What are the Odds of Losing 6 Hands in a Row?

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Among emails I receive, a fairly common question is something like this:

Can you tell me the odds of losing six hands in a row at blackjack?

Sometimes it is 5 hands, sometimes 8, sometimes more.  No matter, I cringe whenever I get this question.

To me, it’s like an airship designer asking a chemist: “Does hydrogen weigh only half as much as helium?”   We all know how THAT turned out.

Hindenburg in flames

In either case, there is nothing wrong with the matter-of-fact question being asked, but it is apparent to the recipient that the question is likely a clue to dangerous thinking, whether it be the Hindenburg or the Martingale progression.

I’ll get back to that in a moment. But first, let me respond to the question, very carefully…

You probably mean “probability”

The first thing I want to do is change the wording of the question from “What are the odds” to “What is the probability“. Most people asking this question want an answer that is a single number or percentage, representing how likely the event is to occur. “Odds” means something slightly different, although the two are often used interchangeably. If you want to understand the difference, Google it.

Your question is incomplete

There is a crucial piece of information missing from your question. How do you plan to play?

Let’s say you sit down next to me at a blackjack table, and I look over and tell you: “This is unbelievable! I’m on the most horrible losing streak. My luck is so bad, I bet you $100 that I lose the next six hands in a row.” If you were foolish enough to bet me, I would quickly demonstrate how the probability of losing six in a row can be 100%!

But for the sake of your question, let’s assume the player will use accurate basic strategy on the game. I cannot resist the temptation of pointing out that virtually no player who asks this question will know a completely accurate basic strategy! But I’ll play along anyway.

Still not clear yet

There is another picky detail to consider. I assume you are not asking for the probability of losing exactly six hands in a row, which implies that the seventh hand cannot be a loss. Instead, you want to know the probability of losing six or more hands in a row. We can easily sidestep that complication, if we simply say that you want to know the probability of losing the next six hands of blackjack.

Finally, an answer?

For a typical shoe game, a basic strategy player will win 43.3% of hands, lose 48.0%, and push the other 8.7%.

If I answer the revised and improved question…

What is the probability of losing the next six hands at blackjack, using basic strategy?

Since each hand has a 48.0% chance of being a loss, the answer is 0.48 ^ 6 = 0.012 = 1.2%.

But wait a minute…

That still wasn’t the right question!

That probably isn’t what you meant either. What if you lose the first hand, push the second hand, and lose the next five hands in a row? You would probably want to call that losing six in a row. We should just ignore pushes altogether, and only count hands that end in a win or a loss. Of non-push hands, players win 47.4% and lose 52.6%.

Finally an answer that may satisfy you:

What is the probability of losing the next six hands at blackjack, using basic strategy, ignoring pushes?

The answer is 0.526 ^ 6 = 0.021 = 2.1%.

That is roughly 1 in 47 attempts.

What about other length losing streaks?

Just because this is a convenient place to do so, I’ll publish the numbers for other lengths of losing streaks.

Probability of losing n hands in a row, ignoring pushes.
n Probability One in
1 loss 52.6% 1.9
2 losses 27.7% 3.6
3 losses 14.6% 6.9
4 losses 7.7% 13
5 losses 4.0% 25
6 losses 2.1% 47
7 losses 1.1% 90
8 losses 0.59% 170
9 losses 0.31% 323
10 losses 0.16% 614
11 losses 0.08% 1168
12 losses 0.04% 2219
13 losses 0.02% 4217

Why I hate answering this question

When players ask questions about how likely it is to lose hands in a streak, it usually means that they are considering a negative progression betting system that would fail if they encounter a certain number of losing hands in a row. Most commonly, they have rediscovered the infamous Martingale system, where you double up after any losing hands to catch up.

The Martingale is the simplest of the negative progression betting systems. The idea is simple. If you lose one hand, just double your bet on the next hand. Eventually, you will win a hand, and make back all of your losses plus a profit of the initial bet. Indeed, this seems to work very reliably, until it doesn’t. The problem is that most people underestimate how likely those “unlikely” streaks of losses really are. Check the table above. The probabilities get small, but not nearly small enough.

