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 05-23-2012, 06:09 AM #1 banned     Join Date: Apr 2012 Location: madnak's biggest fan Posts: 304 probability when premises are false Forgive me most righteous overlord Zeno, but I added a poker hand to help illustrate what I'm talking about. [hand_history]Poker Stars, \$0.25/\$0.50 No Limit Hold'em Cash, 6 Players Hero (BTN): \$60.92 (121.8 bb) SB: \$20.93 (41.9 bb) BB: \$37.90 (75.8 bb) UTG: \$54.51 (109 bb) MP: \$52.95 (105.9 bb) CO: \$50 (100 bb) Preflop: Hero is BTN with K A 2 folds, CO raises to \$1.50, Hero calls \$1.50, SB calls \$1.25, BB folds Flop: (\$5) K 3 2 (3 players) SB checks, CO bets \$3, Hero calls \$3, SB folds Turn: (\$11) T (2 players) CO bets \$8, Hero calls \$8 River: (\$27) 2 (2 players) CO checks, Hero bets \$16.50, CO folds I have statistics saying he opens the CO with 17% of hands over a fairly decent sample, but nonetheless, it is a sample; I think this thought process here is a Bayesian one(please inform if not) but 17% is very tight, much more than the average regular, so one can reason that his real CO opening frequency is more likely to be higher than 17% than it is to be lower than 17%. Easy enough. Combining our statistical and note reads,(our premises) we can deduce that villain comes to the river with a range of KJ+(our conclusion); we have fairly strong reads that he triple barrels flush draws, that he doesn't bet underpairs on that turn, and bets 2pair+ on this river, but what if are premises here are incorrect? What if he double barrels with JJ/QQ? What if he x/f with a busted draw on the river? What if his preflop range here is wider and he has K9s as well, or more? Poker players usually use the words, "it's likely he has KJ+ here" because they factor in the probability that they're incorrect, but how would this be done formally? Is it simply assigning "likelihood coefficients" to each event? So we can say that we have reasons to believe that he'll open AK close to 100%, and due to possible faults in our conclusion perhaps K9s 20%, but isn't that a argument on top of a argument? So because of X, Y, and Z(premises), V is likely to = W(conclusion), but than X may actually = R and Y = P, so we assign the likelihood coefficients of that being so, but than one must assign another likelihood coefficient that R actually =T and P = Q. This is a finite loop(a long one), with every succession's likelihood coefficient becoming progressively smaller. What about with more obscure events; going by my information of the world, I can deduce that the probability that I'll grow wings organically and be able to fly is 0.000(infinite) with a strong amount of certainty. However, what if my deduction's are wrong? What if I've sustained some sort of brain injury that causes my memory/data collection mechanism to be faulty? What if I contract some sort of alien mutation that causes my wings to grow? Can the likelihood coefficient process be done to that as well?
 05-23-2012, 09:03 AM #2 old hand     Join Date: Jul 2007 Location: Losing at Omahaha Posts: 1,483 Re: probability when premises are false Just don't rule out any hand 100% and keep updating your probabilities in a Bayesian way. E.g. don't discard K9s completely from the get go, but just keep it in there with a low probability assignment. EDIT: He's got a finite number of possible hand combinations. No reason not to assign everyone of them a probability >0. Also, reraise preflop.
 05-23-2012, 09:09 AM #3 banned     Join Date: Apr 2012 Location: madnak's biggest fan Posts: 304 Re: probability when premises are false I'm not interested in the poker side of this, that was simply a analogy (obvious wrote that to prevent thread from not existing, from never existing)
 05-23-2012, 03:43 PM #4 Pooh-Bah   Join Date: Feb 2009 Posts: 4,523 probability is deduction so all uncertainty about your conclusion (excluding esoteric stuff) stems from uncertainty about the assumptions and premises you're using. only some of this uncertainty is quantified. for example, take a 95% confidence interval. it doesn't say anything about the uncertainty about a parameter that's due assumptions about the model, distributions etc
 05-23-2012, 05:32 PM #5 banned     Join Date: Apr 2012 Location: madnak's biggest fan Posts: 304 Re: probability when premises are false Why esoteric stuff? Sure it's all deductions from premises, but that doesn't help a ton in regards to modelling the real world; I suppose really, factoring in uncertainty is merely adding another premise by which to deduct from, hmmrmm.
 05-28-2012, 08:16 PM #6 banned     Join Date: Apr 2012 Location: madnak's biggest fan Posts: 304 Re: probability when premises are false So I was thinking about this again; there needs to be some form of evidence to create a premise to create a probability deduction from, because if there isn't everything would be cancelled out: if I deduce that my understanding of reality may be way of and nothing is possible, I could in turn reason that there's a possibility for a +999^99999999999999 unit payoff(or perhaps infinite, not sure how that would work) if I hold my leg and jump in circles, but there's also potential for a -999^999999999999 unit payoff if I perform the same action. If this is the case though, what is adequate evidence? I suppose it would depend on the scope. So I guess what I'm having troubles with is validity; sure, if A than B, but does A even exist? What if A is actually C, and therefore, B doesn't occur?
 05-29-2012, 04:25 PM #7 newbie   Join Date: May 2012 Location: Baltimore Posts: 33 Re: probability when premises are false Every time you ask one of these what-if questions, you are essentially adding another random variable to the "equation", however you don't know the mean or standard deviation of it. In that case, if it really concerns you, you should do enough work to either get a decent sample of it's mean and SD, or at least enough work to know it isn't a having a big impact so you can ignore it. If it doesn't really concern you then your brain has probably already done enough subconscious work to figure out it isn't very important (although once in a while it may miss something subtle that actually does have an impact so spending some effort to check things can help, like talking to other players). For example: "What if he double barrels with JJ/QQ?", well if you don't know whether he does or not then you can't make any solid conclusions. So start trying to figure out if he does by watching him play more or gather the information in some other way (ask other players who also play vs this one, etc.). Then you can assign a sample mean to this variable and start making conclusions using it.
05-29-2012, 10:04 PM   #8
old hand

