Blackjack & Coin tossing

Good morning to All
first of all I beg your pardon for my english. I will do my best to explain my thoughts. Hope not to be stupid in my observations and questions. Forgive me before you read me :-)
I am a BJ newbie. I was fond of Roulette a few years ago. My balance was up when I left (just a good luck streak). I played roulette in most of the european casinos. I am not a pro. Just for fun but using odds to get an edge.
Right now I play mostly BJ on an online casino and just a bit of roulette. I prefer to bet at live BJ tables over the internet, at least I see the physical cards. No algos that resets the odds at every hand.
One week ago I did not even know BJ rules. Then I got to Wizardsofodds website and found very interesting stuff. I do not like math and statistics at all. They were my very first two exams at University. This my approach: try to beat the worst enemies first when you are fresh and full of strength.
By the way, in these days, after playing BJ for hours, few thoughts have emerged. Do not forget, if my math is wrong, feel free to insult me :-)
If I have understood well the House as an edge of less than 1%, maybe 0.50% if you play basic strategy (mr. Wong docet). After a few days of good winnings I lost a few hundreds in 1 night playing blackjack. I had 16 consecutive negative hands! It seemed a cheated game. I played strictly Wong's table. After the loss, I chose to play for free and try to understand if it was bad luck (I do not believe it exists) or simply a couple or more deviation standard from the mean.
On the long run, the House has a clear edge. How can you beat it? I guess, leaving the table every time you have a profit. Plain and simple, isn't it?
Then I started to think that BJ is like Roulette (less than 50% odds to beat the House). But that is "almost" equal to tossing a coin. That is my starting point. How do you manage your money in a tossing coin tournament? Actually I guess you can't. So far. Even if you have 50% odds to win in the long run, you can go underwater in the short term. For example, if you bet $100 on heads for 1000 hands you could lose more than $4000 when tails rules the series.
Here it is the observation/question for you: if I am not mistaken BJ, Roulette or Coin tossing are all playings that revert to the mean. The best way to bet on this stuff is to "buy the dips" i.e. betting when you reach 2 or 3 standard deviations from the mean. You may think "Oh man, you are genius! Ring the bell when you find the right spot". Betting on reversion to the mean could be painful in some instances. But suppose that your odds are higher after a long negative streak. The point is: is it 10, 20 or 100 consecutive negative hands?
Of course if this concept was already analyzed could you please give me some indications?

If this approach does not sound too silly, I could share a few charts to support my primitive analysis.

Thanks in advance for your comments, bad or good.

TT

Hi,
Welcome to the forum. You raise questions that have been answered often here.

There are indeed games where the result is near as damn it 50/50 and where house edge is almost negligible. You COULD beat the house edge of Blackjack by card counting. You COULD maybe get a financial advantage by exploiting bonuses. However YOU CANNOT and WILL NOT 'get an edge' in Blackjack 'buy using the odds'

Just like tossing a coin the more often you take a 50/50 ( or near 50/50 ) bet, the closer your percentage chances will be of hitting the expected return. percentage results do indeed revert to the mean. But Numerical results DO NOT revert to the mean.

e.g toss a coin 3 times and call the result wrong twice and correct once and your percentage success is 33.33 but lets say you call results for another 100 coin tosses and by some miracle you get 50 correct and 50 wrong. That would give you a total of 52 wrong and 51 correct. your percentage success has regressed to 51/103 improving from that 33.33% to 49.51% BUT YOU ARE STILL 2 coin tosses short of expected value. The Universe doesn't keep track of the fact it owes you 1 correct call to square things up. In the example above, the reality is that you might end up with say a total of 46 correct out of your 103 calls. That's 44.66% success: Much better than your original 33.33%, but if you'd been betting $1 per call you would have gone from being $1 down to being $7 down. Regressing to the mean did you no good at all.

Remember STREAKS MEAN NOTHING.
The UNIVERSE DOESN'T KEEP TRACK of what it owes you.
DICE and ROULETTE BALLS HAVE NO MEMORY of what you won or lost on previous rolls.
BUYING THE DIPS or QUITTING While you are ahead means nothing. The Universe doesn't know or care that you left the casino last night. locking in your winnings. Life is just one long session.
See my Blog https://wizardofvegas.com/member/oncedear/blog/#post1370 or search the forum for the words regression and gamblers fallacy and streaks.

