Do you believe in Luck?

[Skeptic Ginger]

See my posts. I think she's asking, in a coin toss (no skill, 1:2 chance of winning), you've won 21 out of 54, is it significant? (I take "luck" or being "lucky" to mean that somehow the results are significant or surprising.)

Then the answer would be, no.

But again, after the fact rather than having predictive value, aren't the odds higher someone will be more 'lucky' than someone else given there is only one option of 50:50 and at least two or more for 49:51 or another outcome? So it more probably one person will be luckier than the other. It just won't have any predictive value which of the two it will be.

 

[JoeTheJuggler]

Then the answer would be, no.

But again, after the fact rather than having predictive value, aren't the odds higher someone will be more 'lucky' than someone else given there is only one option of 50:50 and at least two or more for 49:51 or another outcome? So it more probably one person will be luckier than the other. It just won't have any predictive value which of the two it will be.

I'm not sure I follow.

If we're only considering situations where the odds are 1:2, and we run 54 trials, we wouldn't find a final score of 21-33 to be significantly different than chance. So the hypothesis that the guy's results are due to "bad luck" (as opposed to random chance) is not supported--that is we can't reject the null hypothesis that the outcome is due to chance.

I think the confusion here is in using "luck" different ways. I'd say reading the poll question and responses, the only one it could be is the one I've been using, where "luck" is an alternative explanation for results--or a claim that results are not random. That is, the outcome happened because a player is lucky or unlucky.

I think we're saying the same thing otherwise, though. If the probability of an outcome is 1:2, and we run 100 trials, you can't claim a significant difference from chance just because the result is not exactly 50-50. You're using "lucky" to mean any result other than 50-50, and I'm using it to mean an alternative explanation (that is, an explanation we could only support if results were far enough off of 50-50 to reject the null hypothesis).

And again, I think my usage is more consistent with the poll question and choices.

 

[redziller]

Describe the coincidence of a run of misfortune as bad luck or a run of fortune as good luck if you like, but please don't select a pattern then christen it "luck" as though it were a correlation let alone there were a causal link

 

[redziller]

dupe

 

[JoeTheJuggler]

And this usage is also the primary one given in the dictionary:

LUCK
1
a : a force that brings good fortune or adversity
b : the events or circumstances that operate for or against an individual

______

I think most of us agree, redziller. It's just been a bit confusing as to what exactly the question is.

IMO, even if you had an outcome that would allow you to reject the null hypothesis (say only 1 win in 54 trials with 1:2 odds), I would still not accept the "unlucky player" hypothesis since it smacks of supernaturalism. Instead, I would question the premises--especially that the odds were really 1:2. If I tossed a coin 54 times and got just one head, I'd suspect the coin wasn't fair. But if I tossed a coin 54 times and got 21 heads, I would simply accept the null hypothesis and not bolster ANY alternate explanation.

 

[Beth]

Someone who is better at stats than I am could give you the math, but I'm quite certain that 21 wins out of 54 with roughly 1:2 odds is not statistically significantly different and would not call for rejecting your null hypothesis.

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.

..... In the long run, if you're making the right DECISIONS, the luck will even out for you and for all the players.

Yes, that's basically the assumption I'm trying to test. Will his 'luck' even out over time?

ETA: As was intimated earlier on - simply tracking the frequency with which you are dealt certain starting hands can be used to 'test luck'. You 'should' get dealt pocket aces 1:220 hands (or thereabouts). Indeed, you can easily determine the probability to receive ANY of the Hold'em starting hands. After testing a squillion hands being dealt, you could see how 'lucky' you were on your hand distribution. Your starting cards are 'pure luck' (assuming its a straight-up game).

