Do you believe in Luck?

[TubbaBlubba]

I don't know we can extrapolate to other games. He doesn't complain about being unduly unlucky at other games. Of course, he doesn't play very many games where random chance is a factor.

So is he saying that there is a statistical anomaly in his poker games and only his poker games? It seems to me that one problem here is that even if he got an "average" result you wouldn't stop collecting data there; "yeah but that's just THOSE hands..." and then collect data on other hands until you found one WHERE he was "unlucky" - something that would actually be expected if you pick out enough samplings.

 

[JoeTheJuggler]

So is he saying that there is a statistical anomaly in his poker games and only his poker games? It seems to me that one problem here is that even if he got an "average" result you wouldn't stop collecting data there; "yeah but that's just THOSE hands..." and then collect data on other hands until you found one WHERE he was "unlucky" - something that would actually be expected if you pick out enough samplings.

Yep.

Though I think these concerns can be handled by giving a really tight definition of the hypothesis and not allowing data analysis on subsets of the data. As you mention, and I've said several times, we expect streakiness in the data.

Arbitrary starting and stopping only makes insignificant differences seem to be significant. In a way, it's the Texas Sharpshooter Fallacy, but I've been calling it post hoc hypothesizing.

 

[Finsend]

Lucky Woman

It just would really be scary if it turned out that Beth's husband actually is suffering from significant bad luck in these particular situations!

Wouldn't it?!



http://www.thisis50.com/profiles/blogs/luckiest-person-in-the-world

Luckiest Person In The World: Texas Woman Has Won Lottery 4 Times, Totaling $20.4 Million

 

[JoeTheJuggler]

It just would really be scary if it turned out that Beth's husband actually is suffering from significant bad luck in these particular situations!

Wouldn't it?!

Well, IMO, it is a supernatural explanation, and I think by definition supernatural explanations can't be causative. (That is, if it's causative, it's not supernatural.)

So if we did find that a result that would justify rejecting the null hypothesis, and we could be very very confident that the premises were all correct (primarily that the odds really were what we thought they were and that there was no bias in data collection or other methodological problems), then we'd be talking about something real in the natural world, a hitherto unknown physical force that contradicts mountains of evidence.

While I think the possibility of doing that (especially in this way*) is vanishingly small, I would find it incredibly exciting.

So if you're suggesting that fear of something new and unknown is biasing the "no" votes in the polls, I doubt that very much.

*I think work done by physicists at super high energy particle colliders is far more likely to turn up something like that. And I expect it won't conflict with mountains of current data, but either explain a great deal or refer to other conditions.

 

[Finsend]

It just would really be scary if it turned out that Beth's husband actually is suffering from significant bad luck in these particular situations! Wouldn't it?!

Well, IMO, it is a supernatural explanation, and I think by definition supernatural explanations can't be causative. (That is, if it's causative, it's not supernatural.)

So if we did find that a result that would justify rejecting the null hypothesis, and we could be very very confident that the premises were all correct (primarily that the odds really were what we thought they were and that there was no bias in data collection or other methodological problems), then we'd be talking about something real in the natural world, a hitherto unknown physical force that contradicts mountains of evidence.

I think I agree and if the results would slide slightly into some particular direction we might as well just call him 'a bit unlucky' then, I guess. Or we could collect some more data!

While I think the possibility of doing that (especially in this way*) is vanishingly small, I would find it incredibly exciting.

So if you're suggesting that fear of something new and unknown is biasing the "no" votes in the polls##, I doubt that very much.

*I think work done by physicists at super high energy particle colliders is far more likely to turn up something like that. And I expect it won't conflict with mountains of current data, but either explain a great deal or refer to other conditions.

I just think that it (the luck part) is - as has been said before a matter of words mostly and the meaning people give to them. And I now regret I did not vote for PlanetX btw.

I agree that some projects might be more significant than others, but both are fun imho and I'm just very curious about this one and the results.
As well as the boundaries of this project and it's effects on Beth's husband of course!

