Lucky Streak - Bad or Good - Might Last Your Lifetime ...

My interest here might be described as the interface between the human parameters of a gambler and the mathematics of the games.

I think it is interesting that a person may be an overall lifelong "winner" through no effort or skill but rather as the result of a lucky streak that anyone else might have encountered in their lives.

I imagine that this could be described in mathematical terms. The proportion of winners after a certain number of hands of "perfect play" at any Game A, B, C ... I have seen it reported as the probability of being ahead after a certain number of rounds of, say, American Baccarat. This would be the expected mathematical probability. And one might assume reality would reflect this theory.

My curiosity was peaked when I saw blackjack simulator provide outcomes for a lifetime's play. Repeated runs of the simulator calculated quite a variety of outcomes for the exact same game played with the exact same strategy. Then I found a coin toss simulator where heads won a dollar and tails lost a dollar. That simulator plotted winnings on the vertical against number of flips. Doing a large number of flips did not result in the graph approaching zero. Rather, in each trial the result after, say, 1,000,000 tosses, was hugely variable.

A person could easily become rich this way or lose a fortune just as easily. Luck was, apparently, the sole determining factor.

Well, a person might just be lucky in this life. Lucky as in good luck (blessed) or lucky as in bad luck (cursed). This could apply in general and it might apply in a gambler's life. You might play Blackjack every night for 4 hours along with your neighbour, each of you playing exactly as skillfully. And after a year or 10 years or a lifetimes' play, you might have very different outcomes. Merely as a result of ... luck.

Can someone reveal precisely the mathematical terms used to describe this. I would anticipate that such a description would include the variance of each specific gambling game, the probability of encountering streaks of different lengths, the human life parameters of a gambler (number of years lived, rate of play, and others), maybe some stuff about utility functions or others. I do not want to put words in peoples' mouths as I am not a mathematician.

In coin tossing, skill is zero, luck is, presumably, everything. No matter how long you play. But when you sit down at a Blackjack game to play for an evening, what are the odds that your skill can overcome (bad) luck. Or that (good) luck can overcome your bad skill.

What's the interface between luck and life. Describe this mathematically. ;-)

Your posts are starting to feel robo-ish ... either that or you are attempting to keep your threads alive by repeating them. That is verboten!

As for your question, I can only speak for myself, but you seem to be profoundly interested in a topic interesting enough, but the thing is, you're asking for a very thoughtful response in a manner that is a little off-putting. As in, "get cracking on my problem ye underlings"

Variance

Quote: odiousgambit

Your posts are starting to feel robo-ish ... either that or you are attempting to keep your threads alive by repeating them. That is verboten!

As for your question, I can only speak for myself, but you seem to be profoundly interested in a topic interesting enough, but the thing is, you're asking for a very thoughtful response in a manner that is a little off-putting. As in, "get cracking on my problem ye underlings"

Not a robot; I could not figure out how to move my topic over here when I realized this was likely a more-suitable forum. I deleted the first post & mentioned the move in the other forum. That's all I knew/know how to do.

Sorry you found my tone off-putting. It was intended in jest. A light type of jest. You see the winking smiley-face there?

Was there anything else?

Quote: ncfatcat

Variance

Wow. Thanks for that.

I bet you're thought of as the resident genius around these parts.

relieved you are not a robot [can a bot claim not to be a bot? LOL] Perhaps I am obliged to examine your question again.

Quote:

I think it is interesting that a person may be an overall lifelong "winner" through no effort or skill but rather as the result of a lucky streak

This can be pretty mind-bending actually, for a gambler to realize this. Back when I was using Wincraps a lot, I did many trials and found that a flat-betting player with line bets and max odds will be a lifetime winner a handsome percentage of the time. It depends of course on some parameters. Either the player needs to seldom play, a few sessions a year, or he needs to be able to do at least 5x odds. At 10x odds or more, he could be a very frequent player and wind up a lifetime winner. The problem of course is it is easier to wind up a lifetime loser. I am superstitious enough to believe that bad luck would attend the fellow who attempts to be a lifetime winner with fat odds.

I blogged about this, see on the linked page "10x odds explored"

https://wizardofvegas.com/member/odiousgambit/blog/10/

He's not wrong. Good luck and bad luck are just non-mathematical terms for variance. As soon as you start trying to quantify luck, variance and related statistical terms are what you'll use. What more is there to say?

Quote: MathExtremist

He's not wrong. Good luck and bad luck are just non-mathematical terms for variance. What more is there to say?

Quite a bit really.

And, thankfully, someone's already begun to say it.

I do think it's interesting that luck can overpower our best efforts in this life. And that a streak of luck may be long enough to define a person's success in their entire life. Including their gambling life.

It has implications for how one might approach life or problems within it (say, a gambling game). How much effort to put in. Or how far to lean back and accept the ride.

