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25th June 2011, 11:08 AM  #1 
Philosopher
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Do you believe in Luck?
Okay, here's the situation. My husband's a poker player. He likes the Texas Holdem game and plays quite a bit online and a couple of times a month in a garage or basement game. He's constantly going on about his bad luck, how he never seems to catch the right card no matter what the odds.
I say, you're focusing on the bad beats and not paying attention to the wins. He swears his luck is phenomenally bad. I'm a professional statistician. I tell him to collect data and I compute the probability. So he did. And I did. And he has had consistently bad luck! Given the number of hands he's collected data on, the probability of luck as bad or worse than that is less than 10%. He is running fairly consistently at 40% wins, both overall and for a running 25 game average, for a situation that should be about 50/50. In the next paragraph, I'll explain the data collection and analysis we're doing. I'd appreciate any suggestions for improving either. 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'. 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. 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. He is, at least, feeling vindicated regarding his complaint about bad luck. 
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25th June 2011, 11:21 AM  #2 
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I'm not sure your sample size is large enough to be meaningful. Assuming we treat all races as a 50/50 prop (as you point out, they're 52/48 or in that range, depending on the exact cards, straight / flush possibilities etc...) then he 'should have' won 27/54. He is 6 off that mark  unlucky, but not extremely so. Collect a couple of hundred samples and see if he heads more towards the mean.
One other consideration also, if you're gathering this information when you're multiway, the odds are a LOT different. (A pair vs TWO hands goes down in value, unless the two hands take away some of each others outs.) Finally  if you're playing at a freemoney table, where there is a lot of preflop action, you may further be able to make some assumptions. For example, in freemoney play, you see people going all the way with an Ax. As such if there is a lot of preflop action, I would expect that it is likely there are more aces than normal in people's hands. Presumably then, with 'dead' aces, I would tend to push my larger pairs stronger. Even if only called in one place by an AK, I would expect it likely if there were lots of 'limpers' that someone else folded an Ace. Can't be proven of course, but just a thought. As a serious poker player myself (made the money at the WSOP) my advice is that if he considers himself to be a more skilled player at the table than average, then he should try to avoid raceoff situations except where his chipstack in a tournament, or in a cash game, suggest this is the best value for money. I know you're testing his 'luck' in a specific gaming environment, but there are poker hand simulators you can download where he could run 10,000 hands of QQ vs AK very quickly, to see if his results are in line with the true mathematical odds. AH. 
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25th June 2011, 11:34 AM  #3 
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The data appears to be flawed. You're collecting data long, long after a lot of human intervention has taken place. Every bet and every raise, every person who folded, affected the outcome. Your husband may just be preternaturally bad at knowing when to fold. In fact, it would appear that all you've proven is that he's way, way too agressive overall.
Go back to start and record his hole cards for twenty hands  no matter how those hands turn out. Are his hole cards statistically worse than chance? I would bet that they are not. Now, when he has a pair of nines with a Nine, King and Ace showing after the flop, and the guy to his left bets 100 and the next guy goes all in with 800, does he call, raise, or fold? If he says the answer is anything other than fold, he probably should stop playing poker and find a different hobby. 
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25th June 2011, 11:39 AM  #4 
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I think it depends on what you mean by "luck". In the "races" described, you wouldn't expect outcomes to line up with the odds perfectly unless you had a really large dataset. Even so, within that dataset, we would expect there to be streaks where one side wins more often than he "ought" based on the odds.
By the way, I would describe these nearly 5050 situations as "coin tosses" rather than "races". There is no skill at that point. And even tossing a fair coin, we don't expect the result of 20 tosses to be HTHTHTHTHT. . . 
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25th June 2011, 11:42 AM  #5 
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I'm willing to accept the premise that at that point, whatever happened before, the outcome of the allin heads up play is a coin toss (both hands have a nearly 1:2 chance of winning). In fact, in such games, the cards are turned up, and we can actually calculate the odds with the information in front of us. (We know how many cards remain in the deck and how many of them will win for one player or the other.) So I think at that point, we can indeed ignore what happened before.

