20 hands in a row?! I've been "initiated".

[Mondo]

Hi everyone,

I'm relatively new to advantage play in blackjack. I've been using the KO method (because it's easy for beginners) at low limit tables, mostly just for fun (I have a nice 9-5 job, no interest in being a professional gambler), though I've actually had quite a lot of success with it. I could be getting extremely lucky, but it's still one of the most enjoyable hobbies I've ever started.

I'm glad to have found this forum, and after lurking for some time have gained a lot of respect for the players on here. I look forward to benefitting from your wisdom and experiences and I'm already pretty grateful for the things I have learned just from lurking here w/o posting for a while.

Anyway I feel like I truly "broke my cherry" the other day as the aforementioned good luck ran out and I lost 20 hands in a row using perfect basic strategy (and I know it was perfect as I was using a basic strategy card that I ordered off Amazon lol). So, what are the odds of this happening in a "1 in X" format? This only cost me a hundred bucks as I was betting the table minimum of five dollars. After losing ten hands in a row, I actually decided to keep going just to see how long it would last (my previous record had been 13 hands in a row, but I walked away so it potentially could have lasted longer). I'm aware that 10 hands in a row is actually not that rare (about 1 in 500 odds, with roughly a hundred hands dealt every hour, it happens all the time), but 20 in a row seems pretty severe. Has to be worse than 1 in a million?

And this was 6 decks, if that's relevant, and anyone wants to include that in the calculation. I'm not sure how to calculate these probabilities, so I figured I'd ask here along with the losing streak horror story and self-introduction. (Don't worry about this factor, but it probably goes without saying that I had a negative count throughout the whole streak.) If this post is too silly for the General Blackjack Forum, I'm totally cool with it being moved to the Stuff forum.

Edit to add if there is a good book/resource for probability in blackjack that anyone can recommend? I just order Probability for Dummies so that should give you an idea of where I'm at when it comes to knowledge in this area, lol.

Anyway, great forum.

[Gronbog]

There have been many posts about this kind of thing over the years. You may be comforted to know that you are not alone and that many (myself included) have experienced streaks this long and longer. I don't have time at the moment, but I'm sure that someone will post an estimate of the probability based on the frequency of hands expected to be won/lost/pushed for your rules. However, unless you have evidence that you were cheated, I wouldn't bother. If you play long enough, anything that can happen will happen.

[Mondo]

There have been many posts about this kind of thing over the years. You may be comforted to know that you are not alone and that many (myself included) have experienced streaks this long and longer. I don't have time at the moment, but I'm sure that someone will post an estimate of the probability based on the frequency of hands expected to be won/lost/pushed for your rules. However, unless you have evidence that you were cheated, I wouldn't bother. If you play long enough, anything that can happen will happen.

Oh I didn't think I was cheated, definitely not. Just extreme bad luck. It happens. I mentioned the 10-hand losing streaks... it amazes me to see people freak out at the tables when it happens to them because ten-hand streaks happen all the time. I was just curious about the odds of a 20-hand losing streak.

Another crazy thing I've seen at a table was all five players getting a natural. Now the odds of that happening are, if I am calculating correctly, about 1 in 4 million. But it happened and I witnessed it!

[Dog Hand]

<snip>Anyway I feel like I truly "broke my cherry" the other day as the aforementioned good luck ran out and I lost 20 hands in a row using perfect basic strategy (and I know it was perfect as I was using a basic strategy card that I ordered off Amazon lol). So, what are the odds of this happening in a "1 in X" format?<snip>

Mondo,

Welcome to active participation in the forum, you long-time lurker ;-)

To answer you probability question, we need to know the probability of losing a round in BJ. The Wizard of Odds gives these probabilities for winning, pushing, and losing a round of BJ:

Summarized Net Win in Blackjack
EVENT PROBABILITY
Win 42.43%
Push 8.48%
Loss 49.09%

See this link: https://wizardofodds.com/games/blackjack/variance/

Now the Wiz is using "win" to mean "finishing the round with more money than you started with", so for example if you end up splitting to four hands with one double down, and you win the DD hand, push two of the others, and lose the fourth hand, that's a win: +2+0+0-1 = +1, even though if you just count the hands, you won one and lost two.

So, if we accept a loss probability of 49.09% = 0.4909, and we assume this probability remains constant over the span of 20 hands (which in fact it will not do, unless your game is shuffled after each round), then the probability of losing the next 20 consecutive rounds is

P = 0.4909^20 = 6.605*10^(-7), or roughly 1,514,000 to 1.

