House Edge Calculation
September 29th, 2012 at 7:18:38 PM
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Hi Everyone
Im programming a Basic Strategy and House Edge program but for some reason my Calculations do not match up with Calculations found Here at Wizard of Odds
I have traced the problem to my calculations of when the dealer has an Ace or a Ten
Has anyone else had problem with this calculation
My Problem is the Players' Expected Return by Standing chart my numbers match the wizard exactly except for in the dealers Ace and Dealers 10 column
Any help would be appreciated I must be missing a key calculation
Im programming a Basic Strategy and House Edge program but for some reason my Calculations do not match up with Calculations found Here at Wizard of Odds
I have traced the problem to my calculations of when the dealer has an Ace or a Ten
Has anyone else had problem with this calculation
My Problem is the Players' Expected Return by Standing chart my numbers match the wizard exactly except for in the dealers Ace and Dealers 10 column
Any help would be appreciated I must be missing a key calculation
September 29th, 2012 at 7:26:52 PM
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Are your numbers for peak or no peak? That's probably where the different numbers are from.
“Man Babes” #AxelFabulous
September 29th, 2012 at 7:26:56 PM
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deleted
DUHHIIIIIIIII HEARD THAT!
September 29th, 2012 at 7:38:50 PM
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Quote: mipletAre your numbers for peak or no peak? That's probably where the different numbers are from.
Peak or no peak would only apply to a graph LOL Spell check fails once again !
September 29th, 2012 at 7:39:41 PM
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My Chart of the same type on the wizards page
Player's Expected Return by Standing looks like this
2 3 4 5 6 7 8 9 10 Ace
0-16 -.29 -.25 -.211 -.167 -.153 -.475 -.510 -.543 -.575 -.769
17 -.15 -.11 -.080 -.044 .0117 -.106 -.381 -.423 -.464 -.638
18 -.12 .148 .1758 .1995 .2834 .3995 .1059 -.183 -.241 -.377
19 .386 .404 .4231 .4395 .4959 .6159 .5938 .2875 -.018 -.115
20 .64 .650 .6610 .6703 .7039 .7732 .7918 .7583 .4349 .1460
21 .882 .885 .8887 .8917 .9028 .9259 .9306 .9391 .8116 .3307
Sorry about the spacing
If you compare the Two charts you see I only have trouble with Ace and 10 Column
Player's Expected Return by Standing looks like this
2 3 4 5 6 7 8 9 10 Ace
0-16 -.29 -.25 -.211 -.167 -.153 -.475 -.510 -.543 -.575 -.769
17 -.15 -.11 -.080 -.044 .0117 -.106 -.381 -.423 -.464 -.638
18 -.12 .148 .1758 .1995 .2834 .3995 .1059 -.183 -.241 -.377
19 .386 .404 .4231 .4395 .4959 .6159 .5938 .2875 -.018 -.115
20 .64 .650 .6610 .6703 .7039 .7732 .7918 .7583 .4349 .1460
21 .882 .885 .8887 .8917 .9028 .9259 .9306 .9391 .8116 .3307
Sorry about the spacing
If you compare the Two charts you see I only have trouble with Ace and 10 Column
September 29th, 2012 at 8:59:34 PM
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I might need the wizard on this one
September 29th, 2012 at 9:03:50 PM
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Quote: mixmanmattI might need the wizard on this one
Did you read the other posts that suggested that you may not be including a dealer 'Blackjack' in your calculations? In other words, in Europe you get to play out your hand even if the dealer has a 'Blackjack', unlike the US.
September 29th, 2012 at 9:09:40 PM
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Quote: mixmanmattI might need the wizard on this one
Did you look into what was suggested by the gaming experts who already replied?
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
September 29th, 2012 at 10:32:51 PM
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Yes I have looked into it
I am using European Rules
I have kept troubling shooting but everything adds up to 100% so I can't find the error
I am using European Rules
I have kept troubling shooting but everything adds up to 100% so I can't find the error
September 30th, 2012 at 1:13:45 PM
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If you use european rules, you need to rescale your hands EVs for the possibility of dealers blackjack.
The math for converting a "no holecard" and "holecard" EV calculation is quite simple:
EV(no holecard) = pDBJ * lossDBJ + (1 - pDBJ) * EV(holecard)
where pDBJ is the probability of a dealers blackjack (given his upcard).
On dealers upcard 2 to 9 the dealer cannot have a blackjack, and pDBJ is zero. Hence EV(no holecard) = EV(holecard).
If the dealers upcard is a ten then i.e. pDBJ = 4/51 for a single deck.
"lossDBJ" is the cost of the hand lost against a dealers blackjack. Most often it is -1 if you consider hit / stand / late surrender options (you only lose your initial bet), but it is -2 if you consider split or double down options (since you also lose the additional bet). This very detail will alter basic strategy (i.e. no doubling against a potential blackjack hand).
The math for converting a "no holecard" and "holecard" EV calculation is quite simple:
EV(no holecard) = pDBJ * lossDBJ + (1 - pDBJ) * EV(holecard)
where pDBJ is the probability of a dealers blackjack (given his upcard).
