Expected value
August 3rd, 2011 at 11:23:26 AM
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Just a general question from a curious math student (Perhaps should be moved to blackjack forum?):
Say a casino in my town offers a game of 2 Deck blackjack that hits on soft 17, Does not double after splitting, and only doubles on 9,10, and 11. The wizard Blackjack Appendix 9 states the expected value of this game (2 deck, Does not double after split) at -0.005252 and the rule variation table states the player expected return (I'm assuming that this is a term for expected value of a blackjack game) from the Double 9-11 rule at -.09% (-.0009).
Am I assuming correctly that the total expected value for this rule set is -.006152?
Further, how were these expected values calculated?
I'm sorry if these questions have been answered previously.
Thanks!
Say a casino in my town offers a game of 2 Deck blackjack that hits on soft 17, Does not double after splitting, and only doubles on 9,10, and 11. The wizard Blackjack Appendix 9 states the expected value of this game (2 deck, Does not double after split) at -0.005252 and the rule variation table states the player expected return (I'm assuming that this is a term for expected value of a blackjack game) from the Double 9-11 rule at -.09% (-.0009).
Am I assuming correctly that the total expected value for this rule set is -.006152?
Further, how were these expected values calculated?
I'm sorry if these questions have been answered previously.
Thanks!
August 3rd, 2011 at 11:45:51 AM
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Quote: CCKRK6
Am I assuming correctly that the total expected value for this rule set is -.006152?
that would seem to be right
Quote: CCKRK6
how were these expected values calculated?
quite tediously apparently. The WoO often says he uses an infinite deck, which must make it easier to some extent. But I am not the guy to answer.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
August 3rd, 2011 at 12:13:37 PM
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I'm pretty sure a Monte Carlo simulation with an infinite deck is used to approximate the EVs.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
August 3rd, 2011 at 12:20:29 PM
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Quote: rdw4potusI'm pretty sure a Monte Carlo simulation with an infinite deck is used to approximate the EVs.
I am not sure how Wizard does it, but I don't think so. If this was the case, he would not need infinite deck approximations.
BJ expectations are fairly simple to calculate algorithmically (especially, for an infinite deck), there is no need for a simulator. The idea is that you "play out" the hand,recursively considering every possibility at each step (there aere only ten of them, which makes the task quite manageable), and weigh the outcomes of each considered combination by its respective probability (that's where infinite deck simplification helps enormously because you don't have to consider the effect of card removal, and keep track of all cars "played" at each step, all probabilities are fixed).
"When two people always agree one of them is unnecessary"