Why you should NOT bet the Martingale

If you think the Martingale is a good idea, you are badly mistaken. Yes, it gives you a high percentage chance of winning a small amount, but it does not take long to run out of luck. For a $10 bettor who wants to be able to handle up to 7 losses in a row, he needs to have a bankroll of $2550, and be willing to bet $1280 on the eighth hand. All this, for a $10 win each time.
And he will run into that fatal eighth loss once every 170 trials on average. You can think of that as making $1700 in profit before you eventually lose $2550. (Yes, I am oversimplifying because doubles and splits make the math very messy. The real numbers still make this a very bad idea.)

On top of that, blackjack is a terrible choice for the Martingale system. With the necessary doubles and splits, sometimes both on the same hand, you will actually need a far larger bankroll to play correct basic strategy. If you choose to ignore basic strategy doubles and splits, you can get by with “just” the $2550, but at a substantially increased loss rate on all your bets.

It’s not only the Martingale

Any progressive betting system is doomed to fail. Any series of negative expectation bets is guaranteed to create a negative expectation overall. If you are just playing for fun, you will lose less money by flat-betting. If you are playing for profit, you need to find a true way to get an edge, such as counting cards.

Hopefully you are reading this before you learn the hard way. After all, we don’t fly airships full of hydrogen any more either.

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Anonymous
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Anonymous

Wow. First of all, this article addressed the losing nature of reverse progression as related to BlackJack (almost). It was simplified to large degree. However, the author is corrects in two major points. First being that in and of itself, Martingale will fail at BlackJack over the long run. Second is that a vast majority of players will not make the optimum decisions each and every time to increase their odds given ANY particular strategy. If someone does not understand the math, have the discipline and bankroll to try any system to it’s strictest mathematical constraints, and have a willingness… Read more »

D
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D

The article failed to mention caveats to overall strategy, and objective. I’ll run a negative progression at times. Never by itself of course. That’s stupid. There are ways to MAKE the Casino THINK you’re running negative progression, and actually hide it in something else (No, I’m not giving away everything here). Regardless, as with any mathematical game, you have to take into account strategy, and objective. Of course, this is taking into account that the individual is not a degen, and is actually going to “work” when they walk into the casino. You run counting cards, and the rest of… Read more »

Mike in Las Vegas
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Mike in Las Vegas

Just got back from Ceasers Palance. Tested my suspicions again. 1) New Deck 2) Deck Spread out 3) Deck placed in shoe and never shuffled in front of me 4) EMPTY TABLE – I was the only player at the table IMMEDIATLY LOST 7 HANDS IN A ROW STRAIGHT !!!! Per this website – odds of this are 1.1% or 1 in 90 !!!!! My suspicion has again been confirmed. However I have NO EVIDENCE other than circumstance. So I need to know if anyone else has experienced this. I’m wondering if the casinos are setting up the new decks… Read more »

Alex
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Alex

I agree, their shuffling machine reads the card, so I am suspicious if that in between lines in laws there is a loop hole that they can some how shuffle, that bunch of smalll numbers comes out, so it ruins all your doubles and splits!
Also, Golden nugget that hand shuffle, they change their cards every two hours, I think the way the shuffle, there is a same math to it, and as soon as cards gets shuffle we’ll, two hours cards change comes!

Anonymous
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Anonymous

I think they do. I have witnessed 10 small cards come out in a row and dealers don’t bust. I have also witnessed every player having 20 including the dealer. I think this is due to lack of shuffling. No wonder they allow basic strategy charts. Cards are not coming out random as they should to make the game fair.

D
Guest
D

No. It’s the basic gamblers fallacy in hitting a losing streak (for any number of reasons, which could be they simply did not play basic strategy correctly; Hitting at 15 when the dealer stands at 6 for example. Or it could be a simple mathematical deviation). Regardless … your theory falls apart on your own premise. NO ONE ELSE MUST BE AT THE TABLE, per your own words. That’s not something the Casino controls, or can control. It’s what we refer to in Mathematics, as Non-Linear Complexity variables. Per your own statement, if anyone else walks up to the table… Read more »

Anonymous
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Anonymous

Yes! I know dealer and confirms shufflers stack deck against card counters, but I have ran into the problems you have mentioned. Once they realize what you are doing you will lose.
I have played live online blackjack and after 4 days I kept losing, so to confirm my theory I joined with another name and same thing after 4 days I kept losing.