Well, whether or not the distribution of hands deviates from the expected distribution can be tested, but it wouldn't test the hypothesis in a game situation - i.e. winning the hand. So while it's one measure of luck, it isn't the point we are wanting to test. Further, while I know how to compute the expected probabilities, I'm not sure of how to compute the probability of getting the hands he actually received (or worse), I'm open to looking into it if you have any suggestions on how that should be computed. How should the two hole cards be sequenced from best to worst?

There are software 'add on' tools out there that you can use that will track these kinds of situations for you automatically. The focus is more about whether or not your moves are making you money (as sometimes you are semi-bluffing or stone-cold bluffing when you move all-in post-flop - or you should be, if you expect to ever get called when you actually have a monster and want action). However playing with one of these add ons would help you gather data quickly.

I've suggested this, but until I have a better idea on how to evaluate the data collected, I'll not be successful in talking him into doing that.

Also, getting one of those simulator programs I mentioned would help you as well, although this may lack the sensation of testing 'your' luck. You really would be testing whether or not the math is 'correct'.

Yes, it's not a bad idea in regards to testing my computations for what's expected. But you've already concurred that we have the correct odds for the data we've been collecting.

I'm not sure I follow.

If we're only considering situations where the odds are 1:2, and we run 54 trials, we wouldn't find a final score of 21-33 to be significantly different than chance. So the hypothesis that the guy's results are due to "bad luck" (as opposed to random chance) is not supported--that is we can't reject the null hypothesis that the outcome is due to chance.

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.

 

[Mr. Scott]

Yes, I think the definition meant by the survey is if we think there's a magical force altering chance outcomes. No such force has ever been demonstrated. It's more likely a gut impression from our brain's overreaching pattern finding circuits.

Blaming this magic force on misfortune gets us off the hook, saving face from the alternative, admitting we are unskilled. The opposite, claiming we are "just lucky," allows us to exhibit false modesty.

I agree the sample is smallish. I'm also not absolutely sure the data collection method was air tight.

However, there is bias in this thread. If Beth had been looking for evidence of bad luck, and found the opposite, she would not have begun this thread. I suspect, since Beth wants invisible magical forces to exist, she will not report evidence of their absence.

 

[Mr. Scott]

plays quite a bit on-line

Wait, most of this data was collected from online poker? The cards were dealt by computer? Hmmm there have been allegations and prosecutions of fraud on online gambling sites, including stacking decks. Just wondering. Is he more, or less, lucky playing online compared to in person with a real shuffled deck?

 

[Fredrik]

Unfortunately, that doesn't discriminate between all ins preflop and all ins after the river. Skill plays a big part of that. We wanted to eliminate skill and just see if his cards are not very good.

You must have misunderstood something I said. Maybe I didn't say it clearly enough, I don't know. But the difference between the actual result after the money goes in (on the turn or earlier) and the statistically expected result doesn't depend on skill in any way. You will definitely get a much better estimate of his luck in situations where luck is measurable if you use Hold'em Manager and just check that box. If you still want to look only at the preflop all-ins (for an entirely different reason than eliminating luck), then you can filter the stats to only use those hands.

If his poker client is configured to save hand histories and keep them for a long time, you can just import all the hands he's played and check a box to get a much better estimate than what you currently have. Unfortunately I think the default setting in many poker clients is to delete the hand history files after a pretty small number of days. You should at least download the trial version of Hold'em Manager and check it out. (If there are no hand history files on his computer right now, you should reconfigure the client and collect some new data before you download it, because the trial version only works for a limited time).

This is certainly a big improvement of what you're doing now, but my main point is still that even if you make this big improvement of your estimate, the result still won't tell you if he's been lucky or not. In cash games, you might miss 99.7% of the hands. In tournaments, you're missing...I don't know, let's say 90%...of the hands, so this method appears to be much better for tournaments. However, the fact that you're missing a smaller percentage of hands is to some extent compensated by other things. In particular, chips you lose should be considered more valuable than chips you win. This is a well-known fact among poker players that can be derived from the fact that the winner of the tournament isn't the only person getting paid.