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25th June 2011, 11:44 AM  #6 
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You've got to know when to hold 'em . . . etcetera.
Lucky players don't win at poker  skillful ones do. And viceversa. 
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25th June 2011, 11:47 AM  #7 
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Most poker players use software for that sort of thing. Hold'em Manager is the most popular one. You can compare the graph of your actual result with the graph of your "allin EV". The latter is calculated by replacing your actual results in the hands where you were allin on the turn or earlier with the statistically expected results. This way you can clearly see if you've been lucky or unlucky in those situations. However, it's unlikely that those graphs give you the right idea about how you've been running. I just checked my database for May and June, and it looks like less than 0.6% of the hands I played were allin on the turn or earlier. (I play cash games. Tournament players end up allin much more often).
Because of this, I really think that the money won/lost is a much better measure of how lucky or unlucky he's been than these allin EV graphs. Back in 2008 I had a couple of months when I was about 50 buyins (i.e. 5000 big blinds) below expectation in about 80K hands. I've seen a graph (posted at a poker forum) that was 300 buyins below expectation. Somehow that guy still managed to break even, so he must have been running very well in the other hands. It's definitely possible to run insanely bad over 100K hands or so. It feels like your bad luck is an entity that follows you around. It's extremely frustrating, and it's impossible to continue to play well under those circumstances. I don't know what to make of the poll question. I think you would have to explain what you mean by "luck" for the question to make sense. I believe that if a million people buy a $10 ticket for a lottery that, by the rules of the lottery, awards 50% of that money to a single winner, selected using a random number generator, then someone will win $5M. Does that mean I should answer "yes"? 
25th June 2011, 11:49 AM  #8 
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True enough, and it's also true that someone skilled in martial arts or boxing can beat someone who is less skilled but bigger and stronger. [ETA: But if they're both equally skilled in martial arts, the bigger or stronger one has a distinct advantage.]
However, if both persons are equally skilled (or we ignore all situations where skill matters), the odds still don't tell us that you will win exactly half of all 1:2 chance gambles. There will indeed be streaks of various lengths. These streaks of course don't change the odds of subsequent instancesthey're still 1:2. No one is inherently lucky, but there is certainly an element of chance in poker. (You can see the top skilled players going against each other. It generally comes down to who gets the cards, even though they'll very consistently destroy less skilled players.) 
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25th June 2011, 11:55 AM  #9 
Penultimate Amazing
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"luck" is when preparation meets opportunity.
Skilled (prepared) players win at cards... or anything else. Unfortunate happenstances can beat anyone at any time, though. 
25th June 2011, 11:59 AM  #10 
Penultimate Amazing
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But again, unless I'm grossly misreading the OP, she's asking us *only* to consider situations where all play is finished except the dealer turning cards upthere's absolutely nothing either player can do to change the odds or outcome, and at that point the odds for each player to win are even.
Again, if the premise is correct, we could as well be talking about a series of coin tosses. Even though the odds for heads and tails are equal, it's unreasonable to expect an exact sequence of THTHTHT. . . . And after 10 flips, not getting exactly 5 of each is no big surprise. 
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25th June 2011, 12:04 PM  #11 
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But again, if I'm reading the OP correctly, we already know the odds and then the actual results.
To me the question is, if the odds of these situations are 1:2, and you'd lost 7 out of 10 times (ETA: actual numbers: 21 wins out of 54*), is it meaningful or somehow significant? My answer is, no. That result falls within the realm of what we'd expect due to chance. ETA: If you've lost 90 out of 100 of these, or if you tossed a coin 100 times and came up with 90 heads, then I would suspect that it's not a fair coin or something else is up. (That is, I'd find that outcome significantly different from the hypothesis that the result is due only to chance.) * And that's if the probability of winning were actually 50% and not something more like 48%. If the latter, his 21 out of 54 is almost a perfect reflection of the odds. Even so, we'd still expect streaks and wouldn't be surprised if in 54 trials we don't get exactly the mean number of wins for that probability. 
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25th June 2011, 12:09 PM  #12 
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I made the assumption you're treating these races as allin preflop. If he's waiting postflop and pushing 99 with overcards on the board, then as pointed out, you can throw the 'race' premise out the window.
For a pure 'test' of 'luck' run a simulation of 10,000 hands QQ vs AK preflop. 
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25th June 2011, 12:10 PM  #13 
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25th June 2011, 12:15 PM  #14 
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Did it seem like I was talking about something other than that? My point was just that the hands for which luck is measurable is a very small percentage (0.6% for me apparently) of the total number of hands played.
(Edit: Beth was talking about preflop allins. In my database for May and June, those are less than 0.3% of the total number of hands). 
25th June 2011, 12:15 PM  #15 
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I think she did specify preflop. But the only difference pre and postflop makes is how complicated it is to calculate the probabilities (and thus ignore all hands in a similar situation when the odds of winning aren't 1:2).
From that point on (even preflop), it's heads up allin, and there is no more skill involved. If we know the odds are 1:2, it is exactly the same as flipping a coin. In other words, if I'm reading the OP correctly, we have eliminated skill. If his skill (or his opponent's skill) resulted in him going allin (pre flop or not) with a better hand or a worse hand than his opponent, we're not counting that situation as a trial. So all that's left are the instances when his skill (or lack thereof) has resulted in a 1:2 chance of winning, and there's nothing left to do but watch the dealer throw cards. 
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25th June 2011, 12:20 PM  #16 
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But again, unless I'm mistaken, she's saying that of these 54 hands, 100% of them are this kind of hand. It doesn't matter, how well or poorly he has played in other hands. So I don't think she's interested in the calculation you're offering.
If I'm not mistaken, she's saying he's played 54 cointosses and has won 21 of them, and she's wondering if that's significant. ETA: And just to clarify, when you say "the hands for which luck is measurable" do you mean "hands where at the point no more skill is involved the odds of winning are 1:2"? If not, then I'm definitely misunderstanding you. (This is partly why my first response was to ask for a definition of "luck". That's not really a statistical term.) 
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25th June 2011, 12:20 PM  #17 
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Depends on how you define 'luck'. If you define it as predictive, then no. If you define it as descriptive of what has occurred, then, yes it exists. The lot of each of us clearly is not equal. So assuming the latter, I said, yes.