Wes
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Wes

Their cheating isn’t limited to the circumstances you describe. And yes, it’s ostensibly idiocy for them to risk their licenses but they get away with it so apparently that is an insufficient deterrent or the gaming commission is such that the casinos aren’t actually taking a risk… and you’re seven consecutive losses at Blackjack is nothing compared to my 22 consecutive losses at Baccarat… 3 am… I was alone staring down about four pit people

Mike in Las Vegas
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Mike in Las Vegas

I’ve noticed the same thing as Benjamin. The cards are coming “pre packed”. Can’t help but wonder if there is a certain mathematically proven way to stack the deck. When you arrive to the tables in Vegas the cards are splayed out in a “display” kind of way. Pay attention now: YOU NEVER SEE THEM GET SHUFFLED IN FRONT OF YOU ON A NEW DECK. I walked up to an empty table at MANDALAY BAY , cashed 2 grand in chips , asked the dealer or to shuffle the cards in front of me. The nasty little Vietnamese bitch refused… Read more »

Benjamin
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Benjamin

I know this is an old post. Ive read some of these and am curious. Through observation and the probability somehow favoring the dealer. And I don’t mean by percent alone as in the amount of decks and the hitting or standing on soft 17. I mean it’s like those casinos have a special witch doctor looming behind the scenes. The spread of cards sometimes seems astronomically improbable, such as last night where the dealer gets 4 aces in a row with kings. Now this is a reputable casino of course. I digress. So my question is. I’ve read the… Read more »

Anonymous
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Anonymous

You have a 1/20 prob. of being dealt a blackjack w only a 1/25 chance (assuming 8-deck shoe) of having your blackjack pushed. Suppose you are playing a 13 loss Martingale, then that means you will have 200 strings that end with you getting a blackjack and making $10 plus your bet on the string. Simply counting $10 profit on every string ending in a loss and multiplying by the number of times you can expect to win and then subtracting by the total lost win you do run through the string is incorrect. Perhaps, you can figure the math… Read more »

Anonymous
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Anonymous

You also didn’t factor in the 3/2 payoff on a blackjack that can be the streak ender. If you bet, say $640 after your 6th loss in a row and hit a blackjack, you make $330, not $10. Also, since double-downs and most splits are in your favor, while you certainly need a much bigger bankroll for the possibility that you’ll get deal an 11 when the dealer has a 6, those hands also put the odds in your favor when you have the most money on the table.

Bill Swann
Guest

Question and Observation regarding raising your bet when the count is a negative 7 to 13 true negative of 4′ Has anyone run simulations on this.

So far , 100 hands only, it works almost as well as a true positive count of 4′. If Simulation agree, Why?

luis beckert
Guest
luis beckert

And when bets are only the true count 1 or greater than 1?

Roger
Guest
Roger

Why does your basic strategy recommend always standing on a pair of sevens, where as you hit a hard 14 when the dealer shows 6 or more ?

Federico
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Federico

I know i m off topic but i don t know where to post.
I had a new idea to count down cards.

Is there anyone who can give me an help please?

my mail is federico.betti90 @ gmail.com

Paul
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Paul

How do you know when to increase betting when I play for five or ten bucks I win when I go up I lose? any help on staggering my betting to improve winning percentages.

Anonymous
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Anonymous

Why dont you advise splitting 8s on ten and ace and ace on ace like other srategys thanks

Darren
Guest

Great helpful advice re martingale. The pushes and table maximums make any negative progression a terrible strategy.

jim haik
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jim haik

It’s clear you never heard of “Jim’s rhythm system”. I can’t reveal the details, but it’s a modified anti martingale system that limits your losses and maximizes your gains, best played on a 6 deck shoe, and playing two hands or one hand, depending on the circumstance. If other players at the table don’t like you ‘changing up the cards’ by being in and out with one or two hands, you may want to find an empty table. You will never draw attention from the pit, and you never count cards. This system will lose more than it wins,but the… Read more »

Anonymous
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Anonymous

Nope, There is no system to win in Blackjack, except counting cards. (And even that can not guarantee a win.)

Mike in Las Vegas
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Mike in Las Vegas

Counting cards feels worthless with 6-5 Blackjack taking over the entire strip and downtown. Even El Cortez 6-5 blackjack tables are expanding. People are so so so so stupid they literally see “6-5” and think it’s more than “3-2” because their “feelings” told them it was bigger. It is proof how stupid people are today. I don’t care if you give everyone a fake grading curve group grades college degree. This is undeniable prof most people are dumb as a post when it comes to basic math and by the way MOST college degrees require some kind of College level… Read more »

Anonymous
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Anonymous

sure pal

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