[Winstonm]

A generalized question/discussion.

Years ago I played lots and lots of poker in Las Vegas and over the course of time saw some people who had more than their fair share of luck and others whom luck abandoned time after time.

I've seen similar instances in bridge - the declarer who has a "knack" for making odds-against plays at the right time or who finds more than his or her share of outstanding opening leads.

It has always made me ponder this question, and I've never had the chance to pose this hyposthesis to an outstanding math mind so I'll hope someone or a few will respond.

My understanding is that averages are based on the concept of the Law of large numbers - to me this would seem to say that fluctuations are normal and to be expected. This large number is what.....billions of occurences? I don't know.

But if I may I'd like to use poker as an example, as it's a more clear picture. My hypothesis is that any one person cannot in his or her lifetime play enough hands for the LOLN to operate; therefore, one could play his entire life and be "unlucky" while another could be "lucky" his entire life and neither aberation would affect the overall expectency. Not only do you see this on T.V., but I can assure you it happens in real life as well....one person will seem to look down at his hold em hand and about every third hand will be playable, whereas another player will have to wait through 9 or 10 hands to find a good combination of cards.

Is this lifetime of luck/no luck just a normal variation and one person is on the right side while another is on the wrong side?

Or to put the question another way - if a flush is supposed to make 1/3 of the time and player A always makes his flush while players B and C never do, the overall percentages are right but that doesn't help B and C and makes A look like the greatest of all time.

So is it possible for one person to be lucky his entire card career while another is unlucky his entire career because neither play enough hands for the Law of Large Numbers to be a factor. Is luck/non luck simply a matter of being on the right side of fluctuation?

Thanks,

Winston

[hrothgar]

Winstonm, on Nov 11 2005, 09:11 PM, said:

A generalized question/discussion.

Years ago I played lots and lots of poker in Las Vegas and over the course of time saw some people who had more than their fair share of luck and others whom luck abandoned time after time.

I've seen similar instances in bridge - the declarer who has a "knack" for making odds-against plays at the right time or who finds more than his or her share of outstanding opening leads.

It has always made me ponder this question, and I've never had the chance to pose this hyposthesis to an outstanding math mind so I'll hope someone or a few will respond.

My understanding is that averages are based on the concept of the Law of large numbers - to me this would seem to say that fluctuations are normal and to be expected.  This large number is what.....billions of occurences?  I don't know.

But if I may I'd like to use poker as an example, as it's a more clear picture.  My hypothesis is that any one person cannot in his or her lifetime play enough hands for the LOLN to operate; therefore, one could play his entire life and be "unlucky" while another could be "lucky" his entire life and neither aberation would affect the overall expectency.  Not only do you see this on T.V., but I can assure you it happens in real life as well....one person will seem to look down at his hold em hand and about every third hand will be playable, whereas another player will have to wait through 9 or 10 hands to find a good combination of cards.

Is this lifetime of luck/no luck just a normal variation and one person is on the right side while another is on the wrong side?

Or to put the question another way - if a flush is supposed to make 1/3 of the time and player A always makes his flush while players B and C never do, the overall percentages are right but that doesn't help B and C and makes A look like the greatest of all time.

So is it possible for one person to be lucky his entire card career while another is unlucky his entire career because neither play enough hands for the Law of Large Numbers to be a factor.  Is luck/non luck simply a matter of being on the right side of fluctuation?

Thanks,

Winston

The human evolved to to discover patterns.
We are VERY good at pattern recognition.
We are so good at pattern recognition that we find lots of patterns where none exist.

On to your question: The important thing to remember about the Law of Large numbers is that you don't need at that large a number. Asymptotic normality is a wonderous thing.

I like to believe that people are to differentiate between luck and skill. If a card player is consitantly "lucky" while making technically incorrect plays, he often gets a reputation as a cheat.

[david_c]

Winstonm, on Nov 11 2005, 07:11 PM, said:

Is this lifetime of luck/no luck just a normal variation and one person is on the right side while another is on the wrong side?

No. If the difference is significant enough that you can notice it at the table, then there's no way a player can keep it up for a lifetime. There must be something else going on - "you make your own luck at this game".

(Note - the number of genuinely "lucky" players over a set of n boards can be estimated using the central limit theorem.)

