# Probability of losing x # of hands in a row

• SBT

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.

• Southpaw

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

• tthree

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

• 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%)?

• 21gunsalute
Quote: SBT said:
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.

• sagefr0g
Quote: Sucker said:
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:
……..

• sagefr0g

for the OP

………

• iCountNTrack
Quote: Sucker said:
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

``````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
``````
• kewljason
Quote: Sucker said:
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%)?

The numbers in this chart are different than I have seen from many other sources. Most notably that loss number, which usually is closer to the 49% range in other sources. Win number (win + BJ’s) is also off (higher) than other sources I have seen.

• SBT

Thanks for replies and information. I took .53 (dealer’s win average) to the fifth power. Extrapolating, one has an approximately 4% chance of losing five hands in a row, in any five-hand sequence. That would mean that such a streak happens once per hundred hands, on average. Not sure if this is the proper way to approach the problem mathematically. But some of you have affirmed that you get such a streak once per hour, and longer streaks at times.

• kewljason

I couldn’t even tell the most hands I have lost in a row. I don’t even begin to think about something like that until I have lost probably 10ish and then it might hit me, “hey I’ve lost a bunch in a row”! But was it 10? or 8? or 12? or maybe only 6 but seems like 10 because of splits, DD. Or maybe it’s only 5 or 6 but seems like more because I am max betting and the dealer is magically pulling 6 card 20’s with a big plus count! In reality, as long as the count is still good, how many I have lost in a row is totally irrelevant to me. Although I might begin to consider that I am being cheated which is extremely unlikely, but it will cause me to take a closer look at everything, which isn’t bad.

I am wondering where you are going with this SBT. My first thought when I saw this topic is that you were heading towards a topic better fitted for the voodoo forum.

• SBT

Kewljason, yes, I was considering a voodoo strategy. I was considering raising my bet by one unit each time that I lost a hand. If one wins by the sixth bet progression, you are not behind in total losses. But one cannot protect oneself from randomness. Even though it is only a 2% likelihood of losing six hands in a row, that’s still risky. I would probably only try this system at \$5 table, and only when the count was not low.

• caramel6

how many in a row

anyway, do someone knows how many hands in a row to lose when tc2, tc3, tc4?
I believe should be lower number of hands comparing with a negative counts?

• Sonny
Quote: caramel6 said:
anyway, do someone knows how many hands in a row to lose when tc2, tc3, tc4?
I believe should be lower number of hands comparing with a negative counts?

The percentages don’t change that much in actual play. In fact, the probability of winning actually decreases as the count gets higher!

http://www.blackjackincolor.com/truecount5.htm

-Sonny-

• tthree
Quote: Sonny said:
The percentages don’t change that much in actual play. In fact, the probability of winning actually decreases as the count gets higher!

http://www.blackjackincolor.com/truecount5.htm

-Sonny-

You get more blackjacks and doubles and splits and win a higher percantage of them at high counts. That is were your advantage is found.

• Sonny
Quote: tthree said:
You gat more blackjacks and doubles and splits and win a higher percantage of them at high counts. That is were your advantage is found.

Exactly right. Also, the probability of wins decreases because the probability of pushes increases. The more tens there are, the more likely everyone is to get a 20 and push.

-Sonny-

• Cardcounter

Dealer wins 48 percent of the time player wins 44 percent of the time the other 8 percent it is a push. What is the number of losing hands that you are trying to figure out? Lets say that you throw out pushes you lose approximately 52.174% of your hands so take that number to the power of x and that is the probility of losing X hands in a row.

• iCountNTrack

The odds of winning or losing x hands in a row is a totally useless figure. I , 0.49^(x) is the probability of losing x hands in a row BEFORE any hand is played, meaning before we have any information, however AFTER we play the first x-1 hands and lose them, the probability of losing each of the previous x-1 is 1 because we now have the information, so the probability on the xth hand is 1^1(x-1)*0.49 = 0.49

• leatherguyray

I’m confused

Quote: SBT said:
Kewljason, yes, I was considering a voodoo strategy. I was considering raising my bet by one unit each time that I lost a hand. If one wins by the sixth bet progression, you are not behind in total losses. But one cannot protect oneself from randomness. Even though it is only a 2% likelihood of losing six hands in a row, that’s still risky. I would probably only try this system at \$5 table, and only when the count was not low.

