odd thoughts

this has just been going through my head lately, tell me what you all think. This is in reguards to odds of completing your hand, ie a flush or straight draw. Even though we can get an idea of when the odds are in our favor, we can never ever predict with 100% accuracy that the next card comming will help our hand. The game of cards is a chaotic enviorment, it has infinit odds as to what it is going to do. Say you have had 29 flush draws in a row (this is just theoretically speaking) and you get delt another one, there is no 100% garentee that the next card comming will make your hand. It may, but you can never be for sure. Now how can this happen? It should have come by now but it didnt. Im sure some of you are reading this and going what are you babbling about, if you have 30 flush draws of course your going to hit! Why, how, where is the proof that yes you will hit one of thoughs times, odds are all theoretical anyways arent they, so one starts to think, well since i cant predict exactly when my card that i need is going to come, why take your odds as serious as some of us do? Why take them into consideration at all? Its better to have at least an idea of what should come and when but why do we try to keep theoretical records in a chaotic game where there is no garentees? I have just been thinking about this, not saying it is how i play but it makes for an interesting conversation.

This topic is covered pretty well in introductory probability courses. Basically, we accept the fact that each event is in truth deterministic, but that the forces that determine the outcome are unknowable and random. We build a mathematical model that expresses the distribution of events (a likelihood function) and use it to determine with what frequency a particular event will occur.

I'd also add that the inability to predict when such a event will occur is the precise reason that makes poker a game worth playing.

this pretty much comes down to, we all understand how randomness works. As a result of that, we believe in odds. god only knows what will actually happen to you, but in the world as a whole, every hand that has ever been played, those odds come true. You just gotta believe that they will for you too. Otherwise you'll end up locked in a basement scared of getting hit by meteors or catching mad cow disease.

Originally Posted by Mony B

Why, how, where is the proof that yes you will hit one of thoughs times, odds are all theoretical anyways arent they, so one starts to think, well since i cant predict exactly when my card that i need is going to come, why take your odds as serious as some of us do? Why take them into consideration at all? Its better to have at least an idea of what should come and when but why do we try to keep theoretical records in a chaotic game where there is no garentees?

The 'proof' is called The Law of Large Numbers; sometimes called The Law of Averages. It states:

“If the probability of a given outcome to an event is P and the event is repeated N times, then the larger N becomes, so the likelihood increases that the closer, in proportion, will be the occurrence of the given outcome to N*P.”

To put this in poker terms, this says that if there is a 40% chance to make a certain hand, the more times I try to make it the closer my successes will be to 40%. So, if I try it once I will either be at 100% or 0%, and twice I will be at either 100%, 50%, or 0%. But by the time I try it 100 times it is unlikely that I will be far from 40% AND (this is important) by the time I try it 1000 times I WILL be closer to 40% than I was at 100 tries AND by the time I try it 10,000 times I WILL be closer still.

Armed with this law, the poker player now knows that he should play the hand like he has a 40% chance to make it. Because, over time, he will make the hand 40% of the time.

Technical Note: The I WILL part actually comes from a thing called The Strong Law of Large Numbers, but it is very similar to The Law of Large Numbers.

Pyroxene you are correct with the large number theory, but agian this is just a theory. I also didnt mean over the long haul, obviously as the more times you play a given hand the closer it will approch its given percent, what i ment by this post is during a single session. Im not saying odds are bad or incorrect, I think they give us an edge over a majority of our competition before we even need to make any fancey moves. Like i stated before, this was just some rambled thoughts. You can never ever prove that your hand will be made, you have the probability of that hand being made but it is not set in stone that you will ever hit. Some people could go their entire lifes and never hit a straight or royal flush, theoretically they should have if they have played the given sample of hands, but the key to this is "in theory". Im not however disagreeing with you, but it is mathematically impossible to predict with 100% accuracy whether or not you will make your draw.

Koolmoe, very good point, does it ever make you think that eventually we will be able to make odds more effecient? What if we where at some point able to predict when we will hit. No one thought it could be done in BlackJack until someone did it, maybe its the same with poker. I know its a very slim chance of becoming a reality, but it sometimes makes me think what if. It also helps me explain to some people why your average joe can take down a world poker pro with one mistake, one draw they should not have stayed in for.

Originally Posted by Mony B

It also helps me explain to some people why your average joe can take down a world poker pro with one mistake, one draw they should not have stayed in for.

If this wasn't possible, nobody would play poker.

Originally Posted by Pyroxene

But by the time I try it 100 times it is unlikely that I will be far from 40% AND (this is important) by the time I try it 1000 times I WILL be closer to 40% than I was at 100 tries AND by the time I try it 10,000 times I WILL be closer still.

...

Technical Note: The I WILL part actually comes from a thing called The Strong Law of Large Numbers, but it is very similar to The Law of Large Numbers.

I don't think I believe this. I think eventually you should get closer to 40% than where you start from, but I don't believe that you can say you will be closer at 1000 tries than at 100. You always wiggle around the exact percentage.

What if, on this particular occasion, you hit 40% exactly on 100 tries (40/100). I think chances are good that you could waiver off of that 40%, even by just a little, by the time you get to 1000 tries (say, 399/1000).

This doesn't follow that the law that YOU WILL always be closer when going from 100 to 1000 or 1000 to 10,000.

I know I haven't proved anything, but I believe what I am describing can and does happen.

Well, the way it works is really simple.

Based on what we know (we don't know the specific order of the cards in the deck, but we know that it is supposedly well shuffled and randomized) but we know that there are 9 diamonds left unseen when I'm holding 2 and there are two on the flop, so I have 9 outs, and the odds of me completing my draw are 35%.

