Do you believe in Luck?

[Lothian]

I suggest the answer to this is “Luck exists, some people are inherently more lucky than others. The data gathered in this exercise categorically demonstrates that your husband is inherently unlucky. Whatever skill he has; it will never offset his natural luck disadvantage. He is therefore better off setting aside an amount he expects to lose each week and spending it instead on his wife.”

How you weave Bayesian analysis, chi-square, Gaussian distribution, delta function and Bernoulli trials into your answer depends on how much ‘Maths’ you need to include to get him to accept the desired way forward.

 

[Antiquehunter]

A quick check at www.cardplayer.com, using their search function revealed 61 pages of hits where the word 'race' was used in one of their articles. A number of these instances referred to the precise use above (pair vs two overcards). Their magazine archive only goes back as far as 2006 as far as I can see. A quick google of poker 'glossaries' also includes the term 'race' as described.

My comment was only that you appeared to immediately pounce on the use of (perfectly acceptable - but unknown to you) poker terminology to indicate a judgment of someone's lack of skill. This sort of 'holier than thou' attitude strikes me as a common thread in many of your posts.

 

[Rasmus]

A quick check at www.cardplayer.com, using their search function revealed 61 pages of hits where the word 'race' was used in one of their articles. A number of these instances referred to the precise use above (pair vs two overcards). Their magazine archive only goes back as far as 2006 as far as I can see. A quick google of poker 'glossaries' also includes the term 'race' as described.

My comment was only that you appeared to immediately pounce on the use of (perfectly acceptable - but unknown to you) poker terminology to indicate a judgment of someone's lack of skill. This sort of 'holier than thou' attitude strikes me as a common thread in many of your posts.

I certainly didn't mean to pounce - and I only used it as an indicator here. What I'd find a lot more significant is the assumption that some 50 odd hands could be indicative of a statistical bias.

Holier than though - hardly. I know very well what an analysis of my own poker hands would have as a result: A couple hundred bucks of money given to people that play either a little better than i do or much better than i do. (Or maybe I am guilty as charged - I think poker makes it very easy to ignore one's own lack of skill.)

Anyway - bad derail.

 

[Beth]

Okay, we're now at 21 out of 55 hands, p = 0.0524. Unfortunately, he is not interested in downloading the software to track his hands.

I did however, go over his data with him last night. I now have information on whether he had a pair or overs for the last 36 races. Broken down and computing the odds for pairs (52%) versus overs (48%) leads to p-values of 0.6 and 0.15 respectively. Much less anomolous!

Thanks to everyone for all the suggestions. It's been helpful.

I suggest the answer to this is “Luck exists, some people are inherently more lucky than others. The data gathered in this exercise categorically demonstrates that your husband is inherently unlucky. Whatever skill he has; it will never offset his natural luck disadvantage. He is therefore better off setting aside an amount he expects to lose each week and spending it instead on his wife.”

How you weave Bayesian analysis, chi-square, Gaussian distribution, delta function and Bernoulli trials into your answer depends on how much ‘Maths’ you need to include to get him to accept the desired way forward.

Thanks, that made me smile. Actually, he plays reasonably well IMO (not his). I don't think he has anything to complain about in that regard. He places in tournaments pretty consistently and he's got six or seven million dollars in play money on his on-line account. He supports his hobby of remote control airplanes with his winnings from the real life real money games he plays a couple of times a month.

However, he tries to win without show-downs as much as possible because he feels he's inordinately unlucky with them.

 

[Lamuella]

if there is such a thing as "bad luck" it's caused more by confidence than by probability, especially in poker. Games of chance can have a lot more to them than just chance. Poker especially is a game of bluff, confidence, and swift mathematical skills, with a bed of chance at its core. A lot of people who have "bad luck" really just have not much skill at reading people, or not much of a gauge of when they should walk away from the table.

 

[Lamuella]

How can 80% of people on a skeptic-scientific forum vote for "No, there's no such thing as luck."

Evidence for the existence of luck: Pick any lottery millionaire.

It is not a force, and it is not a predictable or foreseeable phenomenon either, but it is a retrospectively observable statistical fact.

I think we are defining "luck" in a different way from you. You are talking about "luck" as an observable event after the fact. The OP is talking about "luck" as an attribute that someone can have, for example someone thinking that they have "bad luck" with cards.

