Math Behind Blackjack Basic Strategy

FrostieFingerz
Hello kind people!
After reading a lot of other people's posts, I have a question of my own, so this is my first post on this forum :)
The last couple of months I've mastered basic strategy and now I'd like to know what is beyond that, without getting into card counting.
For instance I've read about a rule where it is advised to stand on a 16 vs 10 if it consists of 3 or more cards, as compared to surrendering (or hitting if surrender isn't allowed) when the 16 consists of only two cards. I'd like to know for instance if that is also the case for a 3-card 16 vs Ace, 16 vs 9 or 15 vs 10 (because basic strategy for a 4 to 8 deck game where the dealer stands on a soft 17 advises to surrender).
I understands the odds are changing in the favor of standing on a 3-card 16 vs 10, because you've used a couple of small cards for that particular 16, but can that rule be applied no matter how many decks there are in the game?
Anyway, it's about exceptions like those above I would love to hear more. What books or sites do you guys recommend that will go deeper into this subject?
Thanks!

A good initial hand (which you can stay with) could be a blackjack or a hand of 20, 19 or 18 points. The probability of obtaining such a hand is calculated by totaling the corresponding probabilities calculated above: P = 32/663 + 68/663 + 40/663 + 43/663 = 183/663, in the case of a 1-deck game and P = 64/1339 + 140/1339 + 80/1339 + 87/1339 = 371/1339, in the case of a 2-deck game.

RS
Why don't you just learn to count cards? It's actually not as difficult as it's made out to be. You're not going to find many plays for composition dependent basic strategy, at least for 6-8 deck.
Romes

Anyway, it's about exceptions like those above I would love to hear more. What books or sites do you guys recommend that will go deeper into this subject?
Thanks!


Hey Frostie! Welcome, and thanks for posting an interesting question. While I kind of agree with RS, counting isn't all that difficult, it does take copious amounts of time, study, and dedication. In the end, like anything else, it's just memory though! If you can memorize basic strategy, you can memorize the Illistrious 18 index plays and you're on your way =p. I'm actually going to be releasing a thread: Counting A-Z by the end of the week. Perhaps take a peak at that and see if it touches your interests.
That being said, if counting simply does not interest you, no worries. There's still plenty you can try to do to minimize the house edge. The easiest thing by far, which you've done, is mastering basic strategy (AND the Fab 4 surrenders). In just about any game this will get you to approximately only -.5% to the house. I would say after this is game selection and bankroll management.
Game selection is huge. Understanding what the different rules do to/for the player is a key part of the game that doesn't have to have anything to do with counting. Finding games with the most favorable rules can take a terrible H17 8D game from .66% house edge to a nice 6D S17 game of ~.40%. Simply looking for tables with different rules can certainly change your night! For example, if you play 6-5 blackjack, you're giving the house another 1.39%!!! If you have an 'average' game that pretty much QUADRUPLES the house edge from something like .45% to ~1.84%! A list of all the rule variations can be found on the Wizards odds site here: http://wizardofodds.com/games/blackjack/rule-variations/
Next would come bankroll management. If you're not counting you must understand that you will not make money in the game if you play it long enough. However, if you just go on trips now and then and you don't want to go bust, or want to play within your limits, then this is again a rather important part of the game. Again, the Wizard is so kind as to provide a Risk of Ruin (ROR) calculator! It tells you for how many hands you plan to play on a trip, and how many units you're taking, what your ROR (chance of going completely bust) is. It can be found here: http://wizardofodds.com/games/blackjack/appendix/12/
Example: I'm going to Vegas in a couple weeks. In just base units I'm taking 300 units and I plan to play approximately 3,000 hands (6 hours per day, 80 hands per hour average). Consulting the Wizards ROR calculator betting minimum units I'm < 0.01% to go bust! Of course this differs a bit when counting and spreading, but that will be discussed in my upcoming thread.
There's probably one or two small things that are just escaping my mind currently, but to be honest there isn't a huge list of things for non counters to accomplish. Basic Strategy, game selection, and bankroll management are super important to both counters and non alike. As far as books, I'm not too sure if I could recommend any blackjack books that DON'T have to do with counting as if the author doesn't even know how to count nor the math behind it, I wouldn't take his advice =P. A great book with good stories would be the bible of card counters - Beat The Dealer, by Ed Thorp.
EDIT: Seen a few people asking these things, so I went ahead and posted my A-Z Counting Thread here.
Playing it correctly means you've already won.
Dieter