What these things mean is that no matter what you do, you will not find the answer to the question of whether he's been lucky or not.

I'm also interesting in suggestions for other ways of assessing probabilities of having the winning cards in situations that can be evaluated without including any skill component of the game.

I don't think there are any other situations where skill has no relevance.

 

[Fredrik]

Wait, most of this data was collected from online poker? The cards were dealt by computer? Hmmm there have been allegations and prosecutions of fraud on online gambling sites, including stacking decks. Just wondering. Is he more, or less, lucky playing online compared to in person with a real shuffled deck?

The frauds that you may have heard of were committed by people who could see their opponent's cards. As far as I know, none of those people have been charged with a crime. I don't know why, but I suspect that none of the players even tried to report it to the police in Costa Rica. The only fraud charges that are being prosecuted are about lying to banks about the fact that the money being transferred was being used for online gambling.

There are conspiracy theories about unfair deals, but they are just as crazy as 9/11 conspiracy theories. It wouldn't make much sense for the sites to cheat that way, and the people who have looked for statistical evidence of such things in large samples have found nothing.

 

[Beth]

You must have misunderstood something I said. Maybe I didn't say it clearly enough, I don't know. But the difference between the actual result after the money goes in (on the turn or earlier) and the statistically expected result doesn't depend on skill in any way.

You're right, I misunderstood you. Sorry.

You will definitely get a much better estimate of his luck in situations where luck is measurable if you use Hold'em Manager and just check that box. If you still want to look only at the preflop all-ins (for an entirely different reason than eliminating luck), then you can filter the stats to only use those hands.

I'll look into it. Computing the probabilities of the cumulative actual results gets a bit trickier when combining binomial distributions with varying probabilities of success. That's why he's only been collecting data on the one type of situation.

What these things mean is that no matter what you do, you will not find the answer to the question of whether he's been lucky or not.

We haven't been including chip counts as part of the measure. At this point, I'm not willing to add that complexity to the analysis. Perhaps later if we continue the study, but if we can establish that his results are consistent with random chance expectations, I doubt we'll continue.

I disagree with the idea that this approach will not allow us to find the answer. We don't need all the hands or even a large percentage. A small sample is sufficient as long as it is a representative sample. I'm don't see any reason why results for all-ins should not be considered a representative sample in that sense. All hands are independent of all other hands. While there is bias regarding which hands he's willing to go all in on, the results after doing so should be unaffected by that. Do you know of any reason why this approach would be biased?

I don't think there are any other situations where skill has no relevance.

I agree, but I thought we might have missed some situation. Thanks for the suggestions.

 

[Antiquehunter]

I don't think there are any other situations where skill has no relevance.

Once you've made the decision to go all-in (that DECISION took skill (or not) to make) and you've been called, the RESULT from there takes no FURTHER skill.

ie - I shove all-in on an Ace-high flush draw on the flop, and get called by the guy with top pair.

You can easily calculate the odds for the result on this hand at this stage, and then the 'result' becomes a measure of 'luck'. ie - assuming I have 9 flush outs and 3 good Ace-pair outs, I have 12 outs twice, or roughly 46% or so - a bit less if you take away the outs for my opponent hitting his 2nd pair or trips, and a bit less again if my opponent has taken away a flush out. Any of those odds calculating programs will do the hard math for you.

Now - the question is, was that the right move? Did I choose to go all-in aggressively because I thought my opponent would fold? Did I choose to go all-in because my chipstack dictates that is the right move (pot-equity)? The decisions one takes to get to this point are definitely skill, and it is that decisionmaking process that is much more important.

But once the situation is simply 46% to win, no more decisions to be made - OVER A VERY LONG TIME, you will win 46% of those pots. Luck be damned.

 

[TubbaBlubba]

Wait, you have a sample size of 54, and you're at a 7% chance? Really, come back after at least a 1000.

