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#1
November 21st, 2011, 04:55 PM
 SBT Member 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 60-70 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.
#2
November 21st, 2011, 04:59 PM
 Southpaw Senior Member 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 43-43% of hands.

Spaw
#3
November 21st, 2011, 06:31 PM
 tthree Executive Member Join Date: Mar 2011 Posts: 2,277

If you bar pushes I think it is about 47% wins/decision on average.
#4
November 21st, 2011, 06:53 PM
 sagefr0g Executive Member Join Date: Apr 2006 Posts: 5,141

guess it depends on the game rules...
http://www.blackjackincolor.com/useless3.htm

......... maybe the image below gives an idea
Attached Images

#5
November 21st, 2011, 06:57 PM
 Jacob Member Join Date: Jun 2011 Posts: 83

Quote:
 Originally Posted by sagefr0g 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
Thanks be to Froggie for the link.

Last edited by Jacob; November 21st, 2011 at 07:01 PM.
#6
November 21st, 2011, 08:15 PM
 Sucker Executive Member 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
#7
November 21st, 2011, 08:57 PM
 21gunsalute Executive Member 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 60-70 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.
#8
November 21st, 2011, 09:08 PM
 sagefr0g 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.
#9
November 21st, 2011, 09:20 PM
 sagefr0g Executive Member Join Date: Apr 2006 Posts: 5,141
for the OP

http://www.bjstats.com/8102861108305XXX.jpg
http://www.bjstats.com/bjch.asp
.........

Last edited by sagefr0g; November 21st, 2011 at 09:22 PM.
#10
November 21st, 2011, 09:30 PM
 iCountNTrack 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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