## ?

 

[Beth]

I've already said why--to eliminate the possibility of bias influencing data collection.

What bias? He's recording all hands of that type win or lose. What bias do you think is influencing the data collection?

The potential for bias to corrupt the data.

How so? This is an actual question I'm interested in because I don't know poker well enough. My experiences in the two venues don't lead me to think there would be bias resulting from combining the data from them. What are you thinking would cause bias from combining the two venues when collecting data on that one specific type of hand?

Even you, who I would call a "goat" rather than a "sheep" have been willing to point to analysis of subsets of the data as significant, even though we don't expect the results to be exactly Win-Loss-Win-Loss without any streakiness in the data.

I analyze subsets of data all the time professionally. I don't see the problem you are concerned about here and I haven't claimed any subset of the data as significant nor have I picked out any specific subset of the data that was a streak of losses and claimed that as well. I did point out that at various points during the data collection thus far, the p-value for the data collected up to that point was below 0.05. At the moment, it is slightly above 0.05.

My point has not been that this is a significant finding, but that it doesn't allow us to accept the null with much confidence. Whereas a p-value of, say, 0.4 or above would be a very convincing outcome that his observations were not accurate and he wasn't paying attention to the wins.

Since the easiest way to eliminate this possibility is a lab-type experiment, what is it about the real-game situation that needs to be reproduced?

I don't know.

Fair enough. Why shouldn't a sample of hands from a lab setting be representative of his "luck"?

I don't know why it wouldn't. What I do know is that it's a different situation and it hasn't been established that the same effect, assuming one exists, would hold.

(I think the idea of simply analyzing all the hands he is dealt is just to simplify and accelerate things--and to use some objective data collection like the record keeping of the software.)

Yes, that is my impression. But if that isn't what he wants to do, I don't see any reason to get upset or insist that he do it that way.

Personally, I think the biggest flaw is that you seem unwilling to say how many trials you will count and what confidence interval you will use. That's part of the hypothesis.

No, it's not. It's part of a formal testing procedure, but it's not part of the hypothesis.

Doing it after the fact isn't legit. When will it stop?.

We'll collect data until he is satisfied and doesn't want to continue. This isn't a formal experiment so I don't feel obligated to follow all the formal rules. As far as doing it after the fact, I'm computing the p-value for the cummulative total after every addition to our dataset. That's hardly an 'after the fact' analysis as it's the same analysis every time, I'm just updating the statistics when a new data point comes in. At some point, we should have sufficient data to make a solid conclusion one way or the other.

I agree, but looking at the two cards he is dealt for every hand would.

I disagree. It doesn't test the anomolous outcomes that he has remarked upon, which have to do with showdowns not his hole cards.

OK... maybe getting somewhere now...

Beth - look at these five examples below, and please tell me why any one of them would not be a valid extrapolation / environment for this premise.

1) You and he sit down at the table to play NL Hold'em. You each start with 10 pennies and the blinds are 1-2. You record results of any hand involving an all-in showdown.

That would be okay.

2) He plays online poker at a 'free' site for 'points' against random strangers (who may even not be people). He records, using either the site software, or an add-on software tool every hand played. Any hand involving an all-in showdown becomes included for consideration in the experiment.

That would be okay.

3) You and he sit down at a table, and deal random hold'em hands to two selected, static hands of his selection. (Say QQ vs AKs) The assumption is that these hands are 'all-in' pre-flop. All hands are recorded for the experiment.

That's not a game situation. It would not necessarily replicate what he has experienced.

4) He plays poker at a 'garage' game. He records a shorthand hand recap in a notebook for any hand involving an all-in showdown (where HE is inolved). All such hands are recorded for the experiment - we assume that he is sufficiently responsible to not predispose / fudge on the data collection.

That would be okay.

5) He and x number of friends sit down around a table. You use appropriate randomness/diligence when dealing. Each person buys 10 matchsticks for a dollar. You play NL texas hold'em and record every hand for which there is an all-in showdown involving your husband.

That would be okay.

