Probability Fallacy - help?

Can anyone help me find the name of this fallacy (if it has one, or is even considered a fallacy?)

It's when someone claims that a certain (realized) outcome is very unlikely by assuming that a near-infinite amount of other outcomes were possible and/or equally likely.

I see people making this very often, and I wish I knew how to call them on it more concisely. Here are some examples:

"It's really improbable for the current time to intersect with my life span, so reincarnation might be true"

"It's really improbable for the earth to be perfectly suited to life, therefore God did it"

Basically, when there has to be an outcome, the fact that there are tons of theoretically possible ones does not mean that whatever outcome does occur was really improbable or significant in any way - something HAD to happen. It's like rolling a googol-sided die and then claiming that God made it land on whatever arbitrary number it ends up on because it's so unlikely.

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Originally Posted by thegnome54

It's when someone claims that a certain (realized) outcome is very unlikely by assuming that a near-infinite amount of other outcomes were possible and/or equally likely.

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With the near-infinite amount of other outcomes, there is also a near-infinite amount of time, and a near-infinite amount of scenarios with possible outcomes. Saying there are too many outcomes doesn't apply to the universe, there are too many infinites to consider.

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Originally Posted by thegnome54

"It's really improbable for the earth to be perfectly suited to life, therefore God did it"

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I don't think it is the earth that was perfectly suited to life, but rather, life adapted perfectly to the earth. I think it's actually quite arrogant to assume that god created the earth for us humans, having also created the entire universe. What makes us so special? We're actually in the process of destroying this planet, that doesn't seem like something a race modeled after a god would do.

A good analogy to earth being perfectly suited to life, is a hole being the perfect shape for the puddle in it. It is shaped to the exact form of the puddle, what are the chances of that!?!

I was curious, so I poked around. You might be describing Lindley's Paradox.

Or it might be closer to Berkson's Paradox.

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Originally Posted by skysaw

I was curious, so I poked around. You might be describing Lindley's Paradox.

Or it might be closer to Berkson's Paradox.

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No, both of those are too statistically "deep" - this is even simpler than conditional probabilities and such.

It's really a matter of ascribing significance to an outcome after it has happened, and then claiming that it is unusual for it to have occurred because there were so many other "non-significant" outcomes. In reality, if any of the non-significant outcomes did occur, then they would be considered significant.

It's not actually a fallacy really, although incorrect deductions can be made from it.

Let's take out the factor of consciousness. For example,

There is a bag with 1000000000000 marbles in and a bag with 10 marbles in. You are give a marble and told it is from the small bag.

Naturally you call the person a liar, certainly if this is the first trial. There's absolutely nothing wrong with the maths.

What you're essentially doing though is adding consciousness as a key factor, and asserting the anthropic principle is true. Thing is, not everybody believes that the anthropic principle is logically sound.

The first quote of yours is mine, and it's completely valid. It's just a way of refuting the traditional view of 'current time' as being something which moves from point time 0 to time x irregardless of me or you like a vehicle travelling along a straight road at the same speed constantly which at certain times happens to be between specific points; that our 'nothingness' has been 'waiting' for a few billion years, and now that nothingness is consciousness, and soon it'll be nothing for a few more billion years (so to speak). That view is improbable to the extent that it is impossible, for the above reason: treating time like an impartial vehicle which by a sheer coincidence is on 'your inch' on a road which is a million miles long is clearly incorrect.

The fact that I am conscious now and that the universe is so old does give me faith in the endurance of consciousness, but probably not in the traditional sense of reincarnation into other animals in this universe upon death. See, gnome, nobody knows what consciousness is, nobody has any idea why it arises, nobody knows the nature of reality, in fact we cannot even yet get our observed universe to make sense yet, and nobody understands the nature of time or causality or possibly even logic. That's why the anthropic principle is so dodgy, I personally think it's a cop-out in some respects.

The second quote; well at face value that is wrong because evolution is true. But I'm of the opinion that the universe is fine tuned; I'm guessing there's no need to explain that to you. And then of course you evoke the anthropic principle... yeah, again there's a bit of a problem about making any assertions because we have no idea about the ultimate structure of reality. I'm personally of the view that we are part of a multiverse simply due to its brilliant elegance as a solution (although the multiverse theory still does nothing to explain why it should be there in the first place), but there are some people who reckon it's due to some kind of deity and I respect that opinion to quite a large extent.