I've had quite a few wonky statistical things happen when playing the Fire Emblem games. For one, missing 4 times in a row with a 94% chance to hit (0.001% chance of happening). I've also missed with 98% in one of the later games which amounts to missing with 99.96% due to the way the mechanics worked in those. Granted, I've put some obscene amount of hours into them, but given a small, randomly selected sample of say 50, I could seem very unlucky (or lucky) indeed.

 

[JoeMorgue]

No there is no such thing as luck, only mathematical probability and the ability recognize it and react to it.

 

[ynot]

Does luck exist?

Wasn’t sure so I tossed a coin to find out. Heads was yes and tails was no. I didn’t like the result got so I ignored it. May try again later to see if I can get the result I want.

 

[JJM 777]

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.

 

[Rasmus]

He is only collecting data on one particular type of hand. A showdown situations where he and one other player are All In before the flop. In addition, he's only looking at a the outcome when one of the two sets of two cards is a pair and other person had two over cards. The probability of winning is approximately 50/50. (It's actually more like 48/52 but so far, I've just been computing the odds at 50/50). He terms this a 'race'.

The rest of the poker playing world would call it a coin flip, or just a flip. This might suggest something about his skill level.

You'll find that the odds fluctuate slightly depending on the type of hands plaid - are the over-cards suited? Connected? Do the suits match one or two cards of the under-pair? How big is the gap between the pair and the over-cards, i.e. will some of the straights for the pair connect with one or even both over-cards? (play 5,5 against T,J - a 5-9 straight suddenly is a bad thing for the pair. Different thing if you play 5,5 against AK.)

He started collecting data back in March. He was just keeping a running total of how many 'races' he was in and how many he won. He is currently at 21 wins out of 54 races. Assuming a 50/50 probability of winning races, the probability of wining 21 or fewer out of 54 is 0.0668.

I have been playing poker for just a few years now. I once flopped a Royal Flush (and saw a river, and got paid off nicely, too.) Statistically, that is near impossible to ever happen. I've been in a game recently where my flush was beaten by a straight flush - twice within 5 hands or so. These things happen.

54 games is not a lot, assuming 50/50 odds is an approximation at best, (and it ignores that he might be luckier or unluckier in other situations - not that this would matter for the analysis).

He been meticulous about recording outcomes of all such races win or lose. I've recently talked him into recording what the actual cards were that he won and lost with, so I should be able to start computing the probabilities more accurately.

All that data should be available in the logs of the software he uses if he plays online.

He is, at least, feeling vindicated regarding his complaint about bad luck.

And - ignoring the definition of "luck" he might be right. He might be in a downswing and see a couple of bad cards. But even if the math is right, keep in mind that the next three or four hands might turn him into a lucky player.

 

[Akhenaten]

Does luck exist?

Wasn’t sure so I tossed a coin to find out. Heads was yes and tails was no. I didn’t like the result got so I ignored it. May try again later to see if I can get the result I want.

Good luck with that.

 

[Antiquehunter]

The rest of the poker playing world would call it a coin flip, or just a flip. This might suggest something about his skill level.

A 'race' is a perfectly acceptable term for the classic pair vs two overcards scenario. Watch any of the re-broadcasts of the original WSOP throughout the 80's and 90's and it was referred to as a 'race' all the time, or 'an ace & a race'.

If you only have 'only a few' years of experience playing poker, then perhaps you should not be so quick to highlight perceived skill level deficiencies in others.

 

[Rasmus]

A 'race' is a perfectly acceptable term for the classic pair vs two overcards scenario. Watch any of the re-broadcasts of the original WSOP throughout the 80's and 90's and it was referred to as a 'race' all the time, or 'an ace & a race'.

If you only have 'only a few' years of experience playing poker, then perhaps you should not be so quick to highlight perceived skill level deficiencies in others.

So for the last 10 years or so, where would it still be called a race?

And what does my own lack of skill levels have to do with that of other people?