[Blofeld]

david_c, on Nov 11 2005, 01:33 PM, said:

Winstonm, on Nov 11 2005, 07:11 PM, said:

Is this lifetime of luck/no luck just a normal variation and one person is on the right side while another is on the wrong side?

No. If the difference is significant enough that you can notice it at the table, then there's no way a player can keep it up for a lifetime. There must be something else going on - "you make your own luck at this game".

Except that as Richard points out, people have a tendency to spot patterns that aren't there. If their luck is actually average, but you notice it when they're [lucky/unlucky] but not so much when they're [unlucky/lucky] then you could be seeing false patterns.

As an example.

Other than that I agree with you.

[Winstonm]

david_c, on Nov 11 2005, 01:33 PM, said:

Winstonm, on Nov 11 2005, 07:11 PM, said:

Is this lifetime of luck/no luck just a normal variation and one person is on the right side while another is on the wrong side?

No. If the difference is significant enough that you can notice it at the table, then there's no way a player can keep it up for a lifetime. There must be something else going on - "you make your own luck at this game".

(Note - the number of genuinely "lucky" players over a set of n boards can be estimated using the central limit theorem.)

I wonder then how long this "out of the norm" can last before normalcy returns.

A couple years ago a young man named Moneymaker won the World Series of Poker by taking the worst hand into the pot and winning with it a disproportinaley high percetange of the time - so often that he won the tournament.

Obviously, 3 days in a tournament can be based on luck. But I've also seen poker players have a good run for a year or two and then fade....during the run they seemed to hold a significantly higher percentage of good hands that expectancy would anticipate; so can luck (my definition is being on the right side of normal variations) last for a year or two? From my observations of the poker world, it would seem so.

Winston

[tysen2k]

For poker, you must record your results for 20,000 hands for you to have a reasonable idea about how good you are and 50,000 to be much more sure. But even after 50,000 there is still some error.

In live play at about 30 hands per hour, that's 700-1700 hours of play or 4-10 months of a full-time job.

Playing online and 4 tables at once, you can get up to 240 hands per hour. So 80-200 hours of play will do it: 2-5 weeks full time.

Needless to say, you can't tell anything about anyone's skill level after only a few hours.

Tysen

[Winstonm]

tysen2k, on Nov 11 2005, 01:45 PM, said:

For poker, you must record your results for 20,000 hands for you to have a reasonable idea about how good you are and 50,000 to be much more sure.

In live play at about 30 hands per hour, that's 700-1700 hours of play or 4-10 months of a full-time job.

Playing online and 4 tables at once, you can get up to 240 hands per hour.  So 80-200 hours of play will do it: 2-5 weeks full time.

Needless to say, you can't tell anything about anyone's skill level after only a few hours.

Tysen

Thanks. So if I understand correctly, 50, 000 samples should be enough for the Law of large numbers to reduce variations?

Maybe this is my question: if you look at it as a graph with 50% as expected, fluctuations for a short period of 80% upward then later downward would balance each other out.

My question is does this occur or are the fluctuations less severe? It seems that the rather severe fluctuations can and do occur, and I can assure you that even 100 hands of severe fluctuation can get you broke.

Winston

[tysen2k]

Winstonm, on Nov 11 2005, 10:54 AM, said:

Maybe this is my question:  if you look at it as a graph with 50% as expected, fluctuations for a short period of 80% upward then later downward would balance each other out. 

I don't really understand what you mean here.

Quote

My question is does this occur or are the fluctuations less severe?  It seems that the rather severe fluctuations can and do occur, and I can assure you that even 100 hands of severe fluctuation can get you broke. 

That's why bankroll management is an important poker skill. You need to play at reasonable limits so that this doesn't wipe you out. Fluctuations will occur and you have to be able to ride them out.

[kenberg]

People study this of course but I don't, so not for the first time I will speak from ignorance.

I have been told that an analysis has been done of hitting streaks in baseball. If a guy has a certain probabilty of getting a hit when he comes to bat (varying over a range when from day to day) then of course there is a positive probability he will get at least one hit in each of n consecutive games. There are a lot of players playing a lot of games so pure random fluctuation should produce some long streaks. As I understand it, the DiMaggio streak of 56 games in 1941 is an extreme outlier pretty much no matter how you do the math. Of course most of the streaks go to the better players but even some modest hitters sooner or later should have a long streak.