So I don't act on whether or not my card will come out on this particular hand. I act on pot odds, which tell me that if the statistics do actually work out, I lose my bet 65% of the time, and win my bet plus the pot 35% of the time. I'm not acting on the cards at all here, I'm acting because I believe that I am acting profitably.

Also, the odds of me losing this hand 10 times in a row?
1.3%

20?
.01%

So there's good odds that even though I'm losing my bet a chunk of the time, my winnings will have me break even.

Originally Posted by aleksandr

"You mean Boris the sneaky fuckin' Russian."

Zangief wouldn't like this. He'd probably piledrive you. Twice.

Oh, by the way, on the "Just a theory" comment? Theories are mathematical proofs. They are not in any way "in theory." They are proven.

People try to disprove statistics by pointing out the cases where things don't go by the odds. A statistician will tell you that the odds of something not happening are 1-x, where x is the probability of it happening, so unless something is 100% to happen, there is always a chance it won't.

That was my point the whole time, that we cant predict with 100% accuracy when, how, where. I never said pot odds werent a good thing to follow, maybe some of you where misinterpreting what i was talking about. This whole thread was just thoughts, not arguments not proves not anything. Rambling on, thats it, a bunch of what ifs? I was talking about why we take odds into consideration when we could hit any out at any time. Its obviously more profitable to play with them and im not arguing that point, and all theories are not mathematical proofs. The world is flat was a theory that had no mathematical proofs in it at all. The mathematical def of proof is that in a perfect world this is what is supposed to happen. Its a hypothesis, a best educated guess.

It scares me that no one has sufficiently answered this question.

The reason we use pot odds and other such condierations is to give ourselves, as gamblers with limited bankrolls, the lowest risk or ruin possible. We are trying to ensure that we are making the most "positive" decisions possible in order to preserve and grow our bankrolls to the maximum. While things like odds and statistics have no immediate "truth" in that the outcome of any single wager, or even any less than infinite series of wagers, is completely random, these things have immediate relevance in that they allow a gambler to make an informed and (hopefully) objective evaluation of the bet they are trying to make. The successfull gambler then takes this information, combines it with other usefull data, and chooses to place the bet or not. Think of it like a map. Few maps are completly accurate, but trying to get across the country without one is still a bit of a chore.


Theory Failing #1

out

Originally Posted by CaroIsking

It scares me that no one has sufficiently answered this question.

The reason we use pot odds and other such condierations is to give ourselves, as gamblers with limited bankrolls, the lowest risk or ruin possible. We are trying to ensure that we are making the most "positive" decisions possible in order to preserve and grow our bankrolls to the maximum. While things like odds and statistics have no immediate "truth" in that the outcome of any single wager, or even any less than infinite series of wagers, is completely random, these things have immediate relevance in that they allow a gambler to make an informed and (hopefully) objective evaluation of the bet they are trying to make. The successfull gambler then takes this information, combines it with other usefull data, and chooses to place the bet or not. Think of it like a map. Few maps are completly accurate, but trying to get across the country without one is still a bit of a chore.


Theory Failing #1

out

Yup.

Originally Posted by Zangief

Originally Posted by Pyroxene

But by the time I try it 100 times it is unlikely that I will be far from 40% AND (this is important) by the time I try it 1000 times I WILL be closer to 40% than I was at 100 tries AND by the time I try it 10,000 times I WILL be closer still.

...

Technical Note: The I WILL part actually comes from a thing called The Strong Law of Large Numbers, but it is very similar to The Law of Large Numbers.

I don't think I believe this. I think eventually you should get closer to 40% than where you start from, but I don't believe that you can say you will be closer at 1000 tries than at 100. You always wiggle around the exact percentage.

What if, on this particular occasion, you hit 40% exactly on 100 tries (40/100). I think chances are good that you could waiver off of that 40%, even by just a little, by the time you get to 1000 tries (say, 399/1000).

This doesn't follow that the law that YOU WILL always be closer when going from 100 to 1000 or 1000 to 10,000.

I know I haven't proved anything, but I believe what I am describing can and does happen.

I cannot express the equation of the Strong Law of Large Numbers as it involves a limit of a sumation from 1 to infinity and I do not know how to draw the symbols using the editor.

But to put it in non-math terms, the "Law of Large Numbers" says that as we take more and more independent samples we tend to approach the expected distribution of those sample. Thus, it is unlikely that after significantly more samples the actually distribution would be further from the expected distribution.

The "Strong Law of Large Numbers" goes a bit further. While the "Law of Large Numbers" says that moving further from the expected distribution is unlikely, the "Strong Law of Large Numbers" says it does not happen. To put it in slightly more mathematic terms, it says that if the difference between your expected distribution and your actual distribution is epsilon after N samples, there exists some number of samples M, with M > N, where the difference between your actual and expected distribution is not only less than or equal to epsilon, but also that beyond M samples the difference will NEVER be greater than epsilon again. And that is where the certainty part of the statement comes from. I am making an assumption that in our flush draw sample that increasing the samples by an order of magnitude is sufficient to achieve the effect that the "Strong Law of Large Numbers" describes. I am open to any arguments that an order of magnitude is insufficient, as I cannot prove it. However, the "Strong Law of Large Numbers" dictates that there is such a number, and there is a number beyond that where you will be forever closer still, and so on and so on.

And just to explicitly state the obvious end of this, the "Strong Law of Large Numbers" says that the probability of the measured distribution being equal to the expected distribution in an infinite number of samples is 1. Thus, in an infinite number of samples, you make that 37% flush draw exactly 37% of the time; without exception.

Editted: Confused when epsilon would be less and when it would be less than or equal to. And fixed a glaring spelling error, because speiling is haurd.