Join Date: May 2012
Posts: 1,970
Re: probability when premises are false

Quote:
 Originally Posted by omnimirage the II So I guess what I'm having troubles with is validity; sure, if A than B, but does A even exist? What if A is actually C, and therefore, B doesn't occur?
Take an advanced statistics course. Your problems will be solved if they get into frequentist vs. bayesian points of view and you pay attention.

And stop worrying about whether your concepts are real. They aren't. They are just ways of understanding the world. You do require them to the same extent that you require a way of differentiating your girlfriend from some random homeless girl. Failing to make the "false distinction" or "false categorization" can be the difference between clamidia and syphilus.*

*As far as I know your girlfriend has neither.

 05-30-2012, 06:47 AM #9 Cooler than Sammy Hagar   Join Date: Aug 2005 Location: Salt Lake City Posts: 19,743 Re: probability when premises are false Math describes how well-defined systems work. The validity of any mathematical model depends on the validity of its assumptions. There's no way to do math without assumptions. You can always substitute a different set of assumptions in order to get different results, but you can't get results without assumptions. I don't believe we can discuss anything without sharing certain premises either, and so I think the act of discussion itself presumes the validity of some set of premises. Communicating about a case in which no premises are valid strikes me as a contradiction in terms.
05-31-2012, 05:33 AM   #10
Carpal \'Tunnel

Join Date: Jun 2006
Location: drinking in a saloon
Posts: 11,933
Re: probability when premises are false

As far as I can tell, yes, this approach is a Bayesian one. What that means is your predictions of the future (both what he will show down, and what he will do) depend on the past, or the underlying distribution - the most important thing is his previous actions, but when you don't have enough information on him, you fill in the gaps with an amalgam of your knowledge of other poker players that vaguely fit his description. You add a decent confidence interval to represent the facts that you don't know how well this guy fits into the underlying distribution of poker players and you don't know how well to trust your own experience, and you arrive at a 'range of ranges', as it were, some with a high frequency, some with a low.

I personally see no reason to make any of this formal, though. Your poker maths should be largely intuitive, after a certain point, once you're playing; away from the table, as long as you consider this time spent 'work' rather than 'messing around with maths', your time is better spent on other stuff.

Quote:
 Originally Posted by BrianTheMick2 And stop worrying about whether your concepts are real. They aren't. They are just ways of understanding the world. You do require them to the same extent that you require a way of differentiating your girlfriend from some random homeless girl. Failing to make the "false distinction" or "false categorization" can be the difference between clamidia and syphilus.* *As far as I know your girlfriend has neither.
I've been thinking about this a lot recently as well. A lot of concepts are becoming increasingly abstract to me, in the same way as when you say a word over and over in your head and eventually 'poem' doesn't sound like a real word anymore, it's made-up, or you're not saying it right, or something - but I see the evidence that these concepts exist, they accurately describe the world, that the world follows these rules. Probability is the best example of this. All it does is follow the way the world works, it describes, but it doesn't ascribe. I'm putting a decent level of faith in that relationship when I make a +ev bet. But it wasn't always this way; when I first came to understand ev, this wasn't a problem.

Last edited by wazz; 05-31-2012 at 05:45 AM.

 05-31-2012, 04:18 PM #11 veteran     Join Date: Oct 2010 Posts: 2,617 Re: probability when premises are false There is this thing called Laplacian smoothing that you can use to deal with stuff like 0% and 100% probabilities (it essentially makes them slightly above 0% and slightly below 100%). In other words, it smoothes out the probability function.
06-02-2012, 11:17 PM   #12
old hand

Join Date: May 2012
Posts: 1,970
Re: probability when premises are false

Quote:
Oh, don't do that. At best, you will be chasing your tail. Entertaining to the rest of us to watch, but you won't get anywhere.

