odds of getting 20?

Question

what are the odds of getting 20 on a blackjack hand in the first two cards. either a 10+pic or 2 picture cards.


4 deck shoe if that matters.

The odds are better with fewer players? And a fresh deal?

Answer 1

In 1 deck there are 4 suits and 4 "face" cards (T, J, Q, K) so there are 16 cards of which any 2 will give you a 20.

So the odds of getting 2 cards from those 16 is 16C2/52C2 where 52C2 is the number of ways of getting dealt any 2 cards and 16C2 is the number of ways of getting dealt 2 cards from the 16 "face" cards.

16C2 = 16*15/2
52C2 = 52*51/2

16C2/52C2 = 16*15/(52*51) = 9.05%

There is another way to get 20 than 2 face cards. A9 also works.

The probability of getting A9 from 1 deck is 4C1*4C1/52C2 = 1.21% so the total probability of getting a 20 is 9.05% + 1.21% = 10.26%.

With a 4 deck shoe you have 16*4=64 "face" cards and 52*4=208 total cards so the odds are

64C2/208C2 = 64*63/(208*207) = 9.36%

The probability of getting A9 from a 4 deck shoe is

16C1*16C1/208C2 = 1.19% so the total probability of getting a 20 is 9.36% + 1.19% = 10.55%

Odd that the probability goes up isn't it? ;)

----------------------

Usually these questions assume that you are being dealt from a full shoe. As long as you are not counting cards, then prior hands do not alter the effective probability since the information you have when you place a bet does not change from hand to hand. The number of players never affects the probabilities of getting specific hands.

Probabilities are based purely on the information you have before the deal so when the information available to you does not change then neither does the effective probability. So if all the "face" cards are dealt out before the next shuffle but you don't know this, then your effective probability of getting a 20 remains the same even though the actual probability is 0 (in fact this is why people count cards despite it being against casino rules).

--------------

Imagine that all the cards from a 4-deck shoe are dealt out. This would result in 104 hands. Each hand has the exact same probability as any of the others of being a 20 (or any other hand). So if you played alone or with 100 people, the probqability of being dealt a 20 is exactly the same.

The number of players has absolutely no effect on the probability of getting a specific hand.

Answer 2

number of decks does not matter but a simple formula will show the odds of getting two cards worth ten each. first card is 16/52 then next card depends on whether any tens were dealt to ther players before you were dealt your second card. and the 16/52 only applies specifically to being the first card dealt. generally you multiply the two chances to get both so lets say no other tens and its just you and the dealer then the second cards probability is 15/50 because two cards were already dealt 16/52 * 15/50 = 9.23%.
a lot of the previous answers use only one set of tens with a 208 card deck and this is wrong. note that depending on the number of players and tens dealt before your second card the odds will change slightly, but 9% is accurate. the randomness of these probabilities dictate that computer formulas deal millions of hands to determine outright probabilities of all kinds of outcomes. buy a blackjack mathematics text to learn more about this.
ok with your new questions, the odds with more players and/ or a fresh deal depend on whether or not more or less tens than expected have been dealt from the shoe so far. that is why i explained before that only an approximate % can be given because each card dealt either helps or hinders your chances of a twenty...

Answer 3

It depends on how the cards are delt and how many people there are the table, but we'll assume you were dealt 2 cards right away.

In a given deck, there are four 10s, four Jacks, four Queens and four Kings. So there are 16 "ten" value cards per deck. If you're saying there are 4 decks shuffled together, then there are 64 such cards total in a deck of 52*4 = 208 cards. The probability of getting a ten-valued card first is 64/208. This leaves 207 cards in the deck, 63 of which are tens, so the probability of getting a ten card next is 63/207. So the total probability of that hand is (64/208)(63/207) = about 0.094

Now this INCLUDES the possibility of getting two 10s. If it MUST be 2 pic cards or one 10 and one pic, then subtract the probability of getting two tens, which is (16/208)(15/207), giving about 0.088 (or exactly, 79/897)

Answer 4

There are 4 * 52 cards = 208 cards

In each deck there are 4 @ 10, 4 @ J, 4 @ Q, and 4@ K, or 16 cards. In four decks there are 64 cards.

Let's say you are the first person in line in the deal. The odds of your getting a card of value 10 = 64/208 or about 31%.

However, as each card is dealt, the number goes down. If you are the second person who gets a card, the odds are 64/207 if the first person didn't get a v10 card, and 63/207 if that person did get a v10 card.

If you are simply dealing out cards (take two cards and see what you get), the odds of you getting two value10 cards is 64/208 * 64/207 = 9.5%

As soon as other people start playing, your chances become harder to calculate.

Answer 5

28/299. You have to multiply the probability of getting a picture or a 10 (I'll include 10 in the picture card category from now on for simplicity's sake) by the probability of getting another picture card on the second one. There are 4 kings, 4 queens, 4 jacks, and 4 10's in a standard 52-card deck, so that's 16/52, or 4/13. Multiply by four decks and you still get a simplified form of 4/13. You multiply 4/13 by 63/207 (because you've already removed one picture card), and you get, reduced, 28/299.

Answer 6

In a four-deck shoe you have 208 cards, and 4 or 5 out of each suite of 13 is a "10" (not sure, does the ace count?)

Assuming the ace doesn't count, that means for the first card dealt at random, there is a 16/208 chance it will score 10 points, and for the second card dealt, a 15/207 chance... to calculate cumulative probability you multiply these together...

0.0769 x 0.0725 which equals 0.0056, or a 0.56% chance, very roughly a 1 in 200 chance.

Answer 7

There are 4 out of 13 cards that meet the criterion.

Chance of one face card is 4/13
Chance of 2 is (4/13)^2 = 9.5%

This is with an infinite number of decks. It will go down slightly the fewer decks you are playing with.

Answer 8

i think of them odds are approximately actual tbh. Its as probably that Spain will draw/lose over ninety minutes as win. England have been destroyed with the aid of Italy even even though it nevertheless ended up a draw, Holland destroyed Denmark and lost so it occurs that the greater advantageous team would not win regularlly. Any team woth Ronaldo is a objective take care of and that they are respectable on the lower back so Portugal have a 50/50 risk of a minimum of surviving ninety minutes. Bookies continually conceal themselves because of the fact of this theychronic BMW's and people who guess a lot are broke

Answer 9

the cards needed are 10,J,Q,K
or 16/52
so the chance of getting one of
these cards on the first draw is
16/52. for the second card, the odds are
(16/52)(15/52) = 240/2704

Answer 10

you have 3.25% chance to get that as your first hand... Good luck