It also may affect how much pride we take in our accomplishments. Or how much praise or disdain we have for others who are "successful" or "losers".

Quote: ElWealtho

Quite a bit really.

And, thankfully, someone's already begun to say it.

I do think it's interesting that luck can overpower our best efforts in this life. And that a streak of luck may be long enough to define a person's success in their entire life. Including their gambling life.

It has implications for how one might approach life or problems within it (say, a gambling game). How much effort to put in. Or how far to lean back and accept the ride.

It also may affect how much pride we take in our accomplishments. Or how much praise or disdain we have for others who are "successful" or "losers".

OK, lets get to it. What are you selling to make us all 'El Wealtho"?

Quote: ElWealtho

Quite a bit really.

And, thankfully, someone's already begun to say it.

I do think it's interesting that luck can overpower our best efforts in this life. And that a streak of luck may be long enough to define a person's success in their entire life. Including their gambling life.

It has implications for how one might approach life or problems within it (say, a gambling game). How much effort to put in. Or how far to lean back and accept the ride.

It also may affect how much pride we take in our accomplishments. Or how much praise or disdain we have for others who are "successful" or "losers".

Humans as a species are terrible at comprehending randomness. We're not wired to do it. Our giant convoluted brains evolved to detect patterns and extrapolate the future, even where no causality exists. This is why roulette became so much more popular after the LED readerboards were installed. The fallacy of the maturity of chances is a fallacy for a reason.

There is no mystery in the random distribution of a gambling game. The impact of a player's skill (e.g., counting cards) can be precisely quantified. The probability of a gambler being ahead after N days, months, or years can also be quantified. It's all just statistics.

But I wouldn't try to make the leap to quantify success in life or disdain for others with the same statistics. That's the stuff of self help books and airport hotel seminars. The truth is that gambling games are based on independent random trials: the dice have no memory, etc., and there is a particular kind of math that helps you understand such processes.

Your life isn't like that (unless you live in "Dark City"). Chances are very good that when you wake up tomorrow, your situation will be about where you left it when you go to sleep tonight. The days in your life are not independent from one another so you can't use the same kind of math to describe them. There is *different* math you can use, but that math is irrelevant to gambling games. Except poker.

So I disagree that there's much else to say about your original question, but I also get the feeling that you're not actually asking, you're telling (or you're about to). So what are you telling?

Quote: ElWealtho

I do think it's interesting that luck can overpower our best efforts in this life. .

Luck has no power, luck is not a thing
at all. It's a purely human invention for
describing circumstances that don't
go the way we desire them to. One
persons bad luck can easily be another
persons windfall. Luck is not predictable
outside the parameters of calculated
variance, where that's even possible.

Luck doesn't exist outside of our perception
of what we think luck is.

Quote: ElWealtho

I do think it's interesting that luck can overpower our best efforts in this life.

But it's far more likely that our efforts will overpower luck (for good or bad). How much more likely? The more you play, the closer you get to 100%

Quote: EvenBob

Luck has no power, luck is not a thing
at all. It's a purely human invention for
describing circumstances that don't
go the way we desire them to. One
persons bad luck can easily be another
persons windfall. Luck is not predictable
outside the parameters of calculated
variance, where that's even possible.

Luck doesn't exist outside of our perception
of what we think luck is.

+1.

But I still say good luck and use the term lucky. It just sounds strange to say I had good variance today. Or to say, good variance to you.

Quote: AxelWolf

But I still say good luck and use the term lucky..

Because it's convenient. I don't use it because
I don't believe in it. Just another superstition.
My car won't start in January. It's not bad luck,
it's a bad battery.

Some good stuff here.

Nope, I'm not really about to say anything as if it's definitive. I value the opportunity to explore these subjects with others.

I'm very rusty. I read some quite heavy gambling/stock trading math - as well as the psychology of gambling - about 20 years ago. All that stays with me are the remnants of questions I have been trying to reformulate here.

Well, duckduckgo is our friend and 2ducking gambling utility functions is a good start. Turns out Expected Value is quite a small bit of the way we might best approach any gamble. For starters, each gambler has a distinct circumstance (bankroll, personality, skill set, etc.) That's the interface: where the human part of the equation meets the math of the game.

As far as some of the speculation here - say, about the degree to, or manner in, which luck is likely to affect our lives - people's belief systems are coming to the fore. None of us actually knows the answer. There is philosophy lurking nearby, I think.

I see The Wizard has written on the Kelly Criterion and look forward to reading this. This Wikipedia article on Expected utility hypothesis is also stimulating.

People tend to believe. Life becomes dull and boring without having a dream. Luck is a part of someone's believe, surely, it does not exist, but it's more fun to believe that it does.

