The comprehensive directory of the pages and materials on the subject of blackjack, baccarat, software, systems, and basic strategy.

• Blackjack: Basic Strategy, Card Counting, Charts, Tables, Probability, Odds, Software.
• The Best Blackjack Basic Strategy: Free Cards, Charts.
  All three color-coded charts in one file, in the best decision-making sequence: Split Pairs, to Double Down, to Hit or Stand.
• Gambling Mathematics in Blackjack Proves Deception of Card-Counting Systems.
• Probability Software to Analyze Blackjack Streaks: Wins (W+), Losses (L-), Busts, Pushes.
• Best Card Counting Blackjack Systems, Casino Marketing, Gambling Deception, Fraud.
• The Best Blackjack Strategy, System Tested with the Best Blackjack Software.
• Blackjack Insurance Bet Favorable to All Players.
• DownloadSoftware: Casino Gambling, Roulette, Blackjack, Baccarat, Craps.
• Specific software for blackjack, BJ
  ~ BJAQK and Blackjack: Probability and statistical analyses of thousands of blackjack hands from the perspective of a strict blackjack old basic strategy (OBS) player.

Home Search New Writings Odds, Generator Contents Forums Sitemap