For instance I've read about a rule where it is advised to stand on a 16 vs 10 if it consists of 3 or more cards,


I believe that's mostly applicable to 1 and 2 deck games, not 4-8 deck games.
The number of decks does change strategy. Composition dependent strategy is most applicable to 1 deck. Total dependent strategy is most applicable to infinite deck. Other games are somewhere in between.
Counting, as was suggested, can be more useful yet.
May the cards fall in your favor.
1BB

Hello kind people!
After reading a lot of other people's posts, I have a question of my own, so this is my first post on this forum :)
The last couple of months I've mastered basic strategy and now I'd like to know what is beyond that, without getting into card counting.
For instance I've read about a rule where it is advised to stand on a 16 vs 10 if it consists of 3 or more cards, as compared to surrendering (or hitting if surrender isn't allowed) when the 16 consists of only two cards. I'd like to know for instance if that is also the case for a 3-card 16 vs Ace, 16 vs 9 or 15 vs 10 (because basic strategy for a 4 to 8 deck game where the dealer stands on a soft 17 advises to surrender).
I understands the odds are changing in the favor of standing on a 3-card 16 vs 10, because you've used a couple of small cards for that particular 16, but can that rule be applied no matter how many decks there are in the game?
Anyway, it's about exceptions like those above I would love to hear more. What books or sites do you guys recommend that will go deeper into this subject?
Thanks!


I'm going to address your specific questions and then offer my thoughts.
The dealer breaks less than 20% of the time with an ace up making staying on 16 a terrible decision.
When you hit 16 vs 10 you can get a pat hand and still lose. Same against the 9 but you will win more hands, making hitting the best option.
If you would like to refine the 3 card 16 vs 10 further, hit the following 3 card totals and stay on the rest: 4/6/6, 3/6/7, A/6/9, 2/6/8 and 3/3/10. Here's another. In 6 deck S17 games hit 10,2 vs 4 and stay on all other 12s vs 4. In H17 games stay on all 12s vs 4. All these variations are extremely close and most likely meaningless to all but the consummate professional. We are talking pennies so, as promised, here are my thoughts. Do you really want to fill your head with all this when learning to count is the better option?
Blackjack Attack 3rd Edition has all the charts pertaining to your questions. It is not a book for beginners but go ahead and order it if you're serious because you never know when it will go out of print again.
Many people, especially ignorant people, want to punish you for speaking the truth. - Mahatma Ghandi
FrostieFingerz
Thank you all for your thoughts. You gave me some great topics to search for. I was under the impression I had to master those rare exceptions before learning to count cards, but I'll look into card counting now and from what I've read so far, I think I'll go with the popular Hi-Lo method. I'll definitely be reading your thread, Romes!
Romes

Thank you all for your thoughts. You gave me some great topics to search for. I was under the impression I had to master those rare exceptions before learning to count cards, but I'll look into card counting now and from what I've read so far, I think I'll go with the popular Hi-Lo method. I'll definitely be reading your thread, Romes!


Glad to hear you are interested in counting =). If you didn't catch my edit above, because of this (and other) threads I went ahead and finished up what I could and posted it here.
Playing it correctly means you've already won.

So where does mathematics come in to play in online poker strategy?. Good question.So, how often do we need to win?

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With fast action, a simplistic play style and excellent player odds, it's no wonder that blackjack is so popular. So do any of you have tips or suggestions on what chapter(s)/theories/rule(s) I can use?

If Jai Alai Casino Florida you are dealt a 16 and the dealer has a face card. We are not even necessarily talking about difficult maths. Correct math behind blackjack strategy Basic strategy says you should always split aces, no matter what the tournoi poker ce week end dealer upcard is. This will include the probability of being dealt certain hands and how often they’re likely to win.Hub Video:

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  • The objective of Blackjack is simple - get your cards to add up to 21 (without going past 21) before the dealer.
  • 4,4 Never split.
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This is more about blackjack mathematics than anything else. Ho Chunk Casino Baraboo Poker I dont think there are may other combinations (might be wrong).The best way to understand and explain this is by using a hand walk through, looking at each element individually first, then we’ll bring it all together in order to make a decision on whether we should call the bet.