25th June 2011, 12:21 PM  #18 
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Well postflop, there is a lot more information available (3 out of 5 community cards dealt), and the odds of the AK beating QQ postflop are dramatically different than 52:48 depending on the flop. (If the AK pair up, they're now a monster favorite. If they miss, then they are now a big dog.)
A pure test of 'luck' would be preflop all in, hand X vs hand Y. No more skill involved. Just happens that two overcards to a pair is pretty close to a coin toss, so it makes for an interesting test (I guess  not really interesting to me.) 
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25th June 2011, 12:26 PM  #19 
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25th June 2011, 12:27 PM  #20 
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25th June 2011, 12:27 PM  #21 
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Concur  54 hands is waaay too small a sample.

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25th June 2011, 12:30 PM  #22 
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I understand that, but isn't the premise that at the point where he went all in, his actual odds of winning were ~1:2 (that we can know when both players turn up their cards). Obviously, you could recalculate the odds after the flop, but if they went allin preflop, there's nothing either player can do about it. So we're dealing with the odds of winning the hand as they were at the point when skill was no longer involved.

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25th June 2011, 12:31 PM  #23 
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Or at least too small to find 21 wins significantly different from the probability. If he went 1 for 54, I suspect that would be a significant outcome (and it would make me question the premises before I'd cook up a notion of inherent personal "luckiness" or "unluckiness").

