Can someone help me understand this paper? - "Probability models for blackjack poker"
March 12th, 2018 at 12:19:39 PM
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Probability models for blackjack poker
Author Charlie H.Cooke
Under an Elsevier user licenseopen archive
Abstract
For simplicity in calculation, previous analyses of blackjack poker have employed models which employ sampling with replacement. In order to assess what degree of error this may induce, the purpose here is to calculate results for a typical hand where sampling without replacement is employed. It is seen that significant error can result when long runs are required to complete the hand. The hand examined is itself of particular interest, as regards both its outstanding expectations of high yield and certain implications for pair splitting of two nines against the dealer’s seven. Theoretical and experimental methods are used in order to determine whether the calculation can be truncated after the dealer’s fifth card without significant loss of accuracy. Less than one tenth of one percent difference is observed between the fifth card truncated expectation and the experimentally obtained expectation.
As a bonus, I thought i would enclose this tiny article about the differences in the specific parts of a domain name:
https:// - This is whats known as a protocol. usually allowing you to see if your connection is encrypted or not. This one is so any information you dont give them voluntarily, is safe over the wire to their servers.
www. - this is normally where the subdomain goes. it doesnt need to contain the www but is normally included for deeply techical reasons of even which was too boring for me to learn.
sciencedirect.com - the domain name of which the dns translates into an ip address. interesting huh?
/science/article/pii/S0898122109006543 - the crown gem of a url - the path or telling the computer directly where to find this article at.
Good day!
Author Charlie H.Cooke
Under an Elsevier user licenseopen archive
Abstract
For simplicity in calculation, previous analyses of blackjack poker have employed models which employ sampling with replacement. In order to assess what degree of error this may induce, the purpose here is to calculate results for a typical hand where sampling without replacement is employed. It is seen that significant error can result when long runs are required to complete the hand. The hand examined is itself of particular interest, as regards both its outstanding expectations of high yield and certain implications for pair splitting of two nines against the dealer’s seven. Theoretical and experimental methods are used in order to determine whether the calculation can be truncated after the dealer’s fifth card without significant loss of accuracy. Less than one tenth of one percent difference is observed between the fifth card truncated expectation and the experimentally obtained expectation.
As a bonus, I thought i would enclose this tiny article about the differences in the specific parts of a domain name:
https:// - This is whats known as a protocol. usually allowing you to see if your connection is encrypted or not. This one is so any information you dont give them voluntarily, is safe over the wire to their servers.
www. - this is normally where the subdomain goes. it doesnt need to contain the www but is normally included for deeply techical reasons of even which was too boring for me to learn.
sciencedirect.com - the domain name of which the dns translates into an ip address. interesting huh?
/science/article/pii/S0898122109006543 - the crown gem of a url - the path or telling the computer directly where to find this article at.
Good day!
March 28th, 2018 at 12:01:09 AM
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Basically, what this says is that in the past, when statisticians/mathematicians have analyzed blackjack hands (the author uses for this experiment the expectation of winning if a blackjack player choosing to stand on two 9’s against the dealer’s up card 7) they have typically used a technique called "sampling with replacement" over "sampling without replacement". The author then analyzes how much error there is by choosing the former over the latter.
Finally, he analyzes whether or not, when performing those types of analyses, if it is bad if they stop the simulation after the dealer has dealt 5 cards.
For a layman's explanation of sampling with and without, here is a pretty good one: http://www.statisticshowto.com/sampling-with-replacement-without/
Bottom line, this paper is for statisticians/mathematicians to help them best choose the method for doing this type of analysis which uses Blackjack as the vehicle. It's not really a paper for blackjack players.
Finally, he analyzes whether or not, when performing those types of analyses, if it is bad if they stop the simulation after the dealer has dealt 5 cards.
For a layman's explanation of sampling with and without, here is a pretty good one: http://www.statisticshowto.com/sampling-with-replacement-without/
Bottom line, this paper is for statisticians/mathematicians to help them best choose the method for doing this type of analysis which uses Blackjack as the vehicle. It's not really a paper for blackjack players.
March 28th, 2018 at 12:01:25 AM
permalink
Basically, what this says is that in the past, when statisticians/mathematicians have analyzed blackjack hands (the author uses for this experiment the expectation of winning if a blackjack player choosing to stand on two 9’s against the dealer’s up card 7) they have typically used a technique called "sampling with replacement" over "sampling without replacement". The author then analyzes how much error there is by choosing the former over the latter.
Finally, he analyzes whether or not, when performing those types of analyses, if it is bad if they stop the simulation after the dealer has dealt 5 cards.
For a layman's explanation of sampling with and without, here is a pretty good one: http://www.statisticshowto.com/sampling-with-replacement-without/
Bottom line, this paper is for statisticians/mathematicians to help them best choose the method for doing this type of analysis which uses Blackjack as the vehicle. It's not really a paper for blackjack players.
Finally, he analyzes whether or not, when performing those types of analyses, if it is bad if they stop the simulation after the dealer has dealt 5 cards.
For a layman's explanation of sampling with and without, here is a pretty good one: http://www.statisticshowto.com/sampling-with-replacement-without/
Bottom line, this paper is for statisticians/mathematicians to help them best choose the method for doing this type of analysis which uses Blackjack as the vehicle. It's not really a paper for blackjack players.
April 29th, 2018 at 1:18:03 PM
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The literature article analyzes the difference between an infinite-deck analysis of blackjack and a finite deck analysis for a couple of hands. It almost certainly is from very early days of blackjack analysis.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