You stated Beth, that your husband understands the math. Yet he's saying that his expectations deviate from this. You want to test to see:

- Is there confirmation bias?
- Is there some sort of inherent 'unluckiness' to him, in a very precise, specific situation?
- It could be that the games aren't fair - although the difference between the two environments is so great (to say nothing of the fact that maybe he plays on multiple 'free' sites - and it seems vastly unlikely that all of the free sites are unfair and/or skewed the same way vs him) that this seems to be discardable.

If I am correct that these are the only three possible situations, and your husband isn't disputing the math, then the only plausible answer is #1.

Yes, that's pretty much the situation. Yes, we've effectively discarded the hypothesis that the games aren't fair.

Because #2 is worth a million dollars and would change everything the world 'knows' about gaming.

I don't think that would work because winning a million would definitely be 'lucky'.

So is he saying that there is a statistical anomaly in his poker games and only his poker games? It seems to me that one problem here is that even if he got an "average" result you wouldn't stop collecting data there; "yeah but that's just THOSE hands..." and then collect data on other hands until you found one WHERE he was "unlucky" - something that would actually be expected if you pick out enough samplings.

The data collection is actually more about determining if his observations ahve been accurate or biased. I think that if it turns out he's getting 'average' luck, he'll accept that he just wasn't paying attention to the wins or was just having a long streak of losses that got balanced out with wins in the long run. However, the data thus far leans more towards vindicating his feelings than it does towards bias in his previous observations.

 

[Antiquehunter]

That would be okay.
That would be okay.
That's not a game situation. It would not necessarily replicate what he has experienced.
That would be okay.
That would be okay.

Yes, that's pretty much the situation. Yes, we've effectively discarded the hypothesis that the games aren't fair.

I don't think that would work because winning a million would definitely be 'lucky'.

OK... now we're moving forward a bit.

From my perspective, all five methods are valid, but fine, you don't like #3 so we'll put it aside. My preference would be if you would consider using #1 and/or #5 for data collection, my reasoning being:

- You as the neutral observer can gather the data in a controlled setting. I also suggested the games be structured so they'll be very fast-paced and will involve a lot of 'all-ins'. This is not contrived and is very much a valid 'testing' environment. It is a 'real' game to be sure - the sort of game one would experience late in a tournament, or in a specifically structured cash game. But you should be able to glean a lot of data in a relatively short period of time because of the number of all-ins you will see. Also, it allows your husband to focus solely on the game, and takes the burden of data collection off him.

- The free-site method would get you even more data, but lets keep the testing to as small a subset of external variables as possible. Lets also not cloud the test by having two dramatically different testing environments with whole separate sets of external factors. Also, for whatever reason, he is not willing to use the automated data collection methods, so the relative ease of gathering data from online play is thereby closed.

Facetiousness aside - if you can indeed prove that your husband is indeed some sort of 'cooler' at a very specific game, that this raises a lot of fundamental questions, that could lead to an attempt at the MDC.

 

[Beth]

OK... now we're moving forward a bit.

From my perspective, all five methods are valid, but fine, you don't like #3 so we'll put it aside. My preference would be if you would consider using #1 and/or #5 for data collection, my reasoning being:

- You as the neutral observer can gather the data in a controlled setting. I also suggested the games be structured so they'll be very fast-paced and will involve a lot of 'all-ins'. This is not contrived and is very much a valid 'testing' environment. It is a 'real' game to be sure - the sort of game one would experience late in a tournament, or in a specifically structured cash game. But you should be able to glean a lot of data in a relatively short period of time because of the number of all-ins you will see. Also, it allows your husband to focus solely on the game, and takes the burden of data collection off him.

I don't have any objection to either, but it's unlikely to occur simply because it's not something we do these days. The last time we sat and played poker at our table was a few years ago. On-line games are much more convenient. I don't think we've had friends over to play a game in a couple of decades. We just don't get out much these days. While his current data collection may be too slow for your taste, it isn't bothering either of us. I have collected data on on-line games we both participated in on-line and I might manage to do that again. If I get the chance, I will.

