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You will also find there other issues of probability-based blackjack strategy. See the Books section for details. Check this.


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Blackjack Mathematics: Probability, Odds, Strategies, Systems
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Learning the mathematics behind blackjack isn't overly complicated. Understanding the core blackjack math principles is essential to card counting.


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Blackjack Mathematics: Probability, Odds, Strategies, Systems
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blackjack math problem

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The original question was, exactly, as this: "Dealing yourself a blackjack (Ace AND Face-card or Ten) from a single deck". The calculations above are accurate for.


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The original question was, exactly, as this: "Dealing yourself a blackjack (Ace AND Face-card or Ten) from a single deck". The calculations above are accurate for.


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You will also find there other issues of probability-based blackjack strategy. See the Books section for details. Check this.


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I. Fundamental Probability Issue: True Odds at Blackjack, Software Calculator II. Fundamental Myth of Blackjack Gambling: Counting Cards III. Theory of Streaks:​.


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The original question was, exactly, as this: "Dealing yourself a blackjack (Ace AND Face-card or Ten) from a single deck". The calculations above are accurate for.


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A blackjack game has a dealer and one or more players. Problems. If you are dealt a point total of 16, what is the probability of busting if you hit, assuming that​.


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I. Fundamental Probability Issue: True Odds at Blackjack, Software Calculator II. Fundamental Myth of Blackjack Gambling: Counting Cards III. Theory of Streaks:​.


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The probability is 1, since whatever card you are dealt, you can count the ace as a 1 To solve our problem, we need to figure out how the dealer's second card.


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blackjack math problem

You don't have a "computer model" for blackjack. What if you stand? About my first question, I will edit it. Sign up using Facebook. That's why you should stand. Active 1 year, 4 months ago. Ross Millikan Ross Millikan k 25 25 gold badges silver badges bronze badges. And so on. To my knowledge, it is not very simple to derive basic strategy using just pen and paper because you would have to deal with a number of different cases and keeping track of them all can be tedious. The rules of the game are given. In your example, the prob. After more counting, you could compare that with the winning percentage of draw to 14, and you would have a rigorous answer. I checked the data for the scenario described above. Post as a guest Name. Later he also talks about the methodologies to count, but that is not relevant to my question. And these games are made up cleverly just see Pascal's roulette , there is no need to compute the house's edge, as it has been well calculated for ages. I used the term model to mean 'modelling'. And of course also increases the house edge. Added: counting just changes the frequency distribution of cards that are dealt. Hot Network Questions. I was watching Beating Blackjack with Andy Bloch where he runs through the basic strategy charts that outline the best strategy with playing the game. You can model the dealing of the cards as if they were uniformly random draws from a collection of objects distinct objects if you are using a single deck of cards without replacement. He states in that video that the basic strategy is an outcome of computer simulations, and that suggests to me that its a rather weak method to go about doing it. It only takes a minute to sign up. I might have maiden some mistakes in the above example, but I hope the theory can be seen. It is true that with modern computers a simulation could be implemented a lot faster then doing all computations for probabilities, that is why I think these techniques are so popular nowadays. Also, the dealer can bust on 4 or more card. Related 2. Since it is a game with randomness built in, it is a good candidate for Monte Carlo simulation. I'm not sure I understand your first question. Featured on Meta. Question about basic strategy in Blackjack Ask Question. The best answers are voted up and rise to the top. The dealer should act the same whatever value I stand at. The sort of question you would do with Monte Carlo is to decide "If the dealer shows a 6, what value should I draw to? Sign up to join this community. Perhaps my wording can be improved. This is simply due to the higher number of 10 valued cards in the deck, i. If you go further and look at card counting strategies, things become even more complicated and the methods and strategies appear to be more and more heuristic. This means you have around And I did not compute the chance of you would not bust but the dealer would hit a higher sum than you. The results show that in the case where the player draws and dealer draws 6, and the player stands, the player will win The average loss by standing is If the player hits however, the player will win The average loss by hitting is Notice that the trial size in both of the x cases is higher than the other four cases. The number of decks in play only affects the probability of getting a card what have been seen before what I left out of my example, as I stated , which is not a very big deal in blackjack - not like in poker. In a single deck game, there are also other factors which can have an effect on the overall game odds. Sign up or log in Sign up using Google. That will also affect the computed probability, but I will not deal with this small problem here.

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Meaning using a computer to obtain a monte carlo solution. And of course I do think the above computation could have been done in a lot simpler way using combinatorics, but that was done such a simple way only using the classical theorem of probability. Another issue is that the outcome of a Monte Carlo method could hold an acceptable accuracy with enough repetitions, so human driven planned computations just do not worth the time or energy to deal with. Active Oldest Votes. Feedback post: New moderator reinstatement and appeal process revisions. Generally if the high count cards are depleted you draw more because you bust less. It could be done with a sum of the 2 unknown card being between 11 and Note: you have 4 pieces of all cards in the deck except for the 5, 6 and 10, as you have seen in your or the dealer's hand. I have a two-fold question, one is when is a computer solution considered good enough to be "true", and the second, surely, this is a much easier problem that does not need computer simulations to solve, are there any known methods to derive the basic strategy. Email Required, but never shown. I noticed that there is no consideration of the cases where the dealer ties the player but this is only applicable when the player is hitting. On some tables, the dealer will hit Soft 17, others will stand. So if one strategy is clearly better than another, it won't take too many tries to know that. One of these is deck penetration, another is the number of "rounds" played, which is just the number of times a new hand is played from the same deck before it is shuffled. Asked 9 years, 5 months ago. Every casino table has its own specific rules. You know nothing about the other card of the dealer, but you are quite sure about he will ask for another card. Aryabhata 75k 7 7 gold badges silver badges bronze badges. Also note that the sample sizes the two x cases are not identical to each other. I'm not aware of any elegant solutions to this problem. New post lock available on meta sites: Policy Lock. If they are really close, you will never know, but then it doesn't matter much. As svenkatr states, the details of Blackjack make it difficult to do an analytic solution, but you could in particular cases. Viewed 2k times. Going back to dealer shows a 6, you could say suppose I draw to After tedious counting, you could exactly calculate your winning percentage. So the prob. I have a blackjack Monte Carlo simulation program which runs on my Apple notebook. Sign up using Email and Password. With probability and game theory any outcome can be expressed, and the probabilities and by this: wins and losses could be computed, so the basic strategy could be defined. Question feed. The scenario that you described is a single deck game where the dealer must stand on Soft 17, which is a disadvantage to the casino. Home Questions Tags Users Unanswered. The basic strategy says you have to stand. If they are close, it will take a lot. The calculated I do not think that the basic strategy would be an outcome of any Monte Carlo simulation , as blackjack and other games in casinos had been played a lot before enough computer capacities were available for such computations.