Welcome back by the way, you were a very good poster... how's the neuroscience thing working out? I'm looking at a maths degree at the mo before specialising in computational neuroscience research, but I'm still unsure.

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Originally Posted by thegnome54

No, both of those are too statistically "deep" - this is even simpler than conditional probabilities and such.

It's really a matter of ascribing significance to an outcome after it has happened, and then claiming that it is unusual for it to have occurred because there were so many other "non-significant" outcomes. In reality, if any of the non-significant outcomes did occur, then they would be considered significant.

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I was afraid that was the case... just hoped it might start the search for you. I'm sure there is a simple term for it.

Still can't find a good term for you, but here's someone else's writing on this exact topic:
http://goodmath.blogspot.com/2006/05...le-is-not.html
and
http://goodmath.blogspot.com/2006/05...ble-redux.html

On a slightly related note, I absolutely hate when anyone uses probability to refer to something that has already happened. If something has occurred, the probability of it having occurred is 1. It already did happen. Probability is an approximation tool used for predicting future outcomes and doesn't apply to past events.

This also sounds like it is somehow related to the gambler's fallacy; but not exactly the same.

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Originally Posted by Xaqaria

On a slightly related note, I absolutely hate when anyone uses probability to refer to something that has already happened. If something has occurred, the probability of it having occurred is 1. It already did happen. Probability is an approximation tool used for predicting future outcomes and doesn't apply to past events.

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This.

I agree with the sentiment here. Using probabilities for past events is just plain silly.

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Originally Posted by bluefinger

This.

I agree with the sentiment here. Using probabilities for past events is just plain silly.

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For the most part, yes. But it depends on whether you include a complete reference timeframe. It is sometimes useful to go back to calculate the probability of something, but only if you have a specific point in time you are referring to, as well as a pretty good knowledge of what variables are in play.

Example: I won the lottery! What were the chances of that happening?

There are two correct answers. One is 100% (from today's reference point), and the other is 0.000001%* (from yesterday's reference point). As long as you include the reference, it's not really all that silly.

*or whatever the actual odds for that lottery

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Originally Posted by skysaw

For the most part, yes. But it depends on whether you include a complete reference timeframe. It is sometimes useful to go back to calculate the probability of something, but only if you have a specific point in time you are referring to, as well as a pretty good knowledge of what variables are in play.

Example: I won the lottery! What were the chances of that happening?

There are two correct answers. One is 100% (from today's reference point), and the other is 0.000001%* (from yesterday's reference point). As long as you include the reference, it's not really all that silly.

*or whatever the actual odds for that lottery

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That is if you include such perspectives when using probabilities. However, when people use probabilities in such ways to evaluate past events, they often fail to take into account those two perspectives. Because of this, they go on to making rather fallacious conclusions, not necessarily fallacious calculations.

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Originally Posted by bluefinger

This.

I agree with the sentiment here. Using probabilities for past events is just plain silly.

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But wait I thought....I mean...my biology teacher told me that if you flip quarters 100 times you'll come really close to getting 50 heads and 50 tails.


And what about rolling dice. Doesn't rolling a double 6 with two dice make the likelihood of rolling another double 6 unlikely? (right after)

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Originally Posted by Sandform

But wait I thought....I mean...my biology teacher told me that if you flip quarters 100 times you'll come really close to getting 50 heads and 50 tails.

And what about rolling dice. Doesn't rolling a double 6 with two dice make the likelihood of rolling another double 6 unlikely? (right after)

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Depends on the perspective... if you see it on the perspective of you flipping quarters and recording a sequence, it would be

half -> half -> half -> half -> etc

Which could end up with:

Heads -> Heads -> Tails -> Heads

But from the perspective as a whole, such a sequence would only have a chance of one sixteenth of happening, even though the action only has a probability of one half from being either heads or tails.