Facetiousness aside - if you can indeed prove that your husband is indeed some sort of 'cooler' at a very specific game, that this raises a lot of fundamental questions, that could lead to an attempt at the MDC.

I don't think so. As someone pointed out earlier in this thread, given the millions of people who play poker, it would not be surprising if there were not a few people who had extremely long good/bad luck streaks.

 

[Antiquehunter]

I don't think so. As someone pointed out earlier in this thread, given the millions of people who play poker, it would not be surprising if there were not a few people who had extremely long good/bad luck streaks.

Sure - but just having a long bad luck streak >< proof that your husband is 'unlucky'. If all you're trying to do is show he is currently experiencing a bit of bad luck vis a vis the type of hand you're tracking, well - you can probably say that, with appropriate caveats, and there is no larger meaning to this thread as a whole.

 

[Beth]

Sure - but just having a long bad luck streak >< proof that your husband is 'unlucky'.

We collect data. All the data can potentiallyshow is a long, statistically anomolous streak of bad luck. It seems reasonable to me to conclude that someone who experiences that is unlucky.

What is the difference you perceive between the two? How would you prove someone is 'unlucky' versus showing that they experienced a long streak of bad luck?

 

[Antiquehunter]

I would say that a repeatable and significant demonstration of 'bad luck' would be worth examining further. In much the same way that someone who said they could predict the roulette wheel, or the tumble of craps dice with a significant and repeatable level of accuracy over the mathematic expectation.

For example: If someone said that they could predict the next number on the spin of a roulette wheel with greater than 50% the mathematic expectation, that would be extremely compelling. Done over a series of a large sample of spins, each using separate, tested to be balanced & fair wheels, changing up the dealers, done 'blind' to eliminate any 'skill' in using physics and rapid calculation to pick a number (as Darren Brown attempted - or 'magicked') etc... Someone able to predict roulette outcomes 1:19 spins vs 1:38 spins, over and over again, would be pretty head-scratching, and would set the gaming world on edge.

If your husband alleges similarly but in the reverse ie - I am unluckier by 50% in showdown all-in hands. So if mathematical expectation is 52/48, I won't get any more than 26/74 success, and he can do this over and over again, over a series of trials - well, I think you're experiencing something that defies explanation as I understand it.

A statiscian would be able to state more clearly the number of attempts it would take in a series of trials, the number of trials, and the expected 'improvement' over mathematic expectations. It becomes much the same question as to the bar Randi sets for his classic '5 card' psychic experiment, just using different equipment and a slightly different context.

 

[Rasmus]

There is one more possible explanation:

A player who enters that sort of showdown-situation might simply have a good read on the players who are not involved in the showdown and gain an advantage that way.

Say the husband likes playing aces with good kickers. If an opponent holds a low pair an all-in would be a favorable move for him, but only marginally so. But if the opponent has reason to assume that some other ace was folded, his odds would go up. (I haven't done the math, just checked online quickly: 66o, AKs, A2o come out at 51.55%, 38.75%, 7.43%. This would change again if the other ace would fold, tohugh.)

 

[Antiquehunter]

@Rasmus - I don't fully disagree, but unless cards are flashed, it is impossible to 'KNOW' this for a fact. One could suspect that a player who thought long and hard about releasing his hand MAY be agonizing about laying down an ace (because he plays trashy aces all the time) and one could adjust your internal calculations accordingly. So long as the cards are not known to the players making the decision the odds as impacts their decision are unaffected. When watching poker on TV, they can adjust the odds for the viewers, because they've seen (usually) all the hole cards. The other players don't have that info.

Fundamentally, pre-flop all-ins with only a 2% edge either way, are a gambler's move. There are reasons to push for this sort of showdown : midway-late in a tournament and your chipstack requires you to make a move of some kind; you are against a world-class player who will eat you up if you play him post-flop, so taking the coin-toss against him is about as good as you'll get; your chipstack is so small that you're just tossing it in on any reasonable hand etc...