Blackjack can be beaten by counting, but it's a chore. Bonuses can be exploited. All the info is on the forum if you seek it out.

16 hand loss in a row is more frequent than you might imagine. Some SOME online casinos do cheat! Most don't need to.

Firstly BJ is slightly different to other Even money games. Craps, Roulette, Coin Tossing have no memory of previous results. Thus the next game is totally independent of previous results. For instance HHHHT has the same chance as HHHHH, so after four (or chose your own number) consecutive Heads the chances of a Head remains at 50%.

Secondly the "returning to mean" is a statistic and can be slightly misleading. For instance if you toss 100 coins the average will be 50 Heads but only 95% of the time will your result be within 2Sds or between 40 and 60. If you continue to toss coins you will be closer to the mean, but this does not imply within 10 either side, in fact you're likely to be numerically further away.

The mathematics :
Standard Deviation = SQRT (N p q) using N = 100, p =1/2 q = 1 - 1/2.
Results are within 2 SDs 95% of the time.

As the numbers get bigger you will be closer to the mean but that will be a proportion. So after 1 million your results should be between 49.9% and 50.1% but that also corresponds to being up to 1000 either way; the absolute number actually increases.

Coins Tosses	SD	Range
100	5	40-60
10k	50	4900-5100
1m	500	499000-501000

Regarding your BJ experience, when investigating new games one method is to run simulations. It usually takes well over 100 million hands to get reasonably consistent results. You can find the player evens wins sometimes for runs of only a few thousand. For instance if a coin toss game paid 98c on each Head and took $1 for each Tail the Player has a 31% chance of coming out ahead after 10k tosses. However after 1m the chances are less than 1 in 1Bn!

Thus in a fairly played game, e.g. you're not counting at Blackjack, not peeking at cards, not playing video poker etc.., in the long run the house will win. It makes no difference whether you've just had a good run or a losing run, your chances for the next run are always the same. And they're always in the house's favour!

Quote: twicetrader

feel free to insult me :-)

Here it comes!

Just kidding.

Yes, regression to the mean, that is very easy to misunderstand. In the plainest language I can think of, look at it like this: the cards, dice, balls, whatever, will not care or know if you won or lost or make any effort to get you your money back if you lose it. Then, to make you feel like a fool, in the long run, perversely, the statistics will show they were fair all along by percentages. Not amounts. Percentages.

Another matter: BJ is low in variance, so you are in a game you are supposed to lose at and it is harder somewhat to get lucky and win. [This is shown by the way as you play EV quickly starts to equal SD, the ev/sd ratio]

There is actually a name for this...the gambler's fallacy!

Here is a Wikipedia link and the intro text (which I broke into two paragraphs): https://en.wikipedia.org/wiki/Gambler%27s_fallacy

"The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future (presumably as a means of balancing nature).

In situations where what is being observed is truly random (i.e., independent trials of a random process), this belief, though appealing to the human mind, is false. This fallacy can arise in many practical situations although it is most strongly associated with gambling where such mistakes are common among players."

Quote: MrGoldenSun

There is actually a name for this...the gambler's fallacy!

Here is a Wikipedia link and the intro text (which I broke into two paragraphs): https://en.wikipedia.org/wiki/Gambler%27s_fallacy

"The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future (presumably as a means of balancing nature).

In situations where what is being observed is truly random (i.e., independent trials of a random process), this belief, though appealing to the human mind, is false. This fallacy can arise in many practical situations although it is most strongly associated with gambling where such mistakes are common among players."

This mathematical solution, though inadequate in it's entirety, can be used to explain many things. Yes, there's 1 and 2 and 3 standard deviations to the expected results for any proposed EV. Is there a limit to the number of standard deviations, or do we go with three as being good enough for most gov't work? Can you have a hundred, or a million? Can you have nothing, and then have a universe? How many SDs is that probability?

The bell curve goes on out to infinity and negative infinity. You can have as many standard deviations as you want.

The chance you'll land more than 7 sigmas out is 1 in 390 billion, so you don't need to go very far out before it starts becoming non-practical.

https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule#Table_of_numerical_values

Quote: MrGoldenSun

The bell curve goes on out to infinity and negative infinity. You can have as many standard deviations as you want.