To draw an example, you are talking about "luck" in the sense of someone flipping heads ten times in a row. The OP is talking about "luck" in the sense of someone routinely being able to flip heads 7 times out of 10.

Nobody is disputing that statistical clusters occur or that improbable events happen on a large time scale. What they are disputing is the idea that human attributes can alter the probability of random events.

 

[Antiquehunter]

Okay, we're now at 21 out of 55 hands, p = 0.0524. Unfortunately, he is not interested in downloading the software to track his hands.

Well - if he is going to stay just a casual hobbyist playing predominantly for fun, then this is perfectly fine. But he's going to need to become much more of a numbers guy to compete in online play even at low cash-game stakes. The majority of players now are equipped with tools that analyze not only their own play, but also recall how others play, and assist them to make decisions on the spot based on historical profiles. It is for this reason that I have severely curtailed my online play to pretty much just a few key tournaments now and again. I find the 'grind' involved in playing low stakes ($2/$4 NL Holdem and similar) to be brutal online. My cash game wins are much less online now, than when I first started playing online in 2004/5, and definitely much less than what I track at live games. (Still positive, but a lot 'tighter'.)

Thanks, that made me smile. Actually, he plays reasonably well IMO (not his). I don't think he has anything to complain about in that regard. He places in tournaments pretty consistently and he's got six or seven million dollars in play money on his on-line account. He supports his hobby of remote control airplanes with his winnings from the real life real money games he plays a couple of times a month.

A note of caution - the caliber of play for 'free' play vs cash game play - even if playing online 'micro' stakes, or playing in a small stakes live game is MUCH different. While the specific type of hand you're tracking (Pair vs 2 overs, all-in pre-flop) wouldn't make that much of a difference, certainly gauging how many points one has accumulated playing for 'free' is quite meaningless. A lot of players either don't know how to play seriously at the 'free' tables, and a lot of others simply don't care, and call, call, call basically playing bingo, not poker. I don't play 'free' games at all - and I would encourage anyone wanting to play seriously to get away from them. If you can get to the point where you have tracked say 500 hours of play and are a consistent winner - whether at micro stakes online, or playing 50 cent / $1 no limit with a $40 rebuy (or larger) game live - then why would you waste your time playing for free? If you know over 500 hours that you can expect to make $5 an hour playing low stakes poker, then... the answer is pretty clear. The sort of play you encounter and the sort of lazy play it can encourage in you makes it a losing proposition in my opinion.

However, he tries to win without show-downs as much as possible because he feels he's inordinately unlucky with them.

You see - it is this sort of thinking that too much free play can foster. He has an (incorrect) view that he is 'inordinately unlucky' with showdowns. So he TRIES TO AVOID THEM. Sometimes, it makes the most sense to get your money in the middle for a race. Both in cash games & in tournaments - I'd say especially in tournaments. This 'reluctance' could be a serious leak in his game! Certainly if other opponents knew this predilection, they would be MORE likely to bluff / semi-bluff at him for all his stack, and would be less likely to call him when facing an all-in from him. He also is (most worringly) probably missing opportunities to shove aggressively to move opponents off their hand, facing NO WORSE than a coin-toss/race if called.

Its probably important for your husband to nip this in the bud before it endangers his airplane acquisition...

 

[Antiquehunter]

Just another thought on 'luck' or lack thereof at poker...

Ask your husband this:

When he's had the opportunity to go all-in pre-flop with KK, he's surely run into AA a few times. It happens to us all. It is EXTREMELY rare the occasions where I've folded KK pre-flop, and I've only been right about 75% of the time. Generally, if I have KK and I run into your AA, I say 'good game'. Dan Harrington in 'Harrington on Hold'em' claims he NEVER folds KK pre-flop - his results would suggest he's on to something.

Now - When having the AA, what are the hands I remember? I remember the hands where the guy with the KK sucked out on me and took my money. Often a good size cash pot, or a massive tournament pot - usually followed by my exit. (Happened to me most recently at Binions in a $500 buy-in tournament vs Amarillo Slim, the skinny so and so.) When I have the KK and run into the AA, what are the hands I remember? I remember the times where I have BEEN LUCKY and sucked out on Mr. AA - winning a juicy cash pot, or positioning me to move deep into a tournament. (2008 WSOP $2500 buy-in No Limit Hold'em vs a very skilled online player, who had a bit of an understandable meltdown when I flopped my K.)