Quote: EvenBob

Luck has no power, luck is not a thing
at all. It's a purely human invention for
describing circumstances that don't
go the way we desire them to. One
persons bad luck can easily be another
persons windfall. Luck is not predictable
outside the parameters of calculated
variance, where that's even possible.

Luck doesn't exist outside of our perception
of what we think luck is.

Dunno of much that exists outside of our perception. ;-)

So the concept of luck seems to be an issue. Let's say I changed the thread title to "Gambler's Streak Can Last a Lifetime". Or is this just a rose by any other name?

Could I use the word "fortune"? One fortuitous event - like inheriting wealth or good genes - can forever change a person's life. Just think what a series of them might do.

I don't understand this: "Luck is not predictable outside the parameters of calculated variance, where that's even possible."

Mathematical theory will say that each player must play the best strategy - the one most likely to succeed. But this rules out such concepts as luck, intuition, horse-sense, precognition - not to mention the more obvious human parts of the gambling equation that I have mentioned above. And most people have a sense of the existence of these.

At the end of the day, or indeed lifetime, for one gambler, was the math strategy correct? Nobody knows. Now, for a large casino over a longer period of time, the accuracy of the theory can be better tested.

Quote: Dicenor33

People tend to believe. Life becomes dull and boring without having a dream. Luck is a part of someone's believe, surely, it does not exist, but it's more fun to believe that it does.

Likin' this. A lot. Except the part about luck surely not existing. I do not believe you believe that!

Additionally, we are not even aware of much of what we believe. And, we hold beliefs that are not of our choosing.

I'm going with luck. I see it all around me every day. Good fortune. Misfortune. It's Chance made human.

Quote: MathExtremist

... The impact of a player's skill (e.g., counting cards) can be precisely quantified. The probability of a gambler being ahead after N days, months, or years can also be quantified. It's all just statistics.

This is not correct.

The player may be able to "count cards" perfectly well, but make unforeseen mistakes. Perhaps the result of something they ate, a lack of sleep, becoming mildly dehydrated. Impossible to quantify.

Furthermore, human fallibility aside, while the probability of a strategy "being ahead after N days, months, years" is possible to calculate, there is no way to predict the accuracy of that theory for one particular gambler. To illustrate this, "Joe has a fantastic streak, quite outside the norm." The norm here is a standard deviation or two within the probability distribution, and Joe is probably near that curve somewhere. But it was always impossible to predict where.

Let me use another example. The weatherman predicts a 20% chance of rain. It rains. Was the weatherman's prediction accurate? Nobody can say. Or, say it doesn't rain. Again, the accuracy - the utility - of the weatherman's prediction is completely unknown. There are not enough data points.

This is going to rub some people the wrong way. It's goes against what most of us have been taught for years: it is entirely possible that, for a gambler, a hunch may be more accurate than a mathematical prediction. And that may often be the case.

Quote: ElWealtho

Let me use another example. The weatherman predicts a 20% chance of rain. It rains. Was the weatherman's prediction accurate? Nobody can say. Or, say it doesn't rain. Again, the accuracy - the utility - of the weatherman's prediction is completely unknown. There are not enough data points.
.

On this point particularly, and not to hijack the thread.

A 20% chance of rain does not mean quite what you think it does. There is a forecast area, well-defined to the meteorologist (via lat-longs) but generally not defined to the viewer beyond a vague "here". Probably a fair but rough average is 5000 sq. mi. or a box about 70 miles on a side. It WILL rain on 20% of that geographic coverage area during the time frame of the forecast. Atmospheric conditions (temperature, pressure, air density, air mass movement) and the physics of saturation, condensation, and precipitation cycles give them the percentage to be expected with a near guarantee.

However, they can't tell you if you, there on the corner of First and Main, will be underneath the air mass just as it releases its moisture (though they're getting better at it all the time). So from your perspective, you might have a 20% chance of experiencing rain. On average. Or there can be particular geographical features (terrain, bodies of water) which combine with prevailing winds, where particular parts of your forecast area receive rain 60% of the time, and the rest of the area 5% with those areas moving around enough that the 20% is still accurate for any entire forecast area. But you think the weatherman's right only 1 time in 4, because you're in that 5%, there on First and Main.

So. Accuracy is known to a high degree, as NOAA and others constantly review their accuracy and update their algorithms and modeling, to where now they're accurate in the 90-95% range. But from your stationary POV, you may have an entirely different impression.

Just my two cents on this topic, yours for free.

Gambling. The creation of risk for the sole purpose of assuming that risk. Some folks win, some folks lose. Some folks break even.

Some - they play games where they might use some skill to try and turn the odds more to their favor.

The notion of two separate but equally skilled players playing for a specific period of time and one player being on one side of the bell curve and the second player being on the opposite side ...well, that's not anything strange there. They're just 2 points on the graph.