I am in the process of moving, my books are packed, and I am no expert on probability anyway, but here is a possibly interesting fact. Suppose that you perform a fifity-fifty experiment repeatedly and independently (this is easier said than done). You record the results. If you do this repeatedly for a long time, it is highly probable your success rate will be near fifty percent. No surprise. What might be a little surprising is that it is not so likely that you will be frequently crossing the fifty percent line. After a while, a person will settle in on one side of the line or the other, staying near but not crossing it, for quite a while. It's possible, perhaps, that this would lead to some people being marked as (slightly) lucky, others as unlucky. Of course assuming the game is honest, this does not mean that on any future toss the "lucky" person has a better chance than the "unlucky" one, only that some histories in retrospect will appear lucky.

I imagine "How to gamble if you must", by Savage and Dubins, is usful if someone wants to dive into this. And of course Feller. Me, I'm retired. Someone else can do the work.

Ken

[Kalvan14]

I believe that luck exists (and oviously, bad luck too ). I do not know if "luck" is a blind cosmic principle, a nice mischievous lady or just the fact that some people can grasp patterns or sense underlying principles or whatever.
OTOH, it is obvious that humans evolution was strongly biased by the cpacity or not of recognising patterns: when the rains come, the ducks come...and equally obvious that we are often too quick to identify as a pattern something which is just a coincidence (the other night at the club there were 3 slams in a row in the first 3 hands played: is it a night when all slams make? The answer is no, but you possibly are slightly nudged to be more optimistic). Equally, most people are quick to identify a pattern of misfortune affecting them, while often good luck is assumed to be personal skill.
Bitter experiences (in particular, a famous hand featuring 3 aces against an inside straight) have taught me that odds are at best a non-committing suggestion

[pclayton]

I like Richard's comment - recognizing patterns when none are there. Or worse, bad bidding or play leading to good results, thus 'reinforcing' bad behavior. How many players have we seen in the 3,000 - 10,000 MP category that make a lot of quirky decisions.

Or to quote Adam Smith - we are all dead in the long run.

[han]

I know nothing about poker, but I am confident that there is no unlucky poker player. To be more precise: any poker player who plays a lot and consistently loses is a worse player than the people he plays with.

The same is true for bridge.

(I'm ignoring cheating)

[pbleighton]

"Or to quote Adam Smith - we are all dead in the long run."

That was John Maynard Keynes

Peter

[EricK]

I don't know much about poker, but I know a bit about backgammon. Because backgammon involves dice there is an element of luck, but good players playing against weak players always have the appearance of being lucky. The reason is that they position their pieces so that more dice rolls are good and fewer are bad. In other words they give themselves more chances to be "lucky" and fewer to be "unlucky".

A similar thing must happen in bridge as well. As a simple example, where there is a two way finesse, the expert will gather more clues than the non-expert and so is more likely to guess right - he is giving himself a greater chance to be lucky. A more complex example might be hands where the average player sees a finesse as the only chance to make the contract but the expert sees various other plans to try first and only falls back on the finesse as a last resort. When that sort of scenario is repeated, the expert will take fewer losing finesses by the simple expedient of taking fewer finesses overall - he is giving himself fewer chances of being unlucky.

Eric

[zasanya]

It seemed to me that the original poster was referring to holding good or bad cards and not playing or bidding those cards.It also seeed to me that he was concerned with rubber bridge or chicago where success is measured by money won or lost and not with duplicate bridge. So many of the responders answered a different question than the question asked.
My response is that "Yes.Good and bad streaks do exist."If a strong but unlucky player plays bridge for money against a weak but lucky player the strong unlucky player is not going to win.
However these streaks follow the laws of probability and when the strong player holds good cards he wins much more than the weak player could have, had he held those same cards.

P.S. : Please sort out the clauses in the last sentence

[Rebound]

There is an interesting element to probability that may relate to all of this. Take, for example, a coin toss, where over a large number of tosses, heads and tails will come up close to an equal number of times. If the first 100 tosses come up heads, a further 1000 tosses of the coin may result in an a roughly equal number of heads and tales but the original 100 head advantage will not be cancelled out, i.e., you will have a result of something like 600 heads and 500 tails. Hence, a person who achieves a lucky streak may feel as though he continues to be lucky whereas he/she is much more close to the mean.

Extending the example to poker, if you have a group of roughly equal skill, but 1 player wins the first 10 pots, it is entirely likely for money to change hands on a fairly equal basis for the rest of the night, but the gains made by that player in the first 10 hands should, probabilistically speaking, remain with that player.

