Calculating House Advantage
May 25th, 2010 at 8:08:52 AM
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I am learning about house advantage and how it plays into the favor at a casino. I want to know if their is like an equation or formula that calculates house advantage for each specific rule and payout for blackjack. I know there are percents out there that tell you how much of an advantage each rule applies. But i am just wondering if coming up with like a specific equation that calculates house advantage can be done or would it be too complicated to do such a thing.
The percentages for like how many decks are you play with, doubling rules, if dealer hits soft 17, ect. is exactly what i am looking for. But how do they come up with these percentages? Where did you find these percentages? Are they in some book i could get a hold of? Any comments or suggestions would be greatly appreciated, thank you
The percentages for like how many decks are you play with, doubling rules, if dealer hits soft 17, ect. is exactly what i am looking for. But how do they come up with these percentages? Where did you find these percentages? Are they in some book i could get a hold of? Any comments or suggestions would be greatly appreciated, thank you
May 25th, 2010 at 9:25:40 AM
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while you could calculate everything by hand, its not worth the effort. just use the data thats already there or download some software to run simulations of your own. the wizard has a calculator on his webpage and a fairly lengthy list of different rules that show how much they affect the house edge. so use his calculator to enter the rules for the game you are playing. if there are other rules that the calculator doesnt have, look them up on his list and add or subtract from the house edge based on the specific rule.
https://wizardofodds.com/blackjack/house-edge-calculator-pop.html
These changes are relative to the following rules: 8 decks, dealer stands on soft 17, player may double on any first two cards, player can double after splitting, player may split to 4 hands.
https://wizardofodds.com/blackjack/rule-variations.html
so while the effect of the different rule changes wont be exact if youre not playing 8decks, S17, DAS, they will be a close enough approximation.
https://wizardofodds.com/blackjack/house-edge-calculator-pop.html
These changes are relative to the following rules: 8 decks, dealer stands on soft 17, player may double on any first two cards, player can double after splitting, player may split to 4 hands.
https://wizardofodds.com/blackjack/rule-variations.html
so while the effect of the different rule changes wont be exact if youre not playing 8decks, S17, DAS, they will be a close enough approximation.
May 25th, 2010 at 11:28:26 AM
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On the home page of this site is a table of all the games currently being offered in Las Vegas, and a house edge for each game. If you are not interested in an arbitrary game just look up the house edge for the games being offered.
The mathematics of calculating the best decision for a given set of cards is well known (hit, stand, double split) and easily done, but the mathematics of calculating the overall expected value of a full game is subject to a little bit of interpretation. Some underlying assumptions change the final answer. I only say that because if you look on multiple websites you may see slightly different answers.
To give you an example you always see on cheat sheets that you should hit a sixteen (unless it is a pair of eights) against a dealer 10. To be absolutely precise what that cheat sheet is telling you is that if you are playing one on one, and only three cards have been revealed, then you should hit a 16 against a dealer 10. If you know more information about the count, the cards on the table, or the number of cards in your hand is more than two then sometimes the better move is to stand.
When simulating an entire game certain underlying assumptions make the final EV calculation slightly different. A computer would know when the optimal move is to stand on a 16 against a dealer 10. A computer would know when you should take insurance, and many other decisions. Since the modeler is not assuming the player has perfect memory, you can get different answers.
I am only spelling this out because you may wonder why you are not getting the exact same answer. Don't worry about it to much. The overall pluses or minuses of certain rules are the same for all calculations, but the precise number won't be.
The mathematics of calculating the best decision for a given set of cards is well known (hit, stand, double split) and easily done, but the mathematics of calculating the overall expected value of a full game is subject to a little bit of interpretation. Some underlying assumptions change the final answer. I only say that because if you look on multiple websites you may see slightly different answers.
To give you an example you always see on cheat sheets that you should hit a sixteen (unless it is a pair of eights) against a dealer 10. To be absolutely precise what that cheat sheet is telling you is that if you are playing one on one, and only three cards have been revealed, then you should hit a 16 against a dealer 10. If you know more information about the count, the cards on the table, or the number of cards in your hand is more than two then sometimes the better move is to stand.
When simulating an entire game certain underlying assumptions make the final EV calculation slightly different. A computer would know when the optimal move is to stand on a 16 against a dealer 10. A computer would know when you should take insurance, and many other decisions. Since the modeler is not assuming the player has perfect memory, you can get different answers.
I am only spelling this out because you may wonder why you are not getting the exact same answer. Don't worry about it to much. The overall pluses or minuses of certain rules are the same for all calculations, but the precise number won't be.
