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Numb3rs Double Down Blackjack (also called 21) is a card game which is frequently played in casinos and is the central theme of Activity 2*: More Odds: Calculate the odds that the dealer busts for each starting hand of 11 or bigger.


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The Wizard presents the odds, rules and complete strategy charts for casino Blackjack. These are the authoritative charts copied by everyone.


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Blackjack Strategy: The 3 most misplayed hands in Blackjack

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This is a hand that includes an ace and totals either seven or If the player hits Blackjack, they will be paid at odds of In the event that a player's hand loses​.


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212 Blackjack System - Best System Ever?? Systems Review

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Numb3rs Double Down Blackjack (also called 21) is a card game which is frequently played in casinos and is the central theme of Activity 2*: More Odds: Calculate the odds that the dealer busts for each starting hand of 11 or bigger.


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Using Odds and Probability in Blackjack - Blackjack for Intermediate Players

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Ask the Wizard # I was in Palace Station the other day and saw they had a few 7 to 5 double deck tables now. They may just be testing the idea out, but it.


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One of the first games I posted about on this blog was the blackjack side bet Twenty One Plus Three (21+3). In this post, I showed that there.


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Blackjack Expert Explains How Card Counting Works - WIRED

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How to win at blackjack (21) with gambling expert Michael "Wizard of Odds" Shackleford

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The Wizard presents the odds, rules and complete strategy charts for casino Blackjack. These are the authoritative charts copied by everyone.


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The Maths Behind Blackjack

Along the way, a discussion of generating psuedorandom numbers comes up. Repeat activity 2 with the assumption that there are no aces and no cards of value in the deck, but that the probability of drawing any of the other cards is the same. Since the actual analysis of optimal play is very complex, either a computer or a whole lot of time is needed to figure it out. The constants A,B,M were chosen very poorly, and as a result the numbers it generated were not very random at all. Hint: this is different than the last two, because if she draws a 2, then her total is 16 and she must draw again. Activity 1: Odds of the dealer busting Let's say you're the dealer and you have a 10 and a 6. There is a famous example of a very popular linear congruential generator called RANDU that has been used since the s. That is, you are as likely to draw a 6 as you are to draw a 7 or 10 or Ace, etc. What is the probablility that she busts? You must draw a card but you won't have to draw another one. What if the dealer has cards that sum to 14? Which of these two choices do you think is better?{/INSERTKEYS}{/PARAGRAPH} Write down the first 8 numbers generated. For all of the following assume that the seed is 1. What is the probability that she busts when she draws? To make it easier assume that the odds of drawing all the different ranks of cards are the same. {PARAGRAPH}{INSERTKEYS}The main mathematical topic in this episode are using math to determine strategies for winning against casinos at blackjack. What if the dealer has cards that sum to 15? Testing Random Number Generators: Now let's try a couple linear congruential generators and see how well they work. Activity 3: Here is an extreme example of how knowledge of previous cards can affect the odds of who wins: Repeat activity 2 with the assumption that there are no cards of value 10 nor any aces in the deck, but that the probability of drawing any of the other cards is the same. What are the odds that you bust? Casinos before the 's didn't realize this, and some of them unintentionally used rule sets there were advantageous for players who were playing optimally. As a result, many simulations done with this generator are now looked upon with suspiscion.