Blackjack Hand Win/Loss Run

Over a million hands, does anyone know what is the longest consecutive string of losses to the dealer hand a player could experience?

1 million.

There's no limit to number of losses you could end up with. It just gets smaller and smaller probability.

If I am the player, 1,000,000.

Ha ha. I obviously asked the question all wrong. I don't mean losses of money or chips. I'm talking about hands. Dealer has a hand, player has a hand. Sometimes you beat the dealer, sometimes the dealer beats you. In regular play, I find it's unusual to lose more than 7 hands in a row. I'm just wondering if anyone has data on the longest losing streaks displayed by simulation software, and how often unusually long losing streaks occur.

Quote: Chubbyhubby

Over a million hands, does anyone know what is the longest consecutive string of losses to the dealer hand a player could experience?

You are looking for probabilities of streaks in BJ.
Answers can be found in this DorothyGale thread:
Streaks in blackjack ... some actual data

You can find streak data from cvdata
starting
Data Tables
example
Streak table half way down

For the *average* length of the longest losing run in 1 million hands I come up with about 20 at a 63.323% prob in 1 million hands

I can get an exact value but not with my current computer that I have in front of me.

added:
exact calculations for *average* length of the longest losing run (using BruceZ streak calc VB code version)
with 53.5% losing prob
hands/*average* length of the longest losing run
1000 / 10.24
2500 / 11.71
5000 /12.81
10,000 /13.92
20,000 /15.08

One can see the pattern.

Each time the number of trials doubles we can add 1 to the average length of the longest losing run
(this is consistent with the results from Mark Schilling's findings in his popular "The Longest run of Heads" paper)
continuing the pattern, I get:
40K = 16
80k= 17
160k= 18
320k= 19
640k= 20
1.28k= 21
Enjoy!

First off, the previous answers are correct. If the question is "What is the longest losing streak which could possibly happen?" then the answer is a million hands.

But I think your question is more along the lines of "What is the longest losing streak which is likely to happen?" There have been some threads here in the past about the rather complicated mathematics behind streaks. But I'll provide a guesstimate. Over a million hands, and outcome which has a probability of 1 in a million is "likely" to happen. The probability of losing n coin flips (roughly equivalent to blackjack hands) is 1 in 2^n. 2^n is roughly 1 million for n = 20. So I'd say in a million blackjack hands you are likely to see at least one losing streak of about 20 hands.

Even after you re-asked the question, thecesspit is still correct @ 1 million. Indeed, it's a very, very, small chance, but it is possible.

Thanks all. Very informative.

Quote: Chubbyhubby

In regular play, I find it's unusual to lose more than 7 hands in a row.

Not unusual.
Keep on playing. The more hands played the longer the losing streaks will be, on average.
Maybe you have yet to see the average during your sessions played.
Believe us, they are there!

You can use a simple approximation formula for the longest losing run in n trials:

Long Run = Log(n) / -Log(probab.)

in this case we have n= 1.000.000 and probab. = lets say 51%

=> estimation for longest run = 6 / 0.29242 = 20,51.

Nice. Most use that formula.
And precision is not a factor here but can be somewhere.

Now with easy to use exact recursion formulas we can get exact results. Love fast computers.

Just saying...
The approximation formula's error rate seems to be a constant with it's probability.

From using Exact calculations (and rounding up)
(I used 53.5% lose rate from DorothyGale sim results)
hands/ avg length of longest run
250 / 8.03
500 / 9.14
1000 / 10.24
2500 / 11.71
5000 /12.81
10,000 /13.92
(I have also verified these values with simulations. N=250 ALLRun = 8.0326)

approximation formula
8.83 /250
9.94 /500
11.04 /1000
12.51 /2500
13.62 /5000
14.73 /10000

Enjoy!

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The most hands that I have lost in a row in Blackjack is 20 hands which occurred on 4 seperate occasions in one month.