What I'm getting at here, is that your brain can quickly mislead you into feeling very unlucky or very lucky, by filtering out the more routine results. I couldn't describe to you very accurately the times I've had AA and knocked out / taken a big pot from a player holding KK. But reverse the situation - the times I've lost as a big favorite, or the times I've sucked out being the dog - I recall many of those with remarkable clarity.

It is for this reason that discipline at record-keeping when playing poker seriously is so important.

 

[Beth]

Well - if he is going to stay just a casual hobbyist playing predominantly for fun, then this is perfectly fine. But he's going to need to become much more of a numbers guy to compete in online play even at low cash-game stakes.

Yes, he's just a casual hobbiest and isn't planning on turning professional. He was playing a few low cash games and tournaments before that got shut down by the justice department here in the U.S.

Thanks for all the advice. Your posts have been really informative.

 

[Beth]

[

Just another thought on 'luck' or lack thereof at poker...

What I'm getting at here, is that your brain can quickly mislead you into feeling very unlucky or very lucky, by filtering out the more routine results.

Absolutely. This is why I suggested he start keeping track of his outcomes.

 

[Finsend]

The Hand of God

Hi Beth,

I enjoyed reading this thread.

And I think you husband's (poker)hand(s) might be (at least) a little bit different than this Hand of God, alias Maradona's About the Luck part, for me it is fair enough to say that someone is (un)lucky. "Bad streaks" do happen and nobody knows exactly how long they could be, does anyone know? I mean I could toss up a coin, but there are so many factors involved - if you wish to look at it this way - so I would just call it (Bad) Luck, I guess. But that's because I am lazy, maybe

This leads me to Randomness.

According to several standard interpretations of quantum mechanics, microscopic phenomena are objectively random, I once read. So maybe bigger cards would help?

I guess that if your husband changes something that he might score differently. What this would be I don't know, since I do not understand poker very well. It could be the (bad)-decision-making-part, it could be just bad cards in a nasty bad streak, or maybe something else. And sitting on a table is of course something else than behind the computer. Reading you opponent is very important, I think, both at the table as from behind the computer - as is one's knowledge about chances.

I do not now if the poker game has been calculated out - I guess so (like checkers I think and 3 in a row, but (still) not chess I think. So if you play "perfect" doing the best thing always it comes to bluff and things like that, I guess. Small signals, hesitations, how much you are willing to loose, stack strategies, etc. Plus of course the dealing of the "random" cards!

Anyway good luck to you and of course to your husband, hopefully he will be able to turn this one around into some streak of

Good Luck,
Finsend

 

[stevea]

...
I'm a professional statistician. ...
...for a situation that should be about 50/50.

.... Assuming a 50/50 probability of winning races, the probability of wining 21 or fewer out of 54 is 0.0668.
....
He is, at least, feeling vindicated regarding his complaint about bad luck.

I know little of poker, but assuming your estimates are right ,then the p-value is about 0.13 and alpha ~ 0.12. Not statistically significant but close enough to tantalize. If he runs the same win rate to 33 of 85 then you've hit the 5% significance level. The 'seat of the pantser's' who claim you have far too little data aren't right. You've got about 2/3rd of the data you need to get a decent level of significance.

That your husband believes he is unlucky and has some corroborating evidence yet continues to play implies that he doesn't mind losing or else enjoys the data collection more. Raises questions of credibility. That a pro-statistician wouldn't think of applying some significance test leads me to believe that this story can't pass the sniff test.

Of course luck isn't the explanation if the trend continues. It implies a systemic effect, for example that we've incorrectly calculated the odds, or that the dealer is cheating.

 

[Lothian]

For more on 'lucky' and 'unlucky' people read up on Gilovich's 'Hot hand' study of basketball free throws. It looked at whether players who were successful with their last x free throws (hot) were more likely to score the next than players who had missed their last shots (cold).

I wont spoil the ending........


link

 

[Antiquehunter]

Richard Wiseman's look at 'luck' was interesting as well.

 

[JoeTheJuggler]

Thanks. Given a probability of 50/50, I know how to compute the odds. Using Excel's binomial function, I get BINOMDIST(21, 54, .5, 1) = 0.0668. This isn't perfect, but it's fairly close. I think we can say his luck on these hands falls between 5 and 10%. That's in the territory for rejecting the null or at least continuing to study the situation.