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Originally Posted by Sandform

And what about rolling dice. Doesn't rolling a double 6 with two dice make the likelihood of rolling another double 6 unlikely? (right after)

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A double 6 is unlikely in general, but not any more unlikely if you just rolled one. It's 1/36 every time you throw 'em.

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And what about rolling dice. Doesn't rolling a double 6 with two dice make the likelihood of rolling another double 6 unlikely? (right after)

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Ohhh dear, warped view of reality there. :|

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Originally Posted by Xei

Ohhh dear, warped view of reality there. :|

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So if you have two rolls...and you roll a I dunno...3 and a 4, then you are just as likely as before to roll a 3 and a 4 the next time right after?

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Originally Posted by Sandform

So if you have two rolls...and you roll a I dunno...3 and a 4, then you are just as likely as before to roll a 3 and a 4 the next time right after?

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You are correct, sir!

Yep, probability of 1/36 each time. You really thought that the dice somehow change?

Well fuck Mark Twain lied to me.

I always think it's sad-funny when I hear about people who track the winning lottery numbers looking for patterns. They talk about certain numbers being "due" because they haven't hit in awhile.

Losers all. (In more ways than one.)

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Originally Posted by skysaw

I always think it's sad-funny when I hear about people who track the winning lottery numbers looking for patterns. They talk about certain numbers being "due" because they haven't hit in awhile.

Losers all. (In more ways than one.)

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See I knew that it wasn't right it was just that in the case of the quarters and the case of the die I had heard two people who I thought knew what they were talking about say something opposite of what I thought was true so I just figured they were right about all the other crap in this particular field I might as well agree...

Quarters - biology teacher. I even pointed out to her that it was unlikely to get 50/50 in reality and she said "well it would be really really close." She was talking about the punnet square and probabilities in what the offspring would have and I asked her is that in total (so if you have 4 babies at different birthing periods and there is a 1/4 chance of blah blah, 1/4 blah, 1/4 blah blah, 1/4 bloo blah) you will have one of each, or is that only in one birth. She left the room to confer with another teacher and came back and said something but by that time I didn't care...hehe.

As for the dice, Mark Twain had some story about it that I heard in passing so I figured he knew what he was talking about too.

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Originally Posted by Xei

Yep, probability of 1/36 each time. You really thought that the dice somehow change?

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No...but Mark Twain told me so...=(. Or maybe he was purposely making a false statement to make a point...


Hmm, "no" probably isn't the best word to use there...more like yes in spite of a nagging feeling that it wasn't true?

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Originally Posted by Sandform

Quarters - biology teacher. I even pointed out to her that it was unlikely to get 50/50 in reality and she said "well it would be really really close."

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Tread carefully here...

It is true that if you flip a quarter 100 times, the number of heads is likely to be near 50. But this is a totally different notion than believing that the chance of a heads coming up has anything to do with how many times it has already come up. Again, this comes back to the time framework you are referencing. Here's how you should look at it.

Given a typical (non-trick) quarter and 100 typical flips:

At the start, each flip has a 50% chance of being heads, so you will likely have in the neighborhood of 50 head flips.

After you flip it 50 times, they have all been heads! But the chance for each remaining quarter is still 50%. You will likely have a total of around 75% heads, because you are "starting" with 50 heads, and will probably get around 50% heads on the remaining.

Now you have flipped it 99 times and they have all been heads! But the chance of the last one being a heads is still only 50%. You now have a 50% chance of having them all be heads.

After the final flip, you see you have a perfect series of heads... 100%! There are no more chances to calculate, only a history of what happened.

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Originally Posted by skysaw

I always think it's sad-funny when I hear about people who track the winning lottery numbers looking for patterns. They talk about certain numbers being "due" because they haven't hit in awhile.

Losers all. (In more ways than one.)

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I've used that strategy in keno at a casino. It actually worked really well. Although not exactly the same strategy. I'd watch a few games and see what number hasn't came up in a while. Then I'd bet on that number. If it didn't come up, I'd double my bet, and bet on the same number until it did come up. By the time it finally comes up, I'll win all the money back I've bet and then some.

In this game, 20 numbers are drawn out of 80, and you can pick anywhere from 1 to 20 numbers to bet on. With picking only 1 number, you have a 25% chance it'll come up, and if it does, you get 3x your bet in winnings. I figured if a number hasn't come up in a few consecutive games, it's bound to come up eventually, so I pick that one to bet on the whole time.