The chance you'll land more than 7 sigmas out is 1 in 390 billion, so you don't need to go very far out before it starts becoming non-practical.

https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule#Table_of_numerical_values

I am going to assume that the existence of the universe is well beyond 7 sigmas, which makes this discussion non-practical. I will remove myself immediately ;-)

Good morning to All
thanks for your fast response. Much appreciated.
I would like to give you a better idea of my thought. A picture worths thousands words, isn't it?
unfortunately I see that here is not possible to upload images. Do you have suggestions to do that and keep going on my explanation?

Thanks
TT

Quote: twicetrader

...not possible to upload images....suggestions...

As an example all my pictures are at a hosting site ( http://s781.photobucket.com/user/AbbaPix/library/wizard?sort=3&page=1 ). You could do the same, create an account and post a link to them. I don't know for sure, as you're new, you may not be allowed direct links; if so you may have to fabricate them.

Morning Charlie,
thanks for that. Tried to upload the link but in preview I see no link.
I could change "\" with asterisk but I do not want to violate any rules here.
Could you tell me how can I do that?

Thanks in advance
TT

Further to your PM here is a copy of the picture you sent me a link to.

Thank you very much Charlie!
Now herein the explanation to the chart:

"The chart shows the money line betting $1 on Heads (random sample). As per our conversations, even if I have a 50% odds to win, after 1000 rounds I am actually losing $36 (right axes). In my honest opinion mean reversion does not mean win/loss gyrates on zero level. It simply tell us that if we "detrend" the series we get an "almost" regular ups and downs. The gray line (left axes) is one of the most simple indicator to analyze mean reversion. It oscillates between 0 and 100.
Suppose that I start betting $1 on every hand. When the MRI touches 25 level (green arrow) I start to bet $10. When the MRI crosses above 70 level (red arrow) I return back to $1.
Of course I need an uninterrupted series and for this reason I still play $1 even if the indicator is telling me that odds are against me.
As you could verify we had only one failure and we could avoid the following drawdown stepping back to $1 bet after 3, 5 or 6 consecutive losses (just guessing).
With this approach we could have a profit of "n" dollars instead $35 loss.
Two considerations here:
1. do not concentrate on levels, this is a very crude analysis I am starting these days. Concentrate on the idea.
2. I show you this because I am not an expert and I need to understand if there is a bug with this approach. Remember I am not a math fond.

Thanks in advance
TT"

This is the mathematical answer.

I'm not pretending to fully understand your explanation but essentially you have a random walk based on Heads and Tails and usually betting $1. So I'm guessing if things go wrong and you reach "25" then you start betting $10 until things get better and you reach "70". Then you go back to betting $1.

Essentially this is a variation of a Martingale or similar systems based on adding and crossing off numbers. A Martingale uses bets of $1 $2 $4 etc, essentially making $1 when you eventually get the win. The general idea is that if you start small then if you win you've won (say $1). If you start losing then increase your bets (in your case $10) until you get it all back and make $1. Reset to the starting condition and repeat. Make lots of $1 and you're rich!

The problem with these systems is they usually make you $1. You continue with the process and make a few $1's. However there's always a very small chance, because you only have finite money, that a long run against you wipes you out.

For instance with Martingale you could start with $1023 and unless you get a long run of Tails will keep picking up $1's. So if you ran trials it is perfectly possible to see the system kept making a profit. It is only if you saw a run of Ten Tails (or Eleven if you've built up profits) that your last bet of $512 or more will lose and wipe you out.

This is the non-mathematical answer.

If you play a game where the house has an advantage you can try and use a system where you bet small but increase your bets after a loss. Normally you'll eventually win and make a profit. If you do this over a thousand games it is quite possible to show a profit. I've seen people do this at Roulette and even win over a few weeks.

The downside is if you are increasing your bets, one day you'll hit a really bad streak and run out of money. In the long term your daily profits will be wiped out by the big loss.

Running Simulations

If you're trying to prove something by simulation it is essentially to run enough games (aka trials) to reduce the effect of variance [luck] and, where there are long-shot events that affect the outcome, a reasonable number of these events occur. For instance if you were simulating Video Poker then you have to have lots of situations where you receive or get close to a Royal or Straight Flush.