As Beth has stated, there is no interest in looking at how this perceived 'luck' is impacting the bottom line, nor any interest in improving the game, so its immaterial.

 

[Rasmus]

@Rasmus - I don't fully disagree, but unless cards are flashed, it is impossible to 'KNOW' this for a fact.

Of course.

One could suspect that a player who thought long and hard about releasing his hand MAY be agonizing about laying down an ace (because he plays trashy aces all the time) and one could adjust your internal calculations accordingly.

That's what I had in mind. If such a player limps from middle position and then folds to a raise and a call, e.g. it would not be entirely unlikely that they played Ax or Kx suited.

So long as the cards are not known to the players making the decision the odds as impacts their decision are unaffected.

Of course. But I think the situation described might occur often enough to be readable for a more observant player to at least give him a slightly better edge. (e doesn't have to be sure at all! If he is playing the pair then going against over-cards he's already ahead either way. Suspecting a slightly better edge might allow him to chose spots more precisely, though.

When watching poker on TV, they can adjust the odds for the viewers, because they've seen (usually) all the hole cards. The other players don't have that info.

No, and I agree it would have to be a fairly good read on a folding player. And then, the over-cards would have to be aces or kings.

Fundamentally, pre-flop all-ins with only a 2% edge either way, are a gambler's move.

Yes. And I was ignoring that when judging the decision to go all in with the pair.

There are reasons to push for this sort of showdown : midway-late in a tournament and your chipstack requires you to make a move of some kind; you are against a world-class player who will eat you up if you play him post-flop, so taking the coin-toss against him is about as good as you'll get; your chipstack is so small that you're just tossing it in on any reasonable hand etc...

As Beth has stated, there is no interest in looking at how this perceived 'luck' is impacting the bottom line, nor any interest in improving the game, so its immaterial.

All of the above would be, yes.
But even if he was losing more than chance would predict, there'd still be a simple and rational explanation available. It might be enough to explain what little couldn't be explained by chance alone if it only occurred very rarely.

 

[Antiquehunter]

But even if he was losing more than chance would predict, there'd still be a simple and rational explanation available. It might be enough to explain what little couldn't be explained by chance alone if it only occurred very rarely.

Well not really Rasmus. I see where you're going with this - he's done a Bayesian analysis and decided that there is a 60% chance that an ace is gone, and an 80% chance he's facing a big ace. I don't have the tools with me to do the precise math, but if we look at AQ vs 88 vs A2, then the pre-flop odds are 34.4%, 54.6%, 8.1% (roughly). Assuming the A2 folds, MOST but not all of that 'win' equity goes to the 88. For ease of calculation, lets say that it all accretes to the 88. So a 52/48 is now roughly a 65/35. (88 vs AQ, one ace known to be gone, preflop.) However - unless the cards are flashed, he's only 60% sure of his A2 read, and 80% sure of the AQ read. So the player REALLY cannot add the full value of the (potential) adjusted odds to his hand (hence the Bayesian analysis). Maybe the odds go from 52/48 to effectively 60/40. Few world class players with those kinds of reading skills are going to want to get their money in the middle pre-flop holding only a 60/40 edge. If they can consistently read and calculate to this level, they will be making their big plays post-flop.

Anyways, I see two ways to overcome this, in the (unlikely) event that the data collected suggest someone REALLY is genuinely 'unlucky' over a decent sample.

- Deal out the cards in a rigid lab environment such as option #3 or #1 I suggested above. No other cards available to influence a card 'reader'. Keep the test to a heads-up situation as much as possible.

- Make sure that the mathematical goal for being 'unlucky' is set high enough that the world's best card reader (ie - Negraneau or similar) even using all his skills as described above would still be realizing results way below (or above) expectation.

FWIW - playing online, at free money tables, I think it is a massive stretch to suggest meaningful reads of the caliber described here are possible. Playing free, if you're the sort of player who plays any Ace, if you're playing for free, why would you lay it down pre-flop? And even if you did lay it down pre-flop, would you really be 'agonizing' about it and giving off the FAINTEST of online 'tells'? You'd be just as likely to 'agonize' over laying down a 97 or a J4.

