Maximum Losses/Wins

Has anyone ever done a study on what the percentages are of 7, 8, 9, 10, etc. winning/loosing streak?
If so, can someone please direct me to that study.
I want to know, say in 4000 hands, what are the probabilities of loosing runs and winning runs.
Obviously 1 loss will have the highest percentage, 2 losses in a row a slightly less percentage, etc...
Ultimately, I want to know what the greatest potential downturn (number of losses in a row) could be in 1000, 2000, 4000, etc. hands of blackjack.

Has anyone ever done a study on what the percentages are of 7, 8, 9, 10, etc. winning/loosing streak?
If so, can someone please direct me to that study.
I want to know, say in 4000 hands, what are the probabilities of loosing runs and winning runs.
Obviously 1 loss will have the highest percentage, 2 losses in a row a slightly less percentage, etc...
Ultimately, I want to know what the greatest potential downturn (number of losses in a row) could be in 1000, 2000, 4000, etc. hands of blackjack.

Let's say we have a fair coin, i.e., the probability of heads or tails is exactly 50%.

The probability of the next flip starting a 10 tail streak is 0.5^10 = 0.10%. Therefore, the probability of the next flip not starting a 10 tail streak = 100%-0.10% = 99.90%. The probability that none of the next 4000 flips will start a 10 tail streak is 99.90%^4000 = 2.01%. This means the probability that at least one of the next 4000 flips will start a 10 tail streak is 100%-2.01%=97.99%.

using Panama Rick's approach above just insert the blackjack numbers

Probably of losing at blackjack is 47%, Probability of winning is 43%. (roughly rounded)

Forgive me, but what does "^" mean?

I'm using 44% win, 48% loss, 8% push for my blackjack numbers.
So...it's not exactly a two-sided coin.

So...for 1000 hands what is the probability that I will loose 10 hands in a row?

Forgive me, but what does "^" mean?

x^2 = x to the second power or x squared

I'm using 44% win, 48% loss, 8% push for my blackjack numbers.
So...it's not exactly a two-sided coin.

So...for 1000 hands what is the probability that I will loose 10 hands in a row?

If pushes break up losing streaks, the probability that one of the next 1000 hands starts a 10 hand losing streak = 47.8%.

If we ignore pushes, that's equivalent to 47.8% wins and 52.2% losses. The probability that one of the next 1000 non-push hands starts a 10 hand losing streak is 77.6%.

Before I discovered this site I was asking myself the same question. And if you are asking for the same reason I was, it is because you want to figure out how many bets you can make in a progression system before you reach the table max bet. I figured that I could take seven losses in a row before reaching the table max, and figured since I was only at a slight disadvantage, it might be a winning system. I wrote a computer program to test my theory, and quickly discovered what I would have learned from everyone here, and that is that progressions do not work. It would work sometimes in the short term, but long term it is a guaranteed loser. The most losses I saw in a row after simulating 100 shoes was 14, after ten million shoes it was 25, and my bank was always negative afterwards.

Alright...
I don't know if when you say "progression" it means the same as I what I'm thinking.
I'll just go ahead and spill the beans and let you know what I was thinking when I originally posed the question.
Then, maybe you can comment on what you think.

Okay...
This is the deal. Using basic strategy, 4-8 Decks, S17, DA2, DAS, OBO, No surrender generally yields the following results: 44% win, 8% push, 48% lose.

The betting that I'm in the process of developing works like this:
1. Start your first bet at the table minimum.
2. If you loose, double your bet.
3. If you win, cut your bet in half.
4. If you push, keep the same bet.

Of course, if you sit down at a table and win the first hand, the your second hand is also going to be at the table minimum. A slight variation would be to start a little higher than the table minimum (say $20 at a $5 table) which would allow you to win two times in a row, place a $5 bet for your third hand, lose, and then up your bet to $10 on the fourth bet, etc.

This is how the bet numbers look at a $5 table:
5 10 20 40 80 160 320 640 1280 2560

Believe it or not, I've never been to Vegas (I'm somewhat of a newbie), but I've been told that there are $5-2500 tables there. So, you'd have to place a $2500 bet vs. a $2560 bet.

Theoretically, if you play 100 hands, starting with a $5 bet on your first hand, and always loose any hands that you have a $5 bet on the table with, then:

Your 101th hand would result in a $80 bet.