Note, though, this is NOT the same as saying, "The probability of losing 20 consecutive rounds in my BJ career is 1,514,000 to 1." If you played one trillion rounds and listed the outcome (win, push, loss) of each one, you would be correct in saying, "If we randomly select a starting point, say round 34,623,890, the odds of losing rounds 34,623,890 to 34,623,909 (20 consecutive rounds) is 1,514,000 to 1." However, in a trillion-round sample you are essentially guaranteed to see at least one 20 round consecutive loss streak.

Hope this helps!

Dog Hand

P.S. You'd also be really, REALLY old if you actually played a trillion rounds of BJ ;-)

[aceside]

and you win the DD hand, push two of the others, and lose the fourth hand, that's a win: +2+0+0-1 = +1, even though if you just count the hands, you won one and lost two.
)

Typo here. You won one and lost one.

[Mondo]

________


I know I once won every single hand in an 8 deck shoe in A.C. - the table was not full - I wasn't counting the no. of hands but it had to be at least 20 hands in a row

.

I've never won 20 hands in a row (only been playing since 2019 and AP since last year) but I have won 10+ in a handful of times. It's not that super rare. Odds are roughly one in ~5500, so if you play a hundred hours you're more likely than not to get to savor this very gratifying experience.

[Mondo]

Mondo,

Welcome to active participation in the forum, you long-time lurker ;-)

To answer you probability question, we need to know the probability of losing a round in BJ. The Wizard of Odds gives these probabilities for winning, pushing, and losing a round of BJ:

Summarized Net Win in Blackjack
EVENT PROBABILITY
Win 42.43%
Push 8.48%
Loss 49.09%

See this link: https://wizardofodds.com/games/blackjack/variance/

Now the Wiz is using "win" to mean "finishing the round with more money than you started with", so for example if you end up splitting to four hands with one double down, and you win the DD hand, push two of the others, and lose the fourth hand, that's a win: +2+0+0-1 = +1, even though if you just count the hands, you won one and lost two.

So, if we accept a loss probability of 49.09% = 0.4909, and we assume this probability remains constant over the span of 20 hands (which in fact it will not do, unless your game is shuffled after each round), then the probability of losing the next 20 consecutive rounds is

P = 0.4909^20 = 6.605*10^(-7), or roughly 1,514,000 to 1.

Thanks, this is exactly what I was looking for.

Note, though, this is NOT the same as saying, "The probability of losing 20 consecutive rounds in my BJ career is 1,514,000 to 1." If you played one trillion rounds and listed the outcome (win, push, loss) of each one, you would be correct in saying, "If we randomly select a starting point, say round 34,623,890, the odds of losing rounds 34,623,890 to 34,623,909 (20 consecutive rounds) is 1,514,000 to 1." However, in a trillion-round sample you are essentially guaranteed to see at least one 20 round consecutive loss streak.

Right, I believe the "1" in "1,514,000 to 1" increases by one with every new win-loss chain starting from when one starts playing. So the 10-hand losing streaks that I mentioned earlier, assuming 100 hands an hour with a roughly 1-in-500 chance of happening, become pretty likely to hit you after a few hours of play. Obviously this is a gross oversimplification, but every newcomer to blackjack should be informed "You are going to lose 10 hands in a row, it's going to feel awful, and it will happen to you oh so very soon." lol

Another factor to consider is that, given so many crappy hands, after 20 rounds of awful hands the bust cards should have been fairly depleted, so with that in mind the odds are probably much higher than even "1,514,000 to 1", but of course that would involve keeping track of the specific cards dealt and calculating probability based on that (which is above my pay grade).

Now, I doubt if the number goes up into trillions, but there have to be literal millions of hands dealt in town every year, so I bet that 1-in-4-million occurrence of five naturals that I saw happens several times a year in Las Vegas.

[Dog Hand]

Typo here. You won one and lost one.

aceside,

Good catch... Thanks!

Dog Hand

[MMalmuth]

Many years ago when I was in college I took an introductory course in Agriculture engineering that was taught by a professor who was a little bit nutty. And he told us a story about why he left farming. He said that one year a huge rainstorm came and the word was that a storm this bad only came once every fifty years. The next year there was a rainstorm that was even worse and the word was that a storm this bad only came once every 100 years. The third year a once in 500 year storm came. So, he gave up farming.

By the way, while I'm sure you had a bad run at blackjack, to make things simple we'll assume the probability of losing a hand is 0.50. (It's actually a little higher.) Then the probability of losing 20 hands in a row is something like 0.5 to the 19th power then multiplied by every time you lost a hand after a winning hand. (Some people on here might wonder why I didn't use 20.) Unless you've played an unbelievable number of hands, this should come out to a probability very close to zero.

Best wishes,
Mason