 

[Rasmus]

[...]

Lots to agree with snipped.

Anyways, I see two ways to overcome this, in the (unlikely) event that the data collected suggest someone REALLY is genuinely 'unlucky' over a decent sample.

- Deal out the cards in a rigid lab environment such as option #3 or #1 I suggested above. No other cards available to influence a card 'reader'. Keep the test to a heads-up situation as much as possible.

I have to agree with Beth here: The claim of "being unlucky in poker" only makes sense if "luck" is something supernatural. So it wouldn't work in a lab setting. (Or at least it might not.)

The lab setting is perfectly okay to analyze random chance fluctuations - but we don't need a lab for that, since we know what will happen, right?

- Make sure that the mathematical goal for being 'unlucky' is set high enough that the world's best card reader (ie - Negraneau or similar) even using all his skills as described above would still be realizing results way below (or above) expectation.

FWIW - playing online, at free money tables, I think it is a massive stretch to suggest meaningful reads of the caliber described here are possible. Playing free, if you're the sort of player who plays any Ace, if you're playing for free, why would you lay it down pre-flop? And even if you did lay it down pre-flop, would you really be 'agonizing' about it and giving off the FAINTEST of online 'tells'? You'd be just as likely to 'agonize' over laying down a 97 or a J4.

No, I was thinking of the garage type game here: People are not paying attention to their tells, and one player might well learn how to read a very specific situation in one or two other players.

Like you said earlier: A pro probably wouldn't find himself all-in in that type of situation a lot.

@Beth: I'd be interested in seeing the actual stats, if it's not too much work. Unless the losing overcards tend to include an ace and a king, my idea is rubbish either way.

 

[Antiquehunter]

No, I was thinking of the garage type game here: People are not paying attention to their tells, and one player might well learn how to read a very specific situation in one or two other players.

Perhaps - but Beth's data are gathered from two very different sources: Online 'free' games (I don't know if multiple online sites are involved) - where I think for very good reasons, it is highly implausible that tells would make a hill of beans difference for these sorts of hands.

You would need to analyze both subsets of data separately (live game vs free online play) and you would need to know a good deal more context: Are the players the same game after game, does Beth's husband apply these sorts of principles to his game & keep notes (even mental ones) on the proclivities of the other players?

Fundamentally, if this is what he's doing, (which as I showed mathematically isn't really going to add a whole lot of luck/unluck) then he's simply being disingenuous. The question is no longer whether he's lucky/unlucky, its whether or not he's a good card reader of players at his live game.

Just to expand a bit further - this specific idea ONLY applies when Beth's husband is holding a pocket pair, and has reason to believe that:

a) His opponent has two overcards, with an ace.
b) Someone earlier folded an ace.

It doesn't work the other way - if Beth's husband had the two overs with an ace, and had reason to beleive that someone had mucked another ace, presumably, he acts accordingly. He certainly (I hope) would not get into an all-in heads up situation knowing he was more of a 65/35 dog.

The possible results are:

- He's right. Therefore the 'real' odds on the showdown aren't really 52/48, but 65/35ish - in his favour. He should therefore 'appear to be luckier' based on the mathematical expectation.

- He's right about the player's holding of two overcards, and wrong about the mucked Ace earlier. So its still a 52/48.

- He's right about the mucked ace, he's wrong about the opponents' holding - hand would not be recorded in the data.

- He's wrong and runs into a higher pair. This hand wouldn't even be included in the test data as gathered by Beth. (She's only tracking pair vs 2 overs)

- He's wrong and runs into either a lower pair, or some other hand that is not two overs. As above - wouldn't appear in the data.

So - the only POSSIBLE way this would skew the data, IF INDEED Beth's husband is applying such tactics in a meaningful way, would be that he should be indeed, luckier! Or - that he is DELIBERATELY skewing the results by knowingly going all-in when he 'knows' he's an underdog with a deceptively stronger hand.