This is my thought process:

The further you get away from the averages (44-8-48) the more likely you are to revert back to them. So...it makes sense to me that you should be placing higher bets the further away you get (on the low side) to the winning percentage.

For instance...
You start with a $5 bet.
You loose your first four hands.
At that point your winning percentage is 0, and odds say that you must EVENTUALLY get back to 44%.
So...you place an $80 bet and win.
That's get you get just ahead of your starting point and your winning percent becomes 20. Then you start lowering your bets as your winning percentage gets closer to 44%. So...in effect, whenever your winning percentage is over the average, your placing the lowest bet possible, and when your winning percentage lags your placing higher bets.
I've been utilizing this stategy online and for the most part it works. Currently I'm playing at Grand Casino Online. They have a $1-500 table ($512 is the tenth bet at a $1 table).
There are times when I start my bet at $1 and don't win until my bet becomes $32 dollars. More often then not though, loosing streaks only get to $8-16, and then I'm able to work my way back down, sometimes to multiple wins at $1.
Yes...it is risky, but with enough capital I think it can work. But...it will only work for so long. And that's the key. I'm thinking that I'll have to start back at the table minimum after ever shoe.
Now, sometimes you loose all your money, but more often than not you don't, and sometimes you more than double your money (say if you start with a $1000 pot at a $5 table).
So...if I loose $1000 on one shoe and then make $1000 on the next two shoes, I wind up with $1000 more than where I started with a $3000 bankroll.
What do you think?

A couple comments.

First, I think that the basic premise of your theory is flawed. The law of averages applies to extremely long trials. It is true that in a sample of 10 billion hands the win percentage will be pretty close to your expectation. This is not true in a sample of 100 hands. In other words, it is very likely that you will lose 10 or even 20 hands in a row over 1,000 hands as has been calculated above. In other words, the basic martingale system of doubling after every loss is guaranteed tolead to a loss of your entire bankroll unless you get lucky and don't plan to play for long.

The likelihood of a huge loss is even greater for your system than it is for a true martingale. You do not reset to the base bet after a win. Accordingly, if you are at the max bet in a 10 hand $5 progression of $2,560, then it will require exactly one loss before you are back up to the max bet level since you only cut your bet in half after a win. This modification to the martingale system will only assure that you lose your entire bankroll even quicker than under a standard martingale.

Finally a pet peeve. The opposite of win is "lose", not "loose". Why do so many people insist on using the opposite of tight to describe the opposite of win?

Do percentages of streaks change with multiple sets that equal 1000?
For instance...let's take the 77.6% calculation.
Is it still 77.6% if you play 50 hands, break, play another 50 hands, break, etc. (50 hands 20 times).

If you put all the results end to end, they would be the same, right?

But, I'm thinking that it's much less likely to encounter a 10 hand loosing streak INSIDE of each 50 hand set, right?

I hear what you're saying...
But, if you reset your bet to the base everytime you win, then your taking on risk at every basepoint and only increasing your pot by your initial bet once you get back. The system I'm suggesting allows you to make money on your way back to the averages, and on your way back down (sometimes to the basepoint).

Obviously, it would be much less likely to encounter a 10 loss streak in a 50 hand trial than in a 1,000 hand trial. This is only relevant if you are willing to absorb a session loss and do not require playing until a win before resetting your bet. For example, say that you are using a $5 base and have lost 5 straight hands when you hit your 50 hand limit. You have just suffered a loss of $155. If you now reset your next bet to $5 (with or without a "break"), you will change your pattern of wins and losses so that you have more frequent losing "sessions" and fewer winning "sessions" as compared to your original plan.

There is actually a simple formula that you can use to determine how much you are expected to win or lose in a given number of hands. It is Expectation X Avg Bet X Number of hands played. This formula is true regardless of the betting pattern. Certain betting patterns can impact your volatility of results, but that doesn't change the end result.

My thinking is that I will use the system for one shoe at a time, because the betting gets out of control (over the table limit) otherwise. So, if I'm playing alone with eight decks, that puts me at around 60 hands per shoe.
I haven't been able to test my system out yet because I need to find a simulator that will deal eight decks, at a table with betting limits of $5-2500 (or $1-500), allowing me to start with a bank roll of $2500 (or $500).
I know that there will be shoes in which I lose nearly all my bankroll, but I think (emphasis on "think") that there will be shoes in which I double my bankroll.

Is that you will go broke much faster.

The "system" you are proposing is a progressive system (actually it's called a negative progresion because you increase after losses vs. a postive progression that increases after wins).

