What is the defining formula for conditional probability? P(E|F) = P(E β© F). P(F). 2β. 3. Suppose that you are playing blackjack against a dealer with a standard.

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If you still interested in obtaining the matching result, you can use the following conditional probability formula: Q[bust] = P[bust] / (1 - P[bj]).

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Bovada Casino Mobile Review. blackjack conditional probability. Transcript of Conditional Probability, Blackjack, and Drug Testing. The probability of A given Bβ.

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Definition of conditional probability: Given an event B, we assign new As a warm-up let us compute the probability to get a blackjack with two cards. If there is.

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I have followed the method about "Pair Splitting Ev" discribed on Theory of blackjack 5th pag , which I guess is the same approach that the.

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Finalresult I7 I8 19 20 21 Blackjack Bust Probability 15% 15% [4% 18% 5% 5% the numbers in the table are conditional probabilities given your result, and in.

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Conditional probability also explains why blackjack is the only casino game of chance in which it makes sense to keep track of past occurrences. In roulette.

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The probability of the hands and therefore the round is determined by the N removed is the conditional probability relative to if a paircard had.

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Either a non-split card was dealt N - or the maximum number of hands has be reached and any card including a paircard can be played x as the second card of the hand. It is also important to note that only the effects of removal of the initial N card need to be taken account and not the third, fourth, etc. Thank you, MGP, for all your analysis. And once again the answer is yes for fixed strategy play and sometimes for optimal play. A round for the player can consist of any of the possible different hands that will be played until either the maximum number of splits is reached or until no free pair cards are left. First however we need to figure out what the EV of each round is. Search forums. To calculate the x hands where only a P is removed, e. The probability of each of these possible rounds is listed in the 3rd column. Calculating EV x and EV N for Finite Decks As we know from our calculations on infinite deck splits, EV x and EV N are the weighted averages of the various possible hand that may arise when playing out a single split card, with EV x being the result of any card, and EV N being limited to the results of non-pair cards. The second hand would have the notation: EV x-x. It turns out that for Fixed Strategies the answer is Yes. One could obviously brute-force this, however it's much easier and faster to think in terms of conditional probaiblities again. Again, the answer for fixed strategies is yes and optimal strategy is sometimes. If further splits are allowed, you just do the same thing using the different possible rounds that are listed in the previous post. The shoe states and the conditional relationships for the probabilities and EV's are summarized below. The situation however becomes a bit more complicated if you are limited by finite decks. What's new New posts New profile posts Latest activity. For a better experience, please enable JavaScript in your browser before proceeding. Log in Register. Log in. An additional notation will be introduced for finite splits to account for the effects of removal on N and x hands. New posts. These hands do not need to consist of only 2 cards, however N and x refer to which second cards are allowed. The probabilities used for the rounds are the same. Note that "N" can refer to either the non-paircard or to the hand which began with a non-paircard depending on the context. For optimal play, or varying strategies, the answer is sometimes. I'm not exactly sure why this is but I believe it is because the dealer plays his hand out after the player has played all of his hands. Determining the EV's of N and x hands is the hard part. First of all, even before trying to calculate EV x , the question arises - are the two EV x 's the same? Rows in which nothing only the state is listed need to be calculated directly: Code:. Calculating Split EVs Exactly. It turns out that the EV of a hand given that an N card was removed is the conditional probability relative to if a paircard had been removed. For example, if we wish to determine EV x-N , all we do is first figure out EV x-Full Shoe , EV x-P and p P , where "Full Shoe" represents the deck after the original 2 paircards and dealer upcard are removed, and "x-P" is the shoe after 3 paircards and the dealer upcard are removed. So now we have the probabilities of the rounds and the EV's that need to be calculated. The p N is simply 1-p P. If you remember from above - N refers to the fact that a non-split card was played. Exact EV's of Splits for Finite Decks So far we have described the various deifferent kinds of rounds that can result form splitting and how to use this knowledge to calculate the values of splits for infinite decks. Members Current visitors New profile posts Search profile posts. N and x. Note that each probability needs to be adjusted to account for the fact that the paircard is not included. Search titles only. The second column is how I calculate the EV for a given round, and the third column is where your numbers are coming from. This is very important because it means that only hands in which P cards were removed need to be calculated. The last step we need to do is figure out how to calculate the respective probabilities and EV x 's and EV N 's. Search Advanced searchβ¦. When looking at a round, e. Since the number of hands that can result are limited by the rules, there are only two possible hands that can be end points of a split card. Let's look at 10, 10 vs 6 for simplicity since the strategy is to stand on all hands. In the case of infinite splits, p N , p x , EV N and EV x are not dependent on previous hands and therefore do not change. Again, since we are dealing with infinite decks - we only need to calculate EV x and EV N once, and then we add the appropriate number of EV N 's and EV x 's for each respective round as listed above in the second column. The real question then is how do you remove an N hand? When we play out a split hand - we have the follwing 2 possible types of second card that can be played onto a split card - either the paircard P or a non-pair card N. These facts make our lives a lot easier because they greatly simplify the calculations for the various rounds. In order to facilitate further discussion, I will introduce a new notation. EV x is the same EV x as that described above. Therefore to calculate EV N - we need to calculate the weighted average of all of the possible resulting hands except those that can result from a paircard being dealt. Since the player has equal probability of playing PN or NP for any given pair of rounds that occur with equal probability - the effects of removal appear to be negated. What happens when we split? Once you have calculated this number - you simply multiply it by 2 and you have the exact EV for SPL1.

Forums New posts Search forums. The sum of the probabilities of each of the 3 conditional probability blackjack rounds add up to 1. You must log in or register to reply here.

Interestingly, it turns out that two different sets of shoe states can be used to calculate the exact EV's. The first was determined by thinking about the effects of removal, the second represents the actual shoe state as determined by brute force. Bringing it all together Below is a table with the first column being the various rounds for the corresponding SPL's. The adjustment can be made to the weighted sum all at once.