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25th June 2011, 12:35 PM  #24 
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Assuming the stats are done properly ( no reason for me not to as it does not effect my point.) , there is an easy explination.
**** happens. As someone who loves role playing games, i see dice rolled constantly. And some people just roll worse than others, it is the way random stats work. This isn't to say if the person spent 300 hours rolling a dice it wouldn't even out, but in small doses, the way games are played, someone is going to be the one getting a lot of ****. Because someone else , somewhere is getting no ****. In a set of data as large as " poker players" it would be more weird if there was no anomalies, such as people who win a lot or loose a lot. Think of how many people on earth play poker. 
25th June 2011, 12:35 PM  #25 
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Well, depending on how you define "lucky" I would suggest that you can't find that true no matter what. That's why I prefer the question to be about whether or not the outcome of these hands is significantly different from the null hypothesis (a predicted ~27 wins out of 54).
At any rate, she's not asking about his luckiness for ALL the hands, but only these particular kinds of hands. So we're not looking to draw a conclusion about his success in the 99.4% of hands he plays. We're only talking about whether or not his number of wins in the remaining 0.6% of hands (and since that's all we're talking about, we're actually talking about 100% of these hands). 
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25th June 2011, 12:40 PM  #26 
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Poker is a game both of luck and chance, but smarter players know how to take advantage of certain situations, and read other players' emotions. It's both.
I do believe in other forms of luck though  finding a $100 dollar scratch ticket in a super market parking lot  that's luck. 
25th June 2011, 12:42 PM  #27 
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That's one of the things she expressed an interest in, yes. But that doesn't make my comments irrelevant. So why do you keep suggesting that they are?
Originally Posted by Beth

25th June 2011, 12:48 PM  #28 
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25th June 2011, 12:52 PM  #29 
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Heh. Typical us.
This is going to be a hooge semantic argument in next to no time. 
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25th June 2011, 12:54 PM  #30 
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In regards to this, i would like to point out a story, that is either utterly amazing, or mundane as hell, depending on how you interpret the statistics.
When i was going to get my tattoo, i had a bit of horrid luck, got into a terrible car accident, total wreck for all cars involved ( major bad luck). On the flip side, i came out with not a scratch ( major good luck). Now in calling the tattoo place, i found out the ****** up, and schedualed me for the next week ( major bad luck.). But then i called around the city and found one tattoo artist with a block of free time that day. ( major good luck, as they were all booked up for weeks when i called the first time.) As i wandered around town wasting time, i found a 50 dollar bill in a discount store ( major good luck.). But when i went to the tattoo place, a girl was getting one, and kept changing her mind slightly, extending the process and making me wait quite a bit ( Bad luck.). In wandering around waiting for her to be done i found a film i had been looking for for over a decade, garbage pail kids, for less than 6 bucks ( major good luck.) Finally when i finally got the tattoo, i realized that due to me being " ramped up" from the car accident, i wasn't really feeling it ( i am good at masking pain, but i do not have a high pain tolerance. And i can say i barely felt it, even when my friend was encouraging the man to make it hurt, and the guy was complying, my guess is because i was a 130 pound short fellow not complaining about the pain.) **** happens, sometimes it happens wierdly. 
25th June 2011, 12:58 PM  #31 
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Could you please run a simulation of the said events Sadhatter through about 10,000 occurrences so we can assess whether that really was luck? (Or folly to get a tattoo?)

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25th June 2011, 01:01 PM  #32 
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25th June 2011, 01:04 PM  #33 
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But, again, the OP describes a situation where skillincluding the ability to read your opponent's emotionshas been eliminated.
You've got 2 players allin and both have roughly a 50% chance of winning. There's no more skill involved. The outcome of the hand is just up to chance. In just that situation, if I'm reading this correctly, Beth's husband has won 21 of 54 hands, and she wants to know if this is meaningful or significant. 
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25th June 2011, 01:08 PM  #34 
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If these events are meant to be evidence for personal inherent "luckiness" or "unluckiness" I would suggest it's just an example of confirmation bias. We're lacking the information we'd need to know what the probabilities of any of these events are and, therefore, whether these events are significantly different from random chance with some level of confidence.
Now, if you only define "luck" as events happening consistent with the null hypothesis (that they are due only to random chance), then I would suggest that that's not the conventional way the word is used, especially when the question is, "Do you believe in Luck?" 
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25th June 2011, 01:31 PM  #35 
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The harder I work the luckier I get