A couple things to remember:
1. There's nothing new under the sun.
Progressions have been looked at every way concevable for as long as gambling has existed. They simply do not give the player an advantage. Some systems may slow the rate of loss a little and some give big swings, but ultimately the house will take all your money.

2. Why play Blackjack?
We play Blackjack because it is possible to gain an advantage over the house. That advantage comes by knowing the general mix of cards remaining to be played. If the remaining cards are 10s and Aces then the player has an advantage. If they are small cards the house has an advantage. A progression system doesn't take this into account. Therefore it doesn't matter if the game is blackjack or roulette or most other games in the casino, you are playing at a disadvantage that cannot be overcome in the long run. In fact, because the odds in Blackjack can increase towards the house advantage during a shoe, a progressive system can lead you into disaster by dictating bets based upon random chance rather than on advantage/disadvantage (even on a very negative shoe you can still get a 21 once in awhile).

The best thing you can do is to purchase a Blackjack simulation software package and configure your system then let it run a million or so hands. NOTE: this will cost you a lot less money then going to the casino to try it out!!! And if you are like most people, it's the only way you'll actually be convinced :) (Other than loosing all your money).

The further you get away from the averages (44-8-48) the more likely you are to revert back to them. So...it makes sense to me that you should be placing higher bets the further away you get (on the low side) to the winning percentage.

This is called gambler's fallacy and is why the nights are bright in Las Vegas.

Yes, over the long run, you expect to win at prescribed rate, say 44-8-48. That does not mean that if you suffer a losing streak, you have increased your probability of winning. What happens is that losing streak becomes insignificant in the long run.

I give you an example, suppose you are betting heads on a coin and lost your first 30 flips in a row. You then end up 50/50 the rest of the time. You see the more you play, the less significant that 30 flip losing streak becomes.

After 100 flips: 35 heads = 35.0000%
After 1000 flips: 485 heads = 48.5000%
After 10,000 flips: 4985 heads = 49.8500%
After 100,000 flips: 49985 heads = 49.98500%
After 1,000,000 flips: 49985 heads = 49.9985%

First, you will need a bankroll that is 150% of the table max. If you want to bet $500 with a $5 base bet, then you have already lost $320, so you needed to start with $820. You would actually need alot more to cover potential splits and double downs. $5 units will require 8 losses to reach a $500 table max and a loss of $820 (the last bet should be $640, but the $500 limit is reached). Over a large trial (like regular play for a couple months), you are almost certain to have a loss streak of this long within a 60 hand trial. More to the point, you will also reach the end of the shoe at some point in a losing streak about half the time. Thus you will lose one or more betting units (maybe alot more) from that streak.

Second, while all this is interesting, you need to understand that all you are doing is manipulating the pattern of your wins and losses in the short term. A negative progression will increase the number of winning sessions and will decrease the number of losing sessions. However, the winning sessions will also be smaller than the losing sessions on average. You can expect to lose your expectation X avg bet X number of hands, regardless of how you bet.

The goal for me here is to find a table with limits of $5-2500 (I've been told there are such things) and starting with a $5000 bankroll at the beginning of each shoe (or a table with limits of $1-500 and starting with a $1000 bankroll at the beginning of each shoe). My idea is to have 10 betting levels (5 10 20 40 80 160 320 640 1280 2560). Of course the 2560 would turn into a 2500 at a real table.

I tried 8 shoes using the strategy trainer at blackjackinfo.com (8 decks) and was unable to get through any of the 8 shoes. But, I'm limited there with a $1000 bankroll and a $1000 maximum bet, so I can't fully test my scenario.

Are you saying that you hit a string of 8 consecutive losses in each of 8 straight shoes? Losing streaks are common, but that seems weird. Of course, if you are not resetting to $5 after a win, then this is much more in line with normal expectation.

This will need to be my last post on this thread as the underlying concept is without merit as I have stated several times now.

No, I'm not saying that.
I'm saying that I couldn't continue the negative progression system through each of the eight shoes because I wasn't able to place the next bet that was called for ($1000 bankroll).
I had to stop at the following places in each of the eight shoes:
$440, 22 hands, 27% win
$285, 38 hands, 36% win
$60, 22 hands, 31% win
$195, 28 hands, 46% win
$400, 11 hands, 18% win
$545, 14 hands, 21% win
$800, 58 hands, 43% win
$480, 31 hands, 45% win