I don't think you're reading that correctly. If we set a confidence level at 0.05, it's saying that 21 out of 54 is not significant and you cannot reject the null. And remember, your actual odds weren't 1:2, so that would push the result closer to what was expected. (And might not even be significant at a 0.10 level of confidence.)

[ETA: And I'm still not sure the numbers are right. If I tossed a fair coin 54 times and only got 21 heads, that result doesn't seem at all surprising. I would be shocked that it's statistically significant.]

Even if you could reject the null, I still say it'd be wrong to accept your hypothesis that the result is due to his luck (defined as a force that favors or opposes his interests). I would first challenge the premises, especially that the odds really are 1:2. (It could also be that the game he's playing isn't using a true random number generator to deal out the cards. Or that someone is somehow cheating. All of which, though improbable, are more parsimonious than "luck" in that they don't require the creation of a new entity outside the realm of a huge body of science.)

It depends on your alpha value - the probability at which you decide to reject the null. As I said above, the p-value for 21 heads in 54 flips is 0.0668. If we set the alpha level at 0.10, we could reject the null. At alpha = 0.05, we could have rejected it at some previous points in the data collection process. When he was at 5 wins out of 18 races, p = 0.0481, for 6 wins out of 21 races, p = 0.392, for 14 wins out 40 hands, p = .0402, for 15 wins out of 44 hands, p = 0.244 - this was the lowest cumulative probability for the 54 races. He's continuing to collect data.

And this is post hoc hypothesizing.

Especially the stuff about saying it's significant at 0.05 if we ignore some of the data. (That arbitrary starting and stopping is a methodological problem that plagues psi research by believers.)

And again, the notion that if the result gets closer to the 1:2 odds over more trials means his luck has evened out is not right either. It means you reject your hypothesis that luck is a factor affecting the outcomes. (Otherwise, there's no result that can support any answer to your poll other than "yes". That is, regardless of the result, it is explained by luck.)

Again, look at the first definition of "luck" and look at the usage of the word in your poll. Luck is not a synonym here for "chance"--it's being posited as an alternate explanation for the results.

 

[JoeTheJuggler]

I know little of poker, but assuming your estimates are right ,then the p-value is about 0.13 and alpha ~ 0.12. Not statistically significant but close enough to tantalize. If he runs the same win rate to 33 of 85 then you've hit the 5% significance level. The 'seat of the pantser's' who claim you have far too little data aren't right. You've got about 2/3rd of the data you need to get a decent level of significance.

Thank you.

So again, so far, you cannot reject the null hypothesis.

And really, you should say at the outset how many trials you'll run. That is, this is part of the hypothesis. You can't after the fact arbitrarily calculate p-values for subsets of the dataset. We expect there to be "streaks" in the data. It's not kosher to do the kind of post-hoc hypothesizing Beth was doing in order to exploit streaks in the data.

ETA:

The 'seat of the pantser's' who claim you have far too little data aren't right. You've got about 2/3rd of the data you need to get a decent level of significance.

It sounds like you're contradicting yourself here, stevea. The claim that there is too little data is correct, isn't it? (And actually, my claim wasn't that, but that 21 of 54 doesn't seem statistically significant. My claim takes into account the number of trials and the results. It's only off by 6 from the exact mean. And again, if I got something statistically significant, my first thought would be to challenge the premise that the probability in each trial really was 1:2.)

 

[Beth]

I know little of poker, but assuming your estimates are right ,then the p-value is about 0.13 and alpha ~ 0.12.

How did you compute your estimates of those values? I used EXCEL BINOMDIST(21, 54, .5, 1) = 0.0668.

That your husband believes he is unlucky and has some corroborating evidence yet continues to play implies that he doesn't mind losing or else enjoys the data collection more.

He just enjoys playing, but is finding showdowns frustrating and feels he loses those more frequently that the probabilities predict he should.

Raises questions of credibility. That a pro-statistician wouldn't think of applying some significance test leads me to believe that this story can't pass the sniff test.

Actually, my first reaction when he asked me what I thought of it was that it wasn't accurate. He laughed and agreed that he would suspect the data too except that he was the one collecting it. However, that theory has been discarded as not particularly helpful to him. As far as a significance test goes, I think the p-value is sufficient for our purposes and didn't feel it was needed.

