
November 21st, 2011, 04:55 PM

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Join Date: Nov 2011
Location: Northeast
Posts: 18


Probability of losing x # of hands in a row
I am new to this endeavor. I am wondering, has any blackjack player or writer calculated the probability of losing a certain number of hands in a row (given proper execution of Basic Strategy)? I am aware that one cannot simply raise .5 to the exponent of the number of hands, because the dealer has the edge and this is not like flipping a coin. I have played bj in a casino about 6070 hours so far. I would estimate that losing five or six hands in a row would be rare, but it happens to other players and it has happened to me a couple of times.

November 21st, 2011, 04:59 PM


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Join Date: Nov 2010
Location: United States
Posts: 490


Flash cites the figure often on here, and it would be really easy to look up probably on WoO or using Casino Verite products.
I believe that the player will win something like 4343% of hands.
Spaw

November 21st, 2011, 06:31 PM

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Join Date: Mar 2011
Posts: 2,277


If you bar pushes I think it is about 47% wins/decision on average.

November 21st, 2011, 06:53 PM


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Join Date: Apr 2006
Posts: 5,141


guess it depends on the game rules...
maybe this link will help:
http://www.blackjackincolor.com/useless3.htm
......... maybe the image below gives an idea

November 21st, 2011, 06:57 PM

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Join Date: Jun 2011
Posts: 83


Quote:
Originally Posted by sagefr0g

Thanks be to Froggie for the link.
Last edited by Jacob; November 21st, 2011 at 07:01 PM.

November 21st, 2011, 08:15 PM

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Join Date: Feb 2009
Location: U.S.A.
Posts: 1,504


Perhaps I'M missing something  but there appears to be something wrong with that chart.
According to this chart, in a negative deck you lose 46.7% of the time, and counting BJs you win 45.2% of the time. However; because of the fact that BJ pays 3:2, shouldn't the actual WIN figure for a BJ be counted as 6%, rather than 4%; therefore tipping the scale into the player's favor (47.2% to 46.7%)?
Last edited by Sucker; November 21st, 2011 at 08:34 PM.
Reason: spelling error

November 21st, 2011, 08:57 PM

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Join Date: Aug 2009
Location: Area 51
Posts: 1,144


Quote:
Originally Posted by SBT
I am new to this endeavor. I am wondering, has any blackjack player or writer calculated the probability of losing a certain number of hands in a row (given proper execution of Basic Strategy)? I am aware that one cannot simply raise .5 to the exponent of the number of hands, because the dealer has the edge and this is not like flipping a coin. I have played bj in a casino about 6070 hours so far. I would estimate that losing five or six hands in a row would be rare, but it happens to other players and it has happened to me a couple of times.

Sorry, but it's not that rare at all to lose 5 or 6 hands in a row. I'd dare say it happens to me at least once an hour, and sometimes much, much more than that. I've lost 15 or more hands in a row 3 times in the same week.

November 21st, 2011, 09:08 PM


Executive Member


Join Date: Apr 2006
Posts: 5,141


Quote:
Originally Posted by Sucker
Perhaps I'M missing something  but there appears to be something wrong with that chart.
According to this chart, in a negative deck you lose 46.7% of the time, and counting BJs you win 45.2% of the time. However; because of the fact that BJ pays 3:2, shouldn't the actual WIN figure for a BJ be counted as 6%, rather than 4%; therefore tipping the scale into the player's favor (47.2% to 46.7%)?

i sure don't know, can't even remember where i got the image, it was a long time ago, lol.
one thing maybe could make a difference, the zero count is not depicted far as the win/loss/tie/bj percentages. zero tc carries a house edge, could that make up the difference? perhaps some of those bj's are ties?
what else is strange, i thought in the long run positive counts attributed a small but measurable higher number of wins than negative counts, that also is not the case in the image.
edit: ahhh, ok i got the image from this site:
http://www.bjstats.com/bjch.asp
http://www.bjstats.com/8100961108305XXX.jpg
........
Last edited by sagefr0g; November 21st, 2011 at 09:29 PM.

November 21st, 2011, 09:30 PM


ChemMeister


Join Date: Oct 2008
Posts: 780


Quote:
Originally Posted by Sucker
Perhaps I'M missing something  but there appears to be something wrong with that chart.
According to this chart, in a negative deck you lose 46.7% of the time, and counting BJs you win 45.2% of the time. However; because of the fact that BJ pays 3:2, shouldn't the actual WIN figure for a BJ be counted as 6%, rather than 4%; therefore tipping the scale into the player's favor (47.2% to 46.7%)?

Winning/pushing/losing frequencies are not too useful figures in a game like BJ because they are different payouts because of doubles, splits, double after splits, blackjack. So it is more useful if you get the probabilities of each possible round outcome. So for example for a game with only one split allowed and DAS, the possible outcomes are 4, 3, 2, 1, 0, +1, +1.5, +2, +3, +4 . the following data is for 6D, S17, 1 split, DAS; Player hand 8,8; dealer upCard 6
Code:
player's Hand 8,8
dealer's upCard 6
player's probabilities for standing
p_1 = 0.578747564318
p_0 = 0
p_+1= 0.421252435682
p_+1.5 = 0
EV for standing= 0.157495128637 ± 0.987519764084
player's probabilities for doubling
p_2 = 0.690684064282
p_0 = 0.0441173812318
p_+2= 0.265198554486
EV for doubling= 0.850971019592 ± 1.76050526807
player's probabilities for hitting
p_1 = 0.690684064282
p_0 = 0.0441173812318
p_+1= 0.265198554486
EV for hitting= 0.425485509796 ± 0.880252634033
player's probabilities for splitting
p_4 = 0.00419012222521
p_3 = 0.0650328867493
p_2 = 0.260197245456
p_1 = 0.0767357312541
p_0 = 0.0743673854602
p_+1= 0.0497634029576
p_+2 = 0.334266924866
p_+3 = 0.123229425568
p_+4 = 0.0122168754629
EV for splitting= 0.32786365993 ± 2.08656032979

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