probability combinatorics. Last Saturday night I played at Bally's in Atlantic City and got a hand I could not believe. Dealer had 9 and I was dealt.

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Let us look at the probabilities for a favorable initial hand (the first two cards dealt) to be achieved. The total number of possible combinations for each of the two.

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Find the probability of being dealt a blackjack hand. What approximate percentage of hands are winning blackjack hands?

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What are the odds against winning seven hands of blackjack in a row? The probability of being dealt 3 jokers in a row from a six deck shoe (plus the 3 jokers).

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be in any order. Find the probability of being dealt a blackjack hand. What approximate percentage of hands are winning blackjack hands?

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Detailed probability odds charts for blackjack and how the odds change in figures which represent your probability of losing or winning a hand. The next odds table deals with the first two cards being dealt or the 2 card frequency odds.

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be in any order. Find the probability of being dealt a blackjack hand. What approximate percentage of hands are winning blackjack hands?

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Odds of Being Dealt Specific Hands. Here are the probabilities for being dealt a specific hand: Blackjack – %; Standing Hand () – 30%; Decision Hand.

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Let us look at the probabilities for a favorable initial hand (the first two cards dealt) to be achieved. The total number of possible combinations for each of the two.

Enjoy!

Detailed probability odds charts for blackjack and how the odds change in figures which represent your probability of losing or winning a hand. The next odds table deals with the first two cards being dealt or the 2 card frequency odds.

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This means. Unlike the four of a kind case, we do have to pick suits for those cards because we will only have three of the four possibilities. The first card can have any value but the second card has to have the same value so we don't get to make that choice. If the suits don't matter, I'll just leave out the letters, e. Think about what point value cards will put you over How many of those are there in the deck? You have to subtract out the 9 and the 7 that are already in your hand. If the dealer has an ace, what's the probability that she gets blackjack on her next card? How many ways are there that you can be dealt a straight flush? The current total of your hand is 16 so P going over 21 is the same as P getting 6 or higher. So there are a total of 4 royal flush hands. Think about how many cards are in teh deck that will bring the dealer's total of 21 and divide that by the total number of cards that are left in the deck. How many ways are there to be dealt four of a kind? To write out a poker hand, we'll often just right out the numbers followed by a symbol for the suit, e. This situation is very similar to the four of a kind case but with a few additions. How many ways can you be dealt a straight? For the two non-matching cards, we can chose any of the four suits and we have 12 choices for the possible values because we have to exclude the value that we picked for the matching cards. There are a total of 4 types of ten point cards. Poker hands give us some more interesting examples because the hands are bigger and have more "winning" combinations. How many different ways can you be dealt a pair? We also don't need to pick the suit of the first card because we ultimately have to get all four suits for the card's value, i. If you get a hand that totals 21, i. How many different ways can you be dealt a royal flush? A "royal flush" is a hand with the 10, jack, queen, king and ace, all of the same suit. Suppose that you've been dealt a 9 and an ace. A "four of a kind" is a hand where you have four cards with the same value. How many choices do we have for the second card? However, it's always good to get confirmation that our process is giving us the results that it should. There are 52 cards in a standard deck and, to form a hand, we need to choose 5 of them. If they had the same value then we would have three or four of a kind rather than just a pair. The answer to that is 1. The card can be any of the four suits which means the number of combinations for the first card is:. How many cards are left in the deck after you've been dealt the two 8's?

In previous examples, we've used cards to come up with examples of counting problems. A full house is a hand where you have three cards of one value and two of another value, e. First, we get to pick the three suits for the "three of a kind" cards and we need to make two choices for the non-"three of a kind" cards.

With https://2dvd.ru/blackjack/blackjack-ballroom-casino-500.html blackjack, the rules are pretty simple and you only start off with two cards so it was easy just probability of being dealt a blackjack hand count the number of cards that fell into each category.

For example, if you're dealt two cards then you would ask yourself, "How many different ways can I probability of being dealt a blackjack hand dealt the first card?