I wish I were as smart as so many who post at this site, but I am not. However, my question is a curiosity. If you were playing a nickle bet and did, as you suggested, raise your bet one unit with each loss through six losses, how would you have recovered your losses? Five losses would total \$75 and the sixth bet of \$30 would not negate all that loss. Hardly half unless in my ignorance I am missing something.

• tthree
Quote: leatherguyray said:
I wish I were as smart as so many who post at this site, but I am not. However, my question is a curiosity. If you were playing a nickle bet and did, as you suggested, raise your bet one unit with each loss through six losses, how would you have recovered your losses? Five losses would total \$75 and the sixth bet of \$30 would not negate all that loss. Hardly half unless in my ignorance I am missing something.

I noticed that too but assumed he actually meant double after each lose. What did you mean OP?

• SBT

Responding to icountntrack, I see what you mean that when one is about to be dealt the 5th hand (after say losing four in a row), the probability of loss is the same as when you are dealt the first hand. However, are you saying that it makes no sense to consider runs of losses? Certainly it is more probable that one will win or lose two hands in a row than they will win or lose 50 hands in a row. Or am I missing something here?

Leatherguyray, if I start out betting \$10, then raise one unit to \$20 on the next bet, and win, I have regained my first bet’s win as well as winning the second. If I lose the second hand and then raise my bet to \$30 and win, I have not come out ahead, but I have recovered the bets of all three hands. If I lose the third hand and then bet \$40, and win, I am then even with a flat betting scheme, having lost as much as I would have (2 units overall) from flat betting with losing three followed by a win. I should have said in my earlier post that things begin to go into losses greater than flat betting at the fifth bet progression. Thanks for recognizing and pointing out my math error, Leatherguyray and tthree!

My thought process when I was considering this system — I was assuming that losing two or three in a row is much more likely than losing more than losing five or more in a row, thus one would recover one’s bets at a higher rate. Also, as one raises one’s bet, blackjacks pay more. However, if you get a streak of losing hands, then you go into much greater losses with this system, so it’s risky. I haven’t tried this yet, but was just considering it. Also, my local casino has surrender, which would reduce the risk somewhat.

• 21gunsalute
Quote: SBT said:
Responding to icountntrack, I see what you mean that when one is about to be dealt the 5th hand (after say losing four in a row), the probability of loss is the same as when you are dealt the first hand. However, are you saying that it makes no sense to consider runs of losses? Certainly it is more probable that one will win or lose two hands in a row than they will win or lose 50 hands in a row. Or am I missing something here?

Leatherguyray, if I start out betting \$10, then raise one unit to \$20 on the next bet, and win, I have regained my first bet’s win as well as winning the second. If I lose the second hand and then raise my bet to \$30 and win, I have not come out ahead, but I have recovered the bets of all three hands. If I lose the third hand and then bet \$40, and win, I am then even with a flat betting scheme, having lost as much as I would have (2 units overall) from flat betting with losing three followed by a win. I should have said in my earlier post that things begin to go into losses greater than flat betting at the fifth bet progression. Thanks for recognizing and pointing out my math error, Leatherguyray and tthree!

My thought process when I was considering this system — I was assuming that losing two or three in a row is much more likely than losing more than losing five or more in a row, thus one would recover one’s bets at a higher rate. Also, as one raises one’s bet, blackjacks pay more. However, if you get a streak of losing hands, then you go into much greater losses with this system, so it’s risky. I haven’t tried this yet, but was just considering it. Also, my local casino has surrender, which would reduce the risk somewhat.

Well, you have to lose 2 or 3 in a row before you get to 50 in a row, but the problem is you don’t know how long of a streak you’re going to have to endure before your streak actually ends. You may have only lost 2 or 3 in a row at a given point but you don’t know if the streak is going to end on the next hand or 12-15 hands down the road. What you’re considering doing is still a negative progression and it still will not work in the long run.

• iCountNTrack
Quote: SBT said:
Responding to icountntrack, I see what you mean that when one is about to be dealt the 5th hand (after say losing four in a row), the probability of loss is the same as when you are dealt the first hand. However, are you saying that it makes no sense to consider runs of losses? Certainly it is more probable that one will win or lose two hands in a row than they will win or lose 50 hands in a row. Or am I missing something here?

Yes it is more probable to lose one hand in a row than to lose 50 hands in a row, but how is that useful to you, as you agree with me the probability of losing on the hand you are just about to play is not affected by previous results

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