Blackjack is also the most researched game ever. Townsville Casino Jobs Because of this, one can use probability by outcomes to compute the probabilities of each classification of poker hand.The following tests are designed to make you think about the game.

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So math behind blackjack strategy you may cash express slot big win have a $100 in EV but you CE may only indicate that the game is only worth $50 since your bankroll is so small. How often does our bluff need to work to make money?

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  • After the ante and blinds, players are dealt 2 cards face-down (hidden from other players) and 1 card face-up (revealed to other players).
  • If the player misses his draw on the turn, he multiplies his outs by two to find his probability of filling his hand on the river.

At this stage our best guess is to assume that he has hit top pair and holds a pair of Queens. Pokerstars Alex Payne Then, choose a suit for each of those cards. Casino De Montreal Security Jobs

Basic strategy just gives the player (almost) an even chance. Dresden Casino Ontario A).'the house advantage in this game is about 0.16%'.

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Maths is integral to all forms of gambling – the bookmakers and casino owners work out the Expected Value (EV) for every bet that a gambler makes. In a purely fair game where both outcome was equally likely (like tossing a coin) the EV would be 0. If you were betting on the toss of a coin, the over the long run you would expect to win nothing and lose nothing. On a game like roulette with 18 red, 18 black and 2 green, we can work out the EV as follows: 1 2 4+ PAIRS: Rack 19 Pouces Sur Roulettes

The only way for them truly to establish whether certain plays are correct is by checking to see if the poker math adds up. Say for example you are on the river holding bottom pair and your opponent bets $4 into a $10 pot, what should you do?

IB Maths Revision I’d strongly recommend starting your revision of topics from Y12 – certainly if you want to target a top grade in Y13. The total amount of math behind blackjack strategy money bet by players each round is called the pot.A measure of a player’s experience and maturity is feather falls casino phone number how he handles bad beats.

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  • There are plenty of books dedicated to the so-called mathematics of blackjack.
  • Betting begins with a different player depending on the variant of poker.
  • However, you know that in the shoe there's about 20 more 10's than usual (or 20 more points if you aren't using a simple system), and there's only 2 decks remaining.Otherwise, the player wins if her total is closer to 21 than the dealer's.
  • The above multiple deck basic strategy is valid if the players are allowed to double down after pair splitting.
  • When discussing casino games, one usually finds statements such as the ones above saying something like:The main betting phase typically begins after players have been dealt their cards.

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Thats a lot of calculations! -If you have 17 or higher, always stand; if you have 11 or less, always hit.https://www.quora.com/What-is-the-mathematics-behind-card-counting-in-Blackjack What is the mathematics behind card counting in pharmaguideradhakrishna.com Blackjack?

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  3. Dealers cannot split their hands in standard rules.
  4. Incorrect Question 6 of 10 6.The object of the game is to beat the dealer by getting closer to 21 points without going to 22 or higher.Cards are equal to their number in points from 2-10, face cards are worth 10 points, and Aces can be 1 or 11.
  5. Otherwise, the player wins if her total is closer to 21 than the dealer's.
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The probability of a hard 6 on any given roll is 1/36. If the dealer up card is 6, and your two cards show a total of 14 (perhaps 8 and 6, or 9 and 4, it does not matter 21 Mar 2017 Using basic strategy should be a must for anyone playing blackjack.

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  1. So we can use this in our decision making process.
  2. The main betting phase typically begins after players have been dealt their cards. Odds of being dealt two suited cards The probability of being dealt two suited cards is 23.529%.
  3. The same probability holds for any other two pairs.
  4. 4 of these cards are gone out of the deck leaving 48 (these 4 cards are the first 4 used in play above) 4).You must sign in or sign up to start the quiz.
  5. Hit on A.
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Let’s imagine that this lottery uses one of those ping-pong ball machines, with 60 numbered balls, of which five will be chosen at random as the winning combination of numbers. The following situation is an example of ‘Expected Value’.The only time you should vary from basic strategy is under math behind blackjack strategypoker argentina torneos certain circumstances where you are counting cards.