Luck? I'm not sure I believe in luck. I put more stock into Providence. But - that's another post for another time.

Quote: ElWealtho

At the end of the day, or indeed lifetime, for one gambler, was the math strategy correct? .

Of course not, there is no math for the
player, only the game. There is not even
good math for the casino. The math only
applies to the game, and that means the
game being played on the entire planet,
24/7. That math is extremely reliable.

The rest of it is hit or miss, at best. A casino
can easily have a losing month, or a losing
quarter. But the game being played in
thousands of casinos worldwide, mathwise
ticks along like a Swiss watch.

Quote: EvenBob

But the game being played in
thousands of casinos worldwide, mathwise
ticks along like a Swiss watch.

That's one theory.

As you've said, the math applies to the game only. However, the game is not played globally; there are many variations. Even were all casinos to offer the same game, we've not been able to confirm that a global-sized sample is sufficient.

Who's to say that our tiny corner of the universe is itself not experiencing a statistical aberration. One that might last eons.

Or that the math is correct.

Everywhere, everywhere, everywhere I see the arrogance of mathematics. Well, my guess, FWIW, is that math applies wonderfully - for things that can be measured.

But there seems to be considerably more at play.

You've go to know when to hold 'em; know when to fold 'em,
Know when to walk away; know when to run.

Now, casino table games - excepting poker - and slot machines do lend themselves essentially to statistical analysis. Does that mean no-one should ever play a hand? Or 20 hands? Or 1,000 hands?

I'm gonna go out on a limb and say no-one should ever play 10,000 hands of any negative-expectation casino game. At least at one sitting. ;-)

If the universe is infinite (which I would think is what the law of large numbers assumes) and our individual game is finite, anything is possible.

Several friends of mine made $millions in the stock market in 2008. They then lost most of those millions. Had they gotten out they'd still be multi-millionaires. Had they never gotten in, they'd be poorer but less psychologically damaged. (Losing $millions can take its toll.)

So the question becomes when to get in and when to get out. Can you know this? Well, you can intuit this.

You don't know if you'll live through the day but you take the gamble anyway. The safest bet might be to stay in bed. But that isn't really living for most people on most days. We take the risk and carry on. NO mathematics involved.

Happened upon this today:

Odds Are, It's Wrong

It's about the astonishingly high levels of error made using statistics.

I used to bank games for a corporation in Ca. I was shocked to learn that I could have negative results for over a month at a time at my table, and that my boss thought it no big deal. Then, later, I learned of online poker players who could prove with tracking software that they'd run well below expectation for tens of thousands of hands.

Quote: TomG

But it's far more likely that our efforts will overpower luck (for good or bad). How much more likely? The more you play, the closer you get to 100%

I disagree. If I remember right, Machiavelli spoke of "virtue" and "fortune," and said the latter was far more important, though beyond our control. That's how I tend to think of it.

A lot of it will come down to what you define as luck, chance, fortune, whatever. You happen to be born in a time and place where the game of baseball, with just the right equipment and rules has evolved in such a way that a few quirks about your body allow you to make millions because you can throw a great curveball. Think of all the things that have to happen for that to be the case. Is that luck?

Either way, gambling constructs scenarios in which luck is the dominant factor. Yet it still takes a long time to even out.

I don't think we get tens of thousands of hands in life. You choose your career path only a few times. You enter romantic relationships only a few times. You have kids only a few times.

Never mind your initial draw, in terms of natural gifts, the country you are born into, your parents, your initial economic status and health.

It all depends how you want to describe it. If determinism is true, is everything luck? Nothing?

Quote: Rigondeaux

I used to bank games for a corporation in Ca. I was shocked to learn that I could have negative results for over a month at a time at my table, and that my boss thought it no big deal. Then, later, I learned of online poker players who could prove with tracking software that they'd run well below expectation for tens of thousands of hands.



I disagree. If I remember right, Machiavelli spoke of "virtue" and "fortune," and said the latter was far more important, though beyond our control. That's how I tend to think of it.

A lot of it will come down to what you define as luck, chance, fortune, whatever. You happen to be born in a time and place where the game of baseball, with just the right equipment and rules has evolved in such a way that a few quirks about your body allow you to make millions because you can throw a great curveball. Think of all the things that have to happen for that to be the case. Is that luck?

Either way, gambling constructs scenarios in which luck is the dominant factor. Yet it still takes a long time to even out.

I don't think we get tens of thousands of hands in life. You choose your career path only a few times. You enter romantic relationships only a few times. You have kids only a few times.

Never mind your initial draw, in terms of natural gifts, the country you are born into, your parents, your initial economic status and health.

It all depends how you want to describe it. If determinism is true, is everything luck? Nothing?

Great post. Thanks!