On dealers upcard 2 to 9 the dealer cannot have a blackjack, and pDBJ is zero. Hence EV(no holecard) = EV(holecard).
If the dealers upcard is a ten then i.e. pDBJ = 4/51 for a single deck.
"lossDBJ" is the cost of the hand lost against a dealers blackjack. Most often it is -1 if you consider hit / stand / late surrender options (you only lose your initial bet), but it is -2 if you consider split or double down options (since you also lose the additional bet). This very detail will alter basic strategy (i.e. no doubling against a potential blackjack hand).
September 30th, 2012 at 1:25:33 PM
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I agree with Mango's formula. Remember, here in the U.S. the dealer peeks for blackjack with a ten or ace up before the player acts. Therefore, my EV numbers against a 10 or ace will be higher, because the player can safely assume the dealer doesn't have a blackjack.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 30th, 2012 at 8:05:12 PM
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Hi guys thanks for your help but I think I have already included Dealer BJ in my calculations
This is for infinite deck dealer stands soft 17
I find EV this way:
For player21 vs dealerA I find Stand EV this way:
push = Percent times dealerAce turns into dealer21
lose = Percent times dealerAce turns into dealerBJ
Win = 100% - push% - lose% (This is case Win = 100% - 5.38% - 30.7%)
EvStand21vsA = Win - Lose
This logic has worked for every calculation except for vs dealerA and vs dealer10
This is for infinite deck dealer stands soft 17
I find EV this way:
For player21 vs dealerA I find Stand EV this way:
push = Percent times dealerAce turns into dealer21
lose = Percent times dealerAce turns into dealerBJ
Win = 100% - push% - lose% (This is case Win = 100% - 5.38% - 30.7%)
EvStand21vsA = Win - Lose
This logic has worked for every calculation except for vs dealerA and vs dealer10
September 30th, 2012 at 11:20:13 PM
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I'm sure you have included the Dealer BJ in your calculation in the correct way. The Wizards table is for a different game, where there is no lose scenario on 21vsA since the Dealer cannot have Blackjack as he has checked his hole card before the player could hit to a 21.
Neither is right or wrong - those are just different games. You cannot compare results from different games unless you convert them. The conversion formula is given above.
Neither is right or wrong - those are just different games. You cannot compare results from different games unless you convert them. The conversion formula is given above.
October 1st, 2012 at 2:47:27 PM
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Yes I must find the error somewhere else I guess
See the problem is when I want my program to tell me the house edge for the rules I have programmed It outputs the player an edge of approx. 2.5% which is way off.
See the problem is when I want my program to tell me the house edge for the rules I have programmed It outputs the player an edge of approx. 2.5% which is way off.
October 1st, 2012 at 3:00:43 PM
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I guess you should first think about why a dealers peek to his hole card actually helps the player.
It is a hard way from stand EVs to the EV of the whole game. A convenient way of calculation is: surrender, stand, double, hit, split (in that order).
It is a hard way from stand EVs to the EV of the whole game. A convenient way of calculation is: surrender, stand, double, hit, split (in that order).
October 8th, 2012 at 1:50:41 PM
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Quote: mixmanmattMy Chart of the same type on the wizards page
Player's Expected Return by Standing looks like this
2 3 4 5 6 7 8 9 10 Ace
0-16 -.29 -.25 -.211 -.167 -.153 -.475 -.510 -.543 -.575 -.769
17 -.15 -.11 -.080 -.044 .0117 -.106 -.381 -.423 -.464 -.638
18 -.12 .148 .1758 .1995 .2834 .3995 .1059 -.183 -.241 -.377
19 .386 .404 .4231 .4395 .4959 .6159 .5938 .2875 -.018 -.115
20 .64 .650 .6610 .6703 .7039 .7732 .7918 .7583 .4349 .1460
21 .882 .885 .8887 .8917 .9028 .9259 .9306 .9391 .8116 .3307
Sorry about the spacing
If you compare the Two charts you see I only have trouble with Ace and 10 Column
Your figures seem correct for the ENHC game
I do not have the infinite deck number but for 6 decks the numbers are very close to the numbers you quote for Stand.
As other have explained the figures for ENHC are different for 10 and Ace.
You say that you get an Ev of 2.5%.
Your mistake must be somewhere else, not on the Stand results.
October 8th, 2012 at 3:04:46 PM
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Thanks ACETWO
is there a website where your getting these numbers?
is there a website where your getting these numbers?
October 9th, 2012 at 5:37:07 AM
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Quote: mixmanmattThanks ACETWO
is there a website where your getting these numbers?
I do not think I have ever seen a website with ENHC numbers for infinite deck or finite deck composition dependent numbers for 10 & Ace.
I got these numbers a long time ago using software.
As others have said you can convert Wizzard numbers using the formula quoted to check the numbers and verify them.
October 20th, 2012 at 1:57:52 PM
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Thanks Everyone
I spent a little while converting my strategy to dealer peeks and now all my numbers line up with the wizards, now this means that all my programming must be correct.
I spent a little while converting my strategy to dealer peeks and now all my numbers line up with the wizards, now this means that all my programming must be correct.
