What's the probability of being dealt a blackjack? According to our probability formula: P(getting a blackjack).

Enjoy!

It would depend on the number of decks but it's close to the same regardless. In a fresh deck your odds would be 1 in 13 (13 cards in each suit one of which is an.

Enjoy!

Those hands are also high probabilities, and in fact each is higher in probability than being dealt a Blackjack. Calculations Of The Tables (For The Math.

Enjoy!

It would depend on the number of decks but it's close to the same regardless. In a fresh deck your odds would be 1 in 13 (13 cards in each suit one of which is an.

Enjoy!

The % odds of being dealt a blackjack is an average probability, based on no prior information. Of course if you were to keep track of the total.

Enjoy!

It would depend on the number of decks but it's close to the same regardless. In a fresh deck your odds would be 1 in 13 (13 cards in each suit one of which is an.

Enjoy!

If card counting in blackjack gives you a percent advantage, then how were some Your probability of being dealt 20 is approximately 9%.

Enjoy!

Odds of being dealt a blackjack β About %. Odds are just the likelihood that something will happen. As a blackjack player you deal with this all the time. Letsβ.

Enjoy!

The highest score you can get when being initially dealt two cards is 21 points so you can never go bust. This means if you took a hit on a hard 21, you would haveβ.

Enjoy!

It follows that the likelihood of a 2 being rolled is 1/6 = * = %. Therefore, we calculate the probability of getting dealt a blackjack in the followingβ.

Enjoy!

If we included that option then we would potentially have four of a kind instead of three of a kind. How many ways can I be dealt the second card? If the dealer has an ace, what's the probability that she gets blackjack on her next card? 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. I'm not suggesting that you use this method in every situation. 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. If we pick something higher than a 10 then there won't be four higher cards to finish the straight. For this kind of problem, we'll often have to use our, "pick a value then pick a suit" strategy. 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. Think about what point value cards will put you over How many of those are there in the deck? How many ways are there to be dealt four of a kind? 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. For example, if you're dealt two cards then you would ask yourself, "How many different ways can I be dealt the first card? Poker hands give us some more interesting examples because the hands are bigger and have more "winning" combinations. How many ways are there to be dealt three of a kind? Suppose I wanted to find total ways to choose a ten point card. This situation is very similar to the four of a kind case but with a few additions. Of those 32 cards, 30 of them are still in the deck. How many different ways can you be dealt a pair? Choice 2: This is actually five choices, one for each card. We can take those methods further to calculate the probability of getting specific hands in games like blackjack and poker. 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. There are a total of 4 types of ten point cards. If you get a hand that totals 21, i. 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. What's the probability of going over 21 if you take a card? The card can be any of the four suits which means the number of combinations for the first card is:. That gives us. To start the process, we need to pick the first card in the straight. To answer questions involving different card hands, it helps to focus on the specific choices that you have to make. 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. Suppose you've been dealt two 8's in a game of blackjack. A "three of a kind" is a hand where you have three cards with the same value. There are 5 cards with that value and each card has 4 suits so there's a total of 20 "safe" cards. A straight flush is a hand where you have five cards in a row, all of the same suit, e. A "royal flush" is a hand with the 10, jack, queen, king and ace, all of the same suit. At this point, we've picked the three matching cards. If you aren't familiar with calculating probabilities, I've put a quick explanation in Appendix A. A straight is a hand where all five cards are in sequence but they can be of any suit, e. So what's the probability of being dealt a straight flush? 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. Choice 1: Pick the value of the first card. The answer to that is 1. What's the probability of not going over 21? 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. The last two cards have to have the same value as the first one.{/INSERTKEYS}{/PARAGRAPH} What's the probability of being dealt a royal flush? 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? So there are a total of 4 royal flush hands. Using the method of choosing a value then choosing a suit, the process would look like this:. 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. What's the probability of being dealt a full house? The remaining three cards can be any suit and any value except the value of the first card. With a blackjack, the rules are pretty simple and you only start off with two cards so it was easy just to count the number of cards that fell into each category. How many different ways can you be dealt a royal flush? Once we've got the first two cards, the third card can have any value except the one we choose for the first card. 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. How many ways are there that you can be dealt a straight flush? What's the probability of your taking one more card and going over? However, it's always good to get confirmation that our process is giving us the results that it should. A full house is a hand where you have three cards of one value and two of another value, e. Because the order of the cards in a poker hand doesn't matter, this is an example of a combination. 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. To get blackjack, the dealer needs a ten point card. A pair is a hand with exactly two of the same card, e. The first card can be anything from an ace to a ten. This means. Your goal is to come as close to 21 as possible without going over. 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. How many ways can you be dealt a straight? There are 52 cards in a standard deck and, to form a hand, we need to choose 5 of them. How many ways can you be dealt a full house? 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. To write out a poker hand, we'll often just right out the numbers followed by a symbol for the suit, e. This determines the value of the next three cards. With poker hands, the situations are going to be a little more complicated. 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. You have to subtract out the 9 and the 7 that are already in your hand. 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. 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. Choice 4: This is actually three choices, one for each card. Suppose that you've been dealt a 9 and an ace. 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. What's the probability of being dealt a blackjack? That makes. 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. Suppose you get a 9 and a 7 on your first two cards. If they had the same value then we would have three or four of a kind rather than just a pair. The current total of your hand is 16 so P going over 21 is the same as P getting 6 or higher. What's the probability of being dealt a pair? How many cards are left in the deck after you've been dealt the two 8's? If the suits don't matter, I'll just leave out the letters, e. 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. {PARAGRAPH}{INSERTKEYS}In previous examples, we've used cards to come up with examples of counting problems.