Of course luck isn't the explanation if the trend continues. It implies a systemic effect, for example that we've incorrectly calculated the odds, or that the dealer is cheating.

I think we can discard the dealer cheating theory since most of his data was collected on-line, the rest at garage games where the dealer changes with every hand. Incorrectly calculating the probability is always a possibility. That's why I posted the story here, to get that corrected if I've made an error and to get other ideas on how to measure 'luck' in poker.

 

[Antiquehunter]

Beth - if he doesn't want to gather more data online, but really is curious about testing his 'luck'...

Just get a deck of cards. Deal out a QQ and an offsuit AK where the suits differ from the QQ. Have him choose to be the 'favorite' (QQ) or the 'dog' (AK) on either side of the 52/48 proposition.

Deal out the flop, turn, river, just like in the casino. (Burn a card between each for that extra dose of 'reality' even though its meaningless).

Record the results. Return the board cards to the deck, shuffle THOROUGHLY (7 riffle shuffles with several cuts in between is de rigeur). Deal, repeat.

I'm NOT a professional statisician. But if you ran through at least 100 or so of these quick deals, you would be in a 'real' environment. And you would be testing his hypothesis.

I think we've given you all the pieces to the puzzle in this thread - either he genuinely wants to explore the hypothesis, or he's made up his mind and isn't interested in testing it.

 

[JoeTheJuggler]

He just enjoys playing, but is finding showdowns frustrating and feels he loses those more frequently that the probabilities predict he should.

Again, I think what's most likely is that he's misperceiving even money gambles. (That is, the odds really aren't 1:2.)

It could be an artifact of a game that's not using a true random number generator, but I believe all the big poker sites do.

And it could also simply be confirmation bias, something your efforts would clear up.

I do think what Fredrik is saying is right, though. If your husband is trying to extrapolate a general unluckiness at playing poker from just this small subset of hands, it's not valid. A better measure would be what Fredrik is suggesting, an analysis of ALL the hands he's dealt.

Does your husband only think he's "unlucky" on these particular coin-toss hands?

 

[Beth]

I don't think you're reading that correctly. If we set a confidence level at 0.05, it's saying that 21 out of 54 is not significant and you cannot reject the null. And remember, your actual odds weren't 1:2, so that would push the result closer to what was expected. (And might not even be significant at a 0.10 level of confidence.)

That's correct.

[ETA: And I'm still not sure the numbers are right. If I tossed a fair coin 54 times and only got 21 heads, that result doesn't seem at all surprising. I would be shocked that it's statistically significant.]

You're welcome to check my computations. I might have made an error. Finding errors is one reason I started this thread.

Even if you could reject the null, I still say it'd be wrong to accept your hypothesis that the result is due to his luck (defined as a force that favors or opposes his interests). I would first challenge the premises, especially that the odds really are 1:2.

Actually, breaking it down into over cards and pairs and computing the probability separately for those seems to make quite a bit of difference.

(It could also be that the game he's playing isn't using a true random number generator to deal out the cards. Or that someone is somehow cheating. All of which, though improbable, are more parsimonious than "luck" in that they don't require the creation of a new entity outside the realm of a huge body of science.)

I've wondered about that, but even if it isn't truly random, there's no reason to presuppose a bias one way or the other with respect to him.

And this is post hoc hypothesizing.

Especially the stuff about saying it's significant at 0.05 if we ignore some of the data. (That arbitrary starting and stopping is a methodological problem that plagues psi research by believers.)

I'll have to disagree here. He started collecting data with a very specific hypothesis in mind. After he told me what he was doing, I've been keeping running totals of the probabilities for a month now. It was at one of the low points that I requested permission to post here to get advice in possible ways the analysis or odds computation was incorrect.

And again, the notion that if the result gets closer to the 1:2 odds over more trials means his luck has evened out is not right either. It means you reject your hypothesis that luck is a factor affecting the outcomes. (Otherwise, there's no result that can support any answer to your poll other than "yes". That is, regardless of the result, it is explained by luck.)

Again, look at the first definition of "luck" and look at the usage of the word in your poll. Luck is not a synonym here for "chance"--it's being posited as an alternate explanation for the results.

I'm sorry, but I didn't intend for the term 'luck' to be defined rigorously either for the poll or for this thread. This is for fun, not science and I don't want to get into a debate on the meaning of the word.