I'm not suggesting that you use this method in every situation. What's the probability of not going over 21? Because the order of the cards in a poker hand doesn't matter, this is an example of a combination.

The first card can be anything from an ace to a ten. Assume that no one else has been dealt any cards so that the deck, at this point, has all of the remaining 50 cards in it.

In blackjack, after you get dealt your first two cards, you can get more cards from the dealer. The value of this card can be anything from an ace up to a ten. How many ways can I be dealt the second card?

What's the probability of being dealt a pair? Of those 32 cards, 30 of them are still in the deck. What's the probability of going over 21 if you take a card? How many ways are there to be dealt three of a kind? A whole hand would be the individual cards separated by dashes so 3H-3D-3S-6H-6D would be the three of hearts, the three of diamonds, the three of spades, the six of hearts and the six of diamonds.

A straight flush is a hand where you have five cards in a row, all of the same suit, e. Choice 2: This is actually five choices, one for each card. For this kind of problem, we'll often have to use our, "pick a value then pick a suit" strategy.

What's the probability of being dealt a full house? Using the method of choosing a value then choosing a suit, the process would blackjack matlab like this:.

The last two cards have to have the same value as the first one.

This matches the result that we got in Example 1 from just counting the cards which confirms that the method is giving us correct results. Your goal is to come as close to 21 as possible without going over. With poker hands, the situations are going to be a little more complicated. There are 5 cards with that value and each card has 4 suits so there's a total of 20 "safe" cards. That gives us. Once we pick the value of the first card, the second card has to have the same value but can be from any of the three remaining suits. Suppose you've been dealt two 8's in a game of blackjack. What's the probability of your taking one more card and going over? We don't get to pick the number because it has to be 1 more than the first card we choose and we don't get to pick the suit because it has to be the same as the first card we choose. The procedure for counting those hands will usually involve two steps: first, chose a value for a card and then chose a suit for it. To answer questions involving different card hands, it helps to focus on the specific choices that you have to make. Suppose I wanted to find total ways to choose a ten point card. How many ways can you be dealt a full house? Choice 4: This is actually three choices, one for each card. Suppose you get a 9 and a 7 on your first two cards. The remaining three cards can be any suit and any value except the value of the first card. To get blackjack, the dealer needs a ten point card. What's the probability of being dealt a royal flush? We're only thinking about the numbers at this point, not the suits, so we have to choose one of 10, jack, king or queen. If you already have 16 points then any card with a point value greater than or equal to 6 will put you over If you subtract off the two 8's that you've already been dealt, that leaves a total of 30 cards. We can take those methods further to calculate the probability of getting specific hands in games like blackjack and poker. We don't get to pick the values of any of the cards and once we pick the suit for the first card, the other cards have to have that suit. A pair is a hand with exactly two of the same card, e. I walked through the choice process here although you could probably have come up with that value just by thinking about it: The values are choosen for you so you get to choose one of the 4 suits and all of the cards have to have that value. In Example 1, for example, it was clearly easier just to count the actual cards and say, "There are a total of 16 ten's, jack's, queen's and king's. Once we've got the first two cards, the third card can have any value except the one we choose for the first card. Choice 1: Pick the value of the first card. If you aren't familiar with calculating probabilities, I've put a quick explanation in Appendix A. If we included that option then we would potentially have four of a kind instead of three of a kind. To start the process, we need to pick the first card in the straight. At this point, we've picked the three matching cards. In blackjack, all face cards are worth 10 points and an ace is worth either 1 point or The game starts with each player being dealt two cards. This determines the value of the next three cards. If we pick something higher than a 10 then there won't be four higher cards to finish the straight. What's the probability of being dealt a blackjack? That makes. Once we pick the value of the first card, we know the values of the second, third and fourth cards - they have to have the same value as the first card but with a different suit. So what's the probability of being dealt a straight flush? A straight is a hand where all five cards are in sequence but they can be of any suit, e. A "three of a kind" is a hand where you have three cards with the same value.