If they are, it’s a sure call! There are other situations that incorporate mathematics a little more loosely, but still incorporate them theless.Don't worry, it's not rocket science and you don't need a 15 Mar 2017 - 6 min - Uploaded by Casino MathsJosh from Communication Group 34 takes you through the maths of Craps! 1 week ago • 157 Views Staying Safe And Successful at Online Poker It is still worth checking out top nj gambling sites who you are entrust..However, most of the time, there is no limit on the number math behind blackjack strategy of cards that can be discarded and replaced. Casino Attorney Super Bowl Ad

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  2. If the round has a blind bet, then each player must call the blind bet before they can check.The actual math is straightforward but extremely tedious to work out by hand.
  3. The key is this — rather than treat fourth and fifth streets as separate events, we’ll consider them together, as pairs of cards.
  4. Now I'm just one step away to start my IA, and that is, for the approval of the topic by my IA supervisor.Then, select 2 suits out of the 4 for the pair.
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However, most of the time, there is no limit on the number of cards that can be discarded and replaced. Most Roulette Colours In a Row – Francis Rodgers Aug 3 '11 at 21:03 So exectaxtalent.com for 8+6 vs 6+10, if you stand, he busts drawing 6 or more, which is 28/48 probability.

Notify me of new posts via email. Decision So now we have quickly run the numbers it is clear that this is a good bet for us (44% vs 20%), and we make the call – Total Pot now equals 50 cents.

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Math Behind Blackjack Basic Strategy

Example 1: Problems If you are dealt a point total of 16, what is the probability of busting if you hit, assuming that a whole deck will be used to choose among when you are dealt your next card?

A good initial hand (which you can stay Casino Para Mujeres with) could be a blackjack or a hand of 20, 19 or 18 points. Casino Paris Blackjack It is also a game of mathematics, where you should be able to calculate the odds of either you or your opponent winning the hand in any situation.

Absolutely – our bluff might not work every time math behind blackjack strategy but we only risk $50, and when it works, casino blue chip worth we make a million. You just experienced Variance, my friend. Can I re-raise as a bluff and will this bring me profit in the long run?

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So, how much of the total pot would we be investing with our call? You have to finish following quiz, to start this quiz:

Math Behind Blackjack Basic Strategy

Next Lesson Lesson 12: Edmonton Casino Rogers Place After the Flop (2 Cards to Come) After the Turn (1 Card to Come) Outs Rule of 4 Exact % Outs Rule of 2 Exact % 1 4 % 4.5 % 1 2 % 2.3 % 2 8 % 8.8 % 2 4 % 4.5 % 3 12 % 13.0 % 3 6 % 6.8 % 4 16 % 17.2 % 4 8 % 9.1 % 5 20 % 21.2 % 5 10 % 11.4 % 6 24 % 25.2 % 6 12 % 13.6 % 7 28 % 29.0 % 7 14 % 15.9 % 8 32 % 32.7 % 8 16 % 18.2 % 9 36 % 36.4 % 9 18 % 20.5 % 10 40 % 39.9 % 10 20 % 22.7 % 11 44 % 43.3 % 11 22 % 25.0 % 12 48 % 46.7 % 12 24 % 27.3 % 13 52 % 49.9 % 13 26 % 29.5 % 14 56 % 53.0 % 14 28 % 31.8 % 15 60 % 56.1 % 15 30 % 34.1 % 16 64 % 59.0 % 16 32 % 36.4 % 17 68 % 61.8 % 17 34 % 38.6 % As you can see the Rule of 4 and 2 does not give us the exact %, but it is pretty close and a nice quick and easy way to do the math in your head.

Blackjack Basic Strategy

Regardless on what you use to practice, whether it be a computer 2ne1 blackjack finland blackjack game or simply a deck of cards, you MUST learn basic strategy to have any hope of being a consistent math behind blackjack strategy winner at the blackjack tables.The charts below should be self explanatory. Likewise, pairs only make a set on the flop 12% of the time, which is why small pairs are not always profitable. 13 Stand on 2 to 6.