Further, a study showed that people who consider themselves to be lucky, tend to perceive results in a much more optimistic fashion than those who feel they are unlucky. That is, given the same set of circumstances, a "unlucky person" may feel as though he/she had a bad break, where the "lucky person" will tend to see the silver lining, so to speak. This extends to where the "lucky" sees opportunities the "unlucky" does not because the "unlucky" is not looking for them, feeling him/herself to be too unlucky to benifit anyway.

Frankly I feel the first paragraph to be more relevant to the original post, however, the effect of one's perceptions is not to be underestimated imo.

[Winstonm]

[QUOTE]My response is that "Yes.Good and bad streaks do exist."If a strong but unlucky player plays bridge for money against a weak but lucky player the strong unlucky player is not going to win.

Yes, this was the question but not only may steaks occur but how long can those steaks last and not be outside probablity law.

In theory only, if 1,000,000 people each flipped coins 100 times you have 100,000,000 occurences, which should overall be be close to 50/50 heads or tails - but could not a handful of those involved have instances where the coin came up one way 80-90% of the time without affecting the overall balance - hence the question became: if steaks like this occur, how long might they last? In other words, is there mathematical theory on how far outside expectancy the deviation may be (variance high or low from expectancy) and how long could the deviancy last (over 100,000,000 occurences, 2 or 3 perpetual highs and 2 or 3 perpetual lows or does expectancy act more like gravity, pulling these streaks back toward center)?

Thanks for all the good posts.

Winston

[awm]

Something people often miss is that the probability of some unlikely event happening is actually rather high. To give an easy example of this, the chance that any individual wins the lottery is quite small, but the chance that someone wins the lottery is quite high, and whoever it is will be saying "wow, I was lucky."

To extend the example to poker, say 1000 bad poker players and 10 good poker players enter a tournament. For any individual good poker player, the chance of winning has to be better than for any individual bad player. But the number of bad players is so high, the chances that one of them will win are actually quite good (probably much more than 50%). And whichever one does win, everyone watching will say "wow, he was so lucky, he's a terrible player and yet he won." It's not really that surprising that bad poker players (who very much outnumber good ones) occasionally win major tournaments. I'm sure we see the same thing in bridge, although luck is arguably less of a factor. Note that Moneymaker's performance in subsequent poker tournaments has been more or less what you'd expect given his apparent skill level.

[hrothgar]

Winstonm, on Nov 13 2005, 09:51 PM, said:

is there mathematical theory on how far outside expectancy the deviation may be (variance high or low from expectancy) and how long could the deviancy last (over 100,000,000 occurences, 2 or 3 perpetual highs and 2 or 3 perpetual lows or does expectancy act more like gravity, pulling these streaks back toward center)?

If you a generally interested in this topic, I strongly suggest that you get statistics textbook. Stats is actually a quite interesting topic.... You'll probably find sections related to confidence intervals especially useful.

In answer to your second question: Most introductory statistics classes assume that observations are independent of one another. If I flip a fair coin "X" times, the outcome on flip number N does not depend in any way/shape/form on the any of the earlier outcomes. Assume the following game:

I will flip a coin 100 times. Each time that the coin turns up heads, I will give you one dollar. Each time that the coin turns up tails, you will give me one dollar. Prior to the start of the game, the expected outcome is a wash where neither of us owes the other any money. (Its FAR more likely that I'll owe you money or you'll owe me money than the specific outcome where we precisely have 50 heads and 50 tails, however, thats another story). Assume for the moment that its halfway through the game and I've had a run of good luck. After 50 flips, you owe me 6 dollars. During the next 50 flips, we expect 25 heads and 25 tails with you STILL owing me 6 dollars.

There are branches of statistics that deal with auto-correlation. I found it REALLY hairy stuff. Its extremely useful. For example, many of the algorithms used in computer networking have feedback loops built into them. Equally significant, packet loss conditions are often bursty. If you loss one packet, its very likely that you're going to lose the one in front of it or behind it. Accordingly, you can't assume independent observations.

I could make arguments that this type of behaviour holds true in competitive sports. Assume for the moment that I suffer a very bad board, it rattled my concentration and I blow another board because of it... Highly plausible, especially given how much top players stress the importance of putting bad results behind them. Makes for some REALLY difficult analysis.