25th June 2011, 01:41 PM  #36 
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25th June 2011, 02:04 PM  #37 
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Wow,
Thanks. That was a lot of responses quickly. I agree. Depends on how you define luck. The poll is just for fun. It's not meant to be meaningful, but to spark discussion. I voted planet x. Yes, this is exactly the data he has been collecting. We have a hypothesis. His luck at cards is poor. We set the null hypothesis that it isn't, his luck is just random variation. Now we've been collecting to data to test that assumption. In order to do that, we need, as Antiquehunter noted above, a set of hands were skill is eliminated and that is the data he has been collecting. We're continuing to collect data. As noted elsewhere, preflop all ins are a small percentage of the hands he plays. I can continue to post the results as they come in. When we defined a hypothesis as above, **** happens is rejected as an explanation. If the probability is low enough, we shake our heads and try to figure out why. At the moment, I'm stumped on that point.
Quote:
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. Incidently, I played a couple of tournaments with him and recorded all of our cards and outcomes. I rated the cards from 2 to A = 14. His average card value was 8.08 and 8.09, which is slightly above the expected mean of 8. So his cards aren't particularly bad on that score. Exactly. Thanks for reiterating that. My current estimate of the probability that it was just **** happening is a little less than 10%. Not exactly mindblowingly out of reason, but it's low enough that it can't be used to support the argument that it's just random variation. 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. 
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25th June 2011, 02:17 PM  #38 
Penultimate Amazing
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That clears it up and affirms that I have been correctly reading your OP description.
"Luck" is here defined as an alternate explanation for the resultssomething other than random chance. (I know "luck" and "chance" can seem synonymous, but "variation" really doesn't have the correct meaning in statistics.)
Quote:
Except that she's pretty much defining and using the word "luck" to mean something other than random chance. That is, the null hypothesis is that the results are not significantly different from what we'd expect by random chance with some degree of confidence. The hypothesis is that the outcome is due to bad luck. So the results are not due to bad luck, at least not if you use the term as used in, "Do you believe in Luck?" ETA: Also the poll would be pretty meaningless, I think, if "luck" were being used as a synonym for random chance. 
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25th June 2011, 02:22 PM  #39 
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Well anytime you are allin and have been called (rightly or wrongly) that takes any FURTHER skill out of the situation. Of course preflop this generally only happens when you have 2 big hands against each other, and either there is a big difference in stack sizes, or 2 people with lots of 'gamble'. After the flop there are loads more situations, especially in todays hyperaggressive tournament strategies. Some common ones are flopping a set against someone's big draw (or rarely, set over set), flopping a monster draw like a straightflush draw, and running into someone's set or top two pair... it goes on.
Other 'pure luck' situations would be testing when you play a pocket pair, how often do you flop a set? (should be about 1:8  the precise math eludes me at the moment, but its readily available). Or holding a suited ace, how often do you flop the flush draw, or even flop the flush? Its generally more important to know how to play these hands postflop (and when to play them at all) rather than how often you get 'lucky' with them. Or even how often you get 'unlucky' with them. The secret is always making the 'right' decision  let 'luck' sort itself out, as it will, over time. Some days it seems you can do nothing wrong and the chips are spilling all over in front of you. Other days you get solid starting cards and they consistently get cracked, even though you're playing them well. Some days it seems you get a stream of never ending 83os. Some days you can't miss a flop. In the long run, if you're making the right DECISIONS, the luck will even out for you and for all the players. 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 straightup game). 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 semibluffing or stonecold bluffing when you move allin postflop  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. 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'. 
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"If ignorance is bliss, why aren't there more happy people in the world?" Stephen Fry, 2006 Last edited by Antiquehunter; 25th June 2011 at 02:52 PM. Reason: swapped a 'skill' for 'luck'. Some days I wish I could! 

25th June 2011, 04:19 PM  #40 
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