I always walk away with more money than I come in with, but I do fall into that loser category :?

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Originally Posted by Schmaven

I've used that strategy in keno at a casino. It actually worked really well.

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That's great. Winning money is always fun, and I'm glad it's worked well for you so far. I just hope you realize that the chances of it working better than a random pick are exactly 50%. :)

Well your strategy is completely wrong. You could have betted on any number, it would still have had 25% chance of turning up each game, irregardless of previous games. If you walked out with more money after several games then you got lucky.

I don't understand people who think reality works like this... like some kind of magical power is somehow affecting deterministic events.

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Originally Posted by Xei

Well your strategy is completely wrong. You could have betted on any number, it would still have had 25% chance of turning up each game, irregardless of previous games. If you walked out with more money after several games then you got lucky.

I don't understand people who think reality works like this... like some kind of magical power is somehow affecting deterministic events.

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I think it is perfectly logical to think that the odds of rolling the same number over and over again are low... I don't understand people who use double negatives =P.

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Originally Posted by Schmaven

I've used that strategy in keno at a casino. It actually worked really well. Although not exactly the same strategy. I'd watch a few games and see what number hasn't came up in a while. Then I'd bet on that number. If it didn't come up, I'd double my bet, and bet on the same number until it did come up. By the time it finally comes up, I'll win all the money back I've bet and then some.

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I'm pretty sure that's called "progressive betting", and doesn't have much to do with what number you pick. You can do it on roulette, too. Pick, say, 36 red, bet $5, lose, bet $10, lose, bet $20, etc, etc, bet $1280, WIN.

In those cases you have to check what the actual probability is of hitting the bet limit before hitting your number, and then compare that to the payoff of winning and how much money you actually have to risk, and do the math. You really don't even need to stay on the same number for it to work, so long as the odds remain the same. Go with 1 black instead on turn two. No difference.

Probably the best way to walk away from a casino richer if you do it right, but I'm not sure it's going to be tolerated for long if you're very successful at it.

Oh yeah, that could actually work... though if it went wrong then it'd go very wrong.

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I think it is perfectly logical to think that the odds of rolling the same number over and over again are low... I don't understand people who use double negatives =P.

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Yes, the probability of getting say a 3 ten times in a row on a dice are 1 in 60466716, before you start. But the probability of getting a 3 each roll is still 1 in 6. If you roll nine 3s, by the time you get to the last throw, the chance of you getting another 3 isn't 1 in 60466716, it's 1 in 6.

It's really not that hard to understand... :undecided:

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Originally Posted by Xei

It's really not that hard to understand... :undecided:

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Lol you act like I don't understand :roll:

The point I'm trying to make is that once you decide on a number, the odds aren't in favor of that number...

1 in 6 if you decide 5 right?...

Well there is a 5 in 6 chance of it not being 5. Essentially whatever number it is it is more likely that a number other than that one will come up.

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Originally Posted by Xei

Yes, the probability of getting say a 3 ten times in a row on a dice are 1 in 60466716, before you start.

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What you need to mention so that people understand is that the odds of rolling a 1,3,4,2,6,3,5,3,2,6 (in that order) are also 1 in 60466716, before you start.

Rolling all threes is something we ascribe special significance to, but any other string of numbers is just as unlikely to occur.

The fallacy thing I'm describing involves describing that a string is significant after it occurs.

Respond to my proper post, you. :P

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Originally Posted by DNK

I'm pretty sure that's called "progressive betting", and doesn't have much to do with what number you pick. You can do it on roulette, too. Pick, say, 36 red, bet $5, lose, bet $10, lose, bet $20, etc, etc, bet $1280, WIN.

In those cases you have to check what the actual probability is of hitting the bet limit before hitting your number, and then compare that to the payoff of winning and how much money you actually have to risk, and do the math. You really don't even need to stay on the same number for it to work, so long as the odds remain the same. Go with 1 black instead on turn two. No difference.

Probably the best way to walk away from a casino richer if you do it right, but I'm not sure it's going to be tolerated for long if you're very successful at it.