Of the 54 hands in the sample data, if we assume that 27 came from the live game, and that 1/2 of those 27 hands were where the husband held the pair... (13 hands). There are only 13 hands that COULD possibly be influencing these outcomes. Assuming that he's 80% right on BOTH reads required, 64% of those 13 hands MAY be affected by this action. Or in other words, at absolutely best, 8 hands in the sample could be affected by this play. Of course this number will be significantly reduced because the odds of 2 or more hands at a 9 handed game holding single aces is at best about 45% http://math.sfu.ca/~alspach/comp47.pdf complicated further that the relative position of the players at the table means that Beth's husband couldn't make any use of the 'tell' if it even existed as not all players will give off such tells...

So - that the effect is of nominal 'value', and the likelihood that in the sample we're seeing so far, that Beth's husband has been able to influence meaningfully these results as a result of the 'reading' skills described is pretty remote.

 

[Antiquehunter]

I have to agree with Beth here: The claim of "being unlucky in poker" only makes sense if "luck" is something supernatural. So it wouldn't work in a lab setting. (Or at least it might not.)

The lab setting is perfectly okay to analyze random chance fluctuations - but we don't need a lab for that, since we know what will happen, right?

Which is why I proposed playing 'heads-up' (only 2 players) in a 'real' game setting. (It doesn't seem to make a difference if money is involved, as we're already looking at free game & money game results). People play 'heads-up' poker all the time. It happens at the end of every major tournament, in happens online at special tables geared for people who want to play heads-up, it happens in Vegas, it happens at special 'heads up' tournaments. Its a perfectly legitimate, 'real game' environment.

Playing heads-up eliminates all this external information that MAY (unlikely) be influencing the results. If Beth's husband CHOOSES to go all-in with a QQ, or to call Beth's all-in bet with that same QQ - whether or not he suspects that Beth has an AK, or suspects she has a 72, it is immaterial. When the cards are turned over, its a 52/48, nothing could be simpler.

 

[Rasmus]

...

I was thinking the other way around: Another player is skillful enough to detect that

a) Beth's husband is likely to go all-in with an ace and a high kicker
b) some other regular player in the same garage game will often limp with an ace (possibly a king, too) and a bad kicker but then fold if there is any noticeable opposition.

The garage-type games I know make it not unlikely that you have a combination of players that includes the very good (our unknown opponent who knows how his opponents are playing), intermediate players (beth's husband who at the very least knows when he is gambling) and the pure hobbyists (who think every suited ace is worth a limp.)

Such a situation might be rare - but if the opponent only let's the all-in happen if he finds himself in that precise situation, the overall results of all the flips would not be what's expected.

But this is really just idle speculation, and I fully agree that without much more precise information it is all fairly pointless. I'll happily concede all my points besides this: Even a pre-flop all in doesn't happen entirely randomly. So non-random results are likely explainable by the factors that led to the all-in in the first place.

Going back to your example: If I am holding 88 I need a reason to go all-in with it and expect that my opponent has nothing better than two over-cards. Likewise, if I am holding JK I need a reason to go all-in with it and expect that my opponent really just has a lower pair, instead of something that at the very least dominates my hand.

 

[Rasmus]

Which is why I proposed playing 'heads-up' (only 2 players) in a 'real' game setting. (It doesn't seem to make a difference if money is involved, as we're already looking at free game & money game results). People play 'heads-up' poker all the time. It happens at the end of every major tournament, in happens online at special tables geared for people who want to play heads-up, it happens in Vegas, it happens at special 'heads up' tournaments. Its a perfectly legitimate, 'real game' environment.

Playing heads-up eliminates all this external information that MAY (unlikely) be influencing the results. If Beth's husband CHOOSES to go all-in with a QQ, or to call Beth's all-in bet with that same QQ - whether or not he suspects that Beth has an AK, or suspects she has a 72, it is immaterial. When the cards are turned over, its a 52/48, nothing could be simpler.

True. (unless whichever entity was responsible for the luck and bad luck decides it doesn't want to be tricked by a test-game, of course ...)