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 A lot of concepts are becoming increasingly abstract to me, in the same way as when you say a word over and over in your head and eventually 'poem' doesn't sound like a real word anymore, it's made-up, or you're not saying it right, or something - but I see the evidence that these concepts exist, they accurately describe the world, that the world follows these rules.
Holy run-on sentence Batman!

Concepts are, by definition, abstractions. As long as they work by helping you summarize ("that dude is a douchebag" is a summary of someone's past behavior), predict (earlier douchebag will probably exhibit douchebaggery in the future), and plan your next move (don't invite him to your next party, pitty **** his girlfriend, etc.).

Quote:
 Probability is the best example of this. All it does is follow the way the world works, it describes, but it doesn't ascribe. I'm putting a decent level of faith in that relationship when I make a +ev bet. But it wasn't always this way; when I first came to understand ev, this wasn't a problem.
The best you can say with certainty is "It seems to me like x -> y zz.z% of the time, and I got a theory as to why they are related. Granted, I might actually be a small pile of poached eggs with an overactive imagination, but that just doesn't fit with what I've experienced so far. For instance, I seem to have legs. Why would a small pile of poached eggs imagine that it had legs?"

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Night-time ramblings over as well. I seem to be heading off for a bit of snuggles with my fiancee or perhaps I am breakfast.

Since it seems more likely that I am heading off to bed, I am going with that. I'll adjust my take if someone dips a bit of toast in me to absorb my yolky goodness.

06-03-2012, 11:52 PM   #13
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Join Date: Apr 2012
Posts: 304
Re: probability when premises are false

Quote:
 Originally Posted by REALphysical Every time you ask one of these what-if questions, you are essentially adding another random variable to the "equation", however you don't know the mean or standard deviation of it.
I don't really understand this, would you be so kind to elaborate?

Quote:
 In that case, if it really concerns you, you should do enough work to either get a decent sample of it's mean and SD, or at least enough work to know it isn't a having a big impact so you can ignore it.
Sure, but this is a bit difficult to do when dealing with more abstract issues, like god worshiping payoffs or life paths to take.

Quote:
 Originally Posted by BrianTheMick2 Take an advanced statistics course. Your problems will be solved if they get into frequentist vs. bayesian points of view and you pay attention.
I'm no longer in uni D: I might pick up a probability book and go through all that eventually, but.

Quote:
 And stop worrying about whether your concepts are real. They aren't. They are just ways of understanding the world. You do require them to the same extent that you require a way of differentiating your girlfriend from some random homeless girl. Failing to make the "false distinction" or "false categorization" can be the difference between clamidia and syphilus.*
Do you mean my mental representations of the world are merely abstracts and hence, aren't real? Or I'm just doomed to be way off or something?

eh my representations of the world gives me insight to phenomena that would otherwise go over-looked.

Quote:
 Originally Posted by madnak Math describes how well-defined systems work. The validity of any mathematical model depends on the validity of its assumptions. There's no way to do math without assumptions.
hmmrmm, isn't validity the process of turning the premises into a conclusion? I suppose premises in themselves are arguments but, so they have their own validity; is this what you meant?

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 I don't believe we can discuss anything without sharing certain premises either, and so I think the act of discussion itself presumes the validity of some set of premises. Communicating about a case in which no premises are valid strikes me as a contradiction in terms.
hmrmmm, is this a rather complicated way of saying if one doesn't share any belief with another, it'd be impossible to communicate? That is, without having some sort of similar understanding, no communication would able to be successfully interpreted?

*man points at fruit and gestures in a way that says, "I want you to collect that fruit for me so I can eat it" The other man responds by jumping up and down and rubbing his little finger, spins around and farts*

Suppose that that is a bad example, as the reciprocated recognised he was being communicated to.

Quote:
 Originally Posted by wazz I personally see no reason to make any of this formal, though. Your poker maths should be largely intuitive, after a certain point, once you're playing; away from the table, as long as you consider this time spent 'work' rather than 'messing around with maths', your time is better spent on other stuff.
Thread was more for interest sakes, you have the most awesomeness avatar on 2+2 btw

Quote:
 I've been thinking about this a lot recently as well. A lot of concepts are becoming increasingly abstract to me, in the same way as when you say a word over and over in your head and eventually 'poem' doesn't sound like a real word anymore, it's made-up, or you're not saying it right, or something - but I see the evidence that these concepts exist, they accurately describe the world, that the world follows these rules. Probability is the best example of this. All it does is follow the way the world works, it describes, but it doesn't ascribe. I'm putting a decent level of faith in that relationship when I make a +ev bet. But it wasn't always this way; when I first came to understand ev, this wasn't a problem.
Sounds like you're more of a concrete thinker, the "sensing" on the Myers-Briggs Type Indicator, some guys find comfort in thinking in terms of abstracts, even when the phenomena is starting them straight in the face.

Quote:
 Originally Posted by la6ki There is this thing called Laplacian smoothing that you can use to deal with stuff like 0% and 100% probabilities (it essentially makes them slightly above 0% and slightly below 100%). In other words, it smoothes out the probability function.
I googled this, and it's way beyond me D:

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