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Yeah, that was my main strategy. Just double my bet each time until my number comes up. Because once it does, you've overcame your losses of all the previous bets and made a profit. The minimum bet was $2, and I always started there. A few times I got up to $64 bets and started to worry, but I was never unlucky enough.

My reasoning for always betting on the same number, is I figured it has to come up eventually, even if the odds are 1:4 each time.

Well if you guys are done arguing over gambler's fallacy... :rolleyes:

From what I can tell after much reading, the examples you give are types of the fallacy "argumentum ad ignorantiam" ("appeal to ignorance").

For example, the second example states that the chances of Earth being suitable for life are so incredibly small that it is impossible. Well, who is the judge of that? Apparently the speaker. So what this is more precisely saying is, "The chances of Earth being suitable for life are so incredibly small that I cannot personally accept them - therefore it is impossible." When stated this way, it becomes clear that this is a logical fallacy.

It's important to note that this fallacy is not limited to arguments concerning probability, although it nevertheless can easily apply to such arguments (as it does in this case).

For further reading, here are a couple of the relevant web pages that I read.
http://www.talkorigins.org/indexcc/CA/CA100.html
http://en.wikipedia.org/wiki/Argument_from_ignorance

Also, the two links that skysaw posted much earlier in the thread are a good read. Here they are reposted.
http://goodmath.blogspot.com/2006/05...le-is-not.html
http://goodmath.blogspot.com/2006/05...ble-redux.html

Just explain why they're wrong. Otherwise, simply stating a fallacy name is almost an argument to authority, no? You'll have to explain it anyway. I guess it's nice to know the proper name...

"It's really improbable for the current time to intersect with my life span, so reincarnation might be true"

The first example you gave wasn't an argument really. "Might" implies the speaker's awareness of his ignorance, so it's not overly difficult to say he hasn't made a valid argument, as within it is an inherent acceptance of the poor nature of the argument itself.

Assuming, however, that the "might" is dropped, I couldn't answer your question since the first argument is so vague as to be hard to understand. I would need a fuller argument to point to the actual fallacy. It's clear that it's incorrect, at least based on current knowledge, but the means of arriving at that conclusion aren't fully known. Audiatur et Altera Pars would be the proper one for such a situation, as the premises aren't explicit; non-sequitur would be another proper one, as the conclusion isn't explained.

Unless that is the complete argument, in which case you can cite the author for having used an unvalidated premise ("it is improbable..."). In general, that argument is just a lot of unknowns and unknown unknowns, so it's hard to really "prove" anything in terms of religion, save to prove that one really can't know much at all.

"It's really improbable for the earth to be perfectly suited to life, therefore God did it"

Again, this one rests on an unvalidated premise, specifically that the Earth isn't suited to life. There is no real scientific consensus on what a "life-suitable" planet is, as we don't even know what other massive bodies in our own solar system have or do not have life, or have had or have not had life. Again, I would need to hear a fuller argument, and see why they came to that conclusion, before naming the actual fallacy. It falls into the same two fallacies I mentioned for the previous argument.

If the argument is literally "perfectly" suited for life (I dropped it since it was such an absurd argument with the word included), then obviously one can disprove it as simple probabilities would dictate that a planet only 50% suited for life (whatever that means) would eventually form life, given enough such planets and enough time (whatever the interval is). I'm not sure that's a specific fallacy, or at least what the name is.



I think both of your arguments, as stated, are strawmen of whatever arguments they represent. Granted, on the internet, one sentence arguments are common, but they generally reflect fuller positions that come out piecemeal. If those are the full arguments, then I doubt naming fallacies is going to do much (if that was your intention), as the level of intellectual ability on the part of the authors is extremely low, no offense (to them, if they're reading).

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Originally Posted by DNK

Just explain why they're wrong. Otherwise, simply stating a fallacy name is almost an argument to authority, no?

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Since Gnome was simply asking for a simple term, I assume that that's what he's looking for, not a specific answer to a specific argument. Obscure terms can be useful too. :)

Yes if you take the time out to read this thread you'll find I did expand on it. In no way was it a strawman, considering I was speculating in a philosophical thread and not actually arguing with anybody. If you look back to my post, I was actually talking about our ignorance of how time works and that reincarnation is one solution to that particular statistical problem, although we know so little about the nature of consciousness and reality that it's really impossible to draw any hard conclusions. I've yet to see the actual problem explained mathematically.

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From what I can tell after much reading, the examples you give are types of the fallacy "argumentum ad ignorantiam" ("appeal to ignorance").

For example, the second example states that the chances of Earth being suitable for life are so incredibly small that it is impossible. Well, who is the judge of that? Apparently the speaker. So what this is more precisely saying is, "The chances of Earth being suitable for life are so incredibly small that I cannot personally accept them - therefore it is impossible." When stated this way, it becomes clear that this is a logical fallacy.

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That's not why it's wrong at all. It's wrong because the OP was applying the probability of a planet being hospitable, which are indeed small and not an argument from ignorance (look at the percentage that are hospitable in our solar system; this isn't a disputed fact) to this planet alone, as if we could only have ever been on Earth. That's why it's wrong. It is indeed improbable that any single planet is habitable, but you have to bear in mind that the planet you end up on, on which there are millions of hospitable ones to choose from, must definitely be hospitable by definition. And that's the fallacy we're looking for.

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Originally Posted by Xei

That's not why it's wrong at all. It's wrong because the OP was applying the probability of a planet being hospitable, which are indeed small and not an argument from ignorance (look at the percentage that are hospitable in our solar system; this isn't a disputed fact) to this planet alone, as if we could only have ever been on Earth.

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Our understanding of what is habitable has changed dramatically in the past five or ten years with the discovery of some extremophiles here on Earth already living in conditions previously assumed to be inhospitable to life. These include areas of extreme heat, extreme cold and extremes of pressure.

The number of planets and moons in our solar system that we know could technically support some form of life has also increased as we discover more about the moons of Jupiter and Saturn especially. I saw a fantastic science program on National Geographic channel that showed 6 places in our solar system other than Earth that could support some form of life. On the lower end of probability was Mars, and on the higher end were Europa and Titan, if I remember correctly.

Not really planets... but yes, I know, in fact I believe there may well be life on Europa. I know all about hydrothermal vents. It's still a minority though, I don't think we could invisage life on planets as cold as Neptune or hot as Venus, or on the gas giants, or without liquid, etcetera. That wasn't the point I was making though, of course, what I was talking about was what kind of fallacy it is. Which isn't a fallacy from ignorance. Oh, and we should probably be talking about intelligent life really. I'm not sure if that could inhabit a hydrothermal vent, although that's a much vaguer area of course.

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Originally Posted by Schmaven

I've used that strategy in keno at a casino. It actually worked really well. Although not exactly the same strategy. I'd watch a few games and see what number hasn't came up in a while. Then I'd bet on that number. If it didn't come up, I'd double my bet, and bet on the same number until it did come up. By the time it finally comes up, I'll win all the money back I've bet and then some.

In this game, 20 numbers are drawn out of 80, and you can pick anywhere from 1 to 20 numbers to bet on. With picking only 1 number, you have a 25% chance it'll come up, and if it does, you get 3x your bet in winnings. I figured if a number hasn't come up in a few consecutive games, it's bound to come up eventually, so I pick that one to bet on the whole time.

I always walk away with more money than I come in with, but I do fall into that loser category :?

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The actual 'winning' strategy here is the doubling your bet part, but even still that fails quite a lot and drastically. In theory, with enough money, you can use that strategy and never lose. Unfortunately, most people who use it end up doubling down until all their money is gone.

I actually wrote a rather long post on the odds, etc, and deleted it for being off topic, but here goes:

Assuming the table minimum is $5, and the max is $5000, your odds of really screwing yourself over can be minimal, and don't require a major stash of cash for security. If you're betting roulette, and betting single numbers, then the odds are against you. If the payout is 35:1 or so, then you can easily burn through $100,000 without a payoff with progressive betting. On the other hand, if you're betting table thirds, then it would take 12 consecutive misses before losing money at $5K per bet. The odds of that happening are less than 1%. Sooo... as long as you have enough money on hand, you should be probably safe. Having $20K should cover it (two rounds of 12 misses). Of course, you could always then move up to a table with a higher limit, but that just gets more dangerous. I'd start over.

You lose 1 in 100 attempts, but if you can gain, on average $300 from each round (about 6 tries), then you'll more than make up for those lost rounds (you'll make out doubling overall). The actual probabilities and overall payoffs aren't clear to me since I don't want to compute it all, but I think what is clear is that even one payoff at try 11 for $15000 per 100 tries makes up for the one try in 100 that loses you $10000.

Assuming you're unlucky enough to have that 1 in 100 be your first try, you would need to have the second one hit in about the next 30 tries, assuming you didn't get any big payoffs, which is extremely unlikely, so your odds of totally lucking out are less than a third of a percent. Remember that the longer you go, the more you make, until you hit your limit. You actually want bad luck streaks, they pay more.

And if you're betting red/black or table halves, then the odds of missing 12 consecutive times in a row is 1 in 10,000. Certainly that happens, but it's extremely rare. I'd say it's more likely you'll take a major stock hit...

But I assume the dealers, etc, are trained to spot progressive betting, and you'll probably end up getting the boot for doing it at some point. Not sure if they let you keep your money in those circumstances.

First off, sorry to be digging up such an old topic. :P

I recently read a book chapter which dealt pretty directly with the topic in the OP (although it doesn't touch on religious/philosophical applications), and I thought that thegnome and maybe a few others would be interested in reading it, so I figured I would post it here. It's an 11-page (not including references) psych literature review, and the author has made it publicly available via his website. So without further ado:
Twisted Pair: Counterfactual Thinking and the Hindsight Bias (pdf)
:cheers:

Great link, thanks!

The fallacy I'm talking about seems to be an example of subjectively easily created counterfactuals biasing people away from the effects of hindsight bias, and making the current situation seem far less likely than it may be. The fallacy then lies in falsely linking the ease with which counterfactuals are imagined to their actual likelihood. Just because you can imagine a million different ways the universe "could have been" doesn't mean that any of these were likely outcomes. It's the whole "imaginable = possible" thing gone horribly wrong.

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Originally Posted by DNK

I actually wrote a rather long post on the odds, etc, and deleted it for being off topic, but here goes:

Assuming the table minimum is $5, and the max is $5000, your odds of really screwing yourself over can be minimal, and don't require a major stash of cash for security. If you're betting roulette, and betting single numbers, then the odds are against you. If the payout is 35:1 or so, then you can easily burn through $100,000 without a payoff with progressive betting. On the other hand, if you're betting table thirds, then it would take 12 consecutive misses before losing money at $5K per bet. The odds of that happening are less than 1%. Sooo... as long as you have enough money on hand, you should be probably safe. Having $20K should cover it (two rounds of 12 misses). Of course, you could always then move up to a table with a higher limit, but that just gets more dangerous. I'd start over.

You lose 1 in 100 attempts, but if you can gain, on average $300 from each round (about 6 tries), then you'll more than make up for those lost rounds (you'll make out doubling overall). The actual probabilities and overall payoffs aren't clear to me since I don't want to compute it all, but I think what is clear is that even one payoff at try 11 for $15000 per 100 tries makes up for the one try in 100 that loses you $10000.

Assuming you're unlucky enough to have that 1 in 100 be your first try, you would need to have the second one hit in about the next 30 tries, assuming you didn't get any big payoffs, which is extremely unlikely, so your odds of totally lucking out are less than a third of a percent. Remember that the longer you go, the more you make, until you hit your limit. You actually want bad luck streaks, they pay more.

And if you're betting red/black or table halves, then the odds of missing 12 consecutive times in a row is 1 in 10,000. Certainly that happens, but it's extremely rare. I'd say it's more likely you'll take a major stock hit...

But I assume the dealers, etc, are trained to spot progressive betting, and you'll probably end up getting the boot for doing it at some point. Not sure if they let you keep your money in those circumstances.

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Guys, Martingale is not a good idea. If the events you are betting on are independent, and each bet has a negative expected value (roulette is an example), then it doesn't matter how much you bet or when, as long as your